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Laser-tissue interactions in the arterial wall

Roberts, Cynthia Jane, Ph.D.

The Ohio State University, 1989

UMI 300 N.ZeebRd. Ann Arbor, MI 48106 Laser-Tissue Interactions in the Arterial Wall

A Dissertation

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosophy in the

Graduate School of the Ohio State University

Cynthia Roberts, M.S.E.E., B.S.N.

£ jfc # Jfc #

The Ohio State University

1989

Dissertation Committee: Approved by:

Professor J. F. Cornhill

Professor R. L. Hamlin () Adviser Biomedical Engineering Professor H. Hsu Center Copyright by

Cynthia Jane Roberts

1989 ACKNOWLEDGEMENTS

I wish to express my great respect and appreciation to my advisor and mentor,

Dr. J. Fredrick Cornhill. His confidence in my abilities, his intellectual guidance, and the resources he provided for my research made this work possible. I also thank the other members of my dissertation committee, Dr. Hsiung Hsu and Dr.

Robert Hamlin, for their insight and interest in my work.

I would like to acknowledge my use of the image processing and computing facilities of the Laboratory of Vascular Diseases. My sincere gratitude goes to Ed

Herderick, System Manager, who was always willing to give generously of his time and technical expertise in the many invaluable discussions we had. My thanks also go to Shu-Fen Chang and Liz Field for modifying the specialized image processing software which allowed my images to be analyzed, and to John Meimer for his assistance with the experimental work.

I would like to acknowledge the allocation of resources on the Cray X-MP by the Ohio Supercomputer Center, in support of the theoretical portion of this study.

My deepest appreciation is for my husband, Robert H. Small, whose faith in me is the backbone of all my accomplishments. I wish to thank him and my family for the constant encouragement and the strength they provide. VITA

November 22, 1958 ...... Born —■ Chicago, Illinois

1979 B.S. in Nursing, The University of Iowa Iowa City, Iowa 1980-1983 ...... Registered Nurse, The University of Iowa Hospitals and Clinics 1986 M.S., Electrical Engineering The Ohio State University

PUBLICATIONS

Hsiung Hsu, Clifford Shang, and Cynthia Roberts. Soliton Phase Conjuga tion in Four-Wave Nonlinear Interactions. In Proceedings of the A'F International Conference on Quantum Electronics, 1987.

Cynthia Jane Roberts. Large Signal Characteristics of Phase Conjugation with Variable Split Pumps in Degenerate Four-Wave Mixing. Master’s Thesis, The Ohio State University, 1986.

Cynthia Roberts and Hsiung Hsu. Generalized Large Signal Theory of Phase Conjugation in Four-Wave Interactions. In Proceedings of the 14th Congress of the International Commission for Optics, 1987.

FIELDS OF STUDY

Major Field: Biomedical Engineering

Studies in Atherosclerosis Professor J. Fredrick Cornhill

Studies in Cardiovascular Phsysiology Professor Robert Hamlin

Studies in Nonlinear Optics Professor Hsiung Hsu TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

V IT A iii

LIST OF FIGURES vii

LIST OF TABLES xv

I. Introduction 1

1.1 Accepted Treatment Modalities for Atherosclerotic HeartDisease: 2

1.2 Emerging Technologies for the Treatment of Atherosclerosis: . . 3

1.3 Direct Laser Angioplasty ...... 5

II. Direct Laser Angioplasty: Review of Current Literature 6

2.1 Introduction ...... 6

2.2 Feasibility of Laser Angioplasty ...... 7

2.3 Laser-Tissue Interaction ...... 15

2.3.1 Tissue Response to Light ...... 16

2.3.2 Thermal/Mechanical Mechanisms ...... 17

2.3.3 Ablative Photodecomposition and theExcimer Laser . . 21

2.3.4 Debris and Photoproduct F o rm a tio n ...... 25

2.3.5 Effects of Pulse Duration and Laser F luence ...... 30

2.3.6 Lasing M e d iu m ...... 35

iv 2.3.7 Wavelength-Dependent Tissue Absorption ...... 38

2.3.8 Preferential Energy Absorption: Selective Ablation . . . 42

2.3.9 Exogenous A g e n ts ...... 46

2.3.10 Photoemission Properties ...... 52

2.4 Conclusions drawn From Current Literature ...... 58

2.4.1 Optimal Lasing Parameters, Tissue Properties ...... 60

2.4.2 Areas of Further Study ...... 63

2.4.3 Additional Considerations ...... 68

III. Experimental Materials and Methods 69

3.1 Tissue Preparation ...... 69

3.2 Laser In ju ry ...... 69

3.3 Histology ...... 70

3.4 Image P rocessing ...... 71

3.5 A n aly sis ...... 75

IV. Experimental Results 79

4.1 Isolating the Effects of Power, Exposure, and E n e rg y ...... 80

4.2 Comparison of Normal and Atherosclerotic Tissue Injuries . . . 95

4.3 C onclusions ...... 97

4.4 Sources of E rro r ...... 100

V. Model of Light Absoprtion, Heat Conduction, and Ablation

in Laser-Irradiated Tissue 101

5.1 Development of the Model ...... 102

5.1.1 Forms of the SourceTerm ...... 107

5.2 Implementation of the M o d e l ...... 112

v 5.3 Validation of the M odel ...... 117

5.4 Model Predictions and Comparison to Experimental Results . . 118

5.4.1 Onset of Ablation ...... 121

5.4.2 Constant E n e rg y ...... 123

5.4.3 Constant Pow er ...... 126

5.4.4 Constant Pulse D uration ...... 127

5.4.5 Time Evolution of Injury ...... 129

5.4.6 Constant vs. Variable Thermal P ro p erties ...... 129

5.5 Discussion and Conclusions ...... 134

5.5.1 Implications for Laser A n g io p lasty ...... 138

VI. Arqas of Further Study 139

APPENDICES 145

A. Number of Iterations for Accuracy Data 146

B. Simulation Data for Constant Energy 154

C. Simulation Data for Constant Power 167

D. Simulation Data for Constant Pulse Duration 172

E. Fortran Program for the Simulation of Light Absorption

and Heat Conduction in Arterial Tissue using

Finite-Difference Methods 189

References 207

vi t

LIST OF FIGURES

1 Relationship between laser burn dimensions and total laser energy

in swine aorta under CW CO 2 irradiation; from Gerrity, 1983 [31]. 11

2 Relationship Between Crater Width, Crater Depth and Number of

XeCl pulses at 308nm, 10.6J/cm^, (10-50//.z) and 10ns; from

Grundfest,1985 [37] ...... 24

3 Nonlinear Relationship Between Depth of Penetration and Number

of XeF Pulses at 351nm, 5 J/ cm?/pulse, 10ns, and 10 Hz\ from

Murphy-Chutorian, 1986 [6 9 ] ...... 25

4 Ablation debris following 1 [is pulses of 465nm laser radiation; from

Prince, 1986 [76] ...... 28

5 High-speed flash photograph'of atheroma ablation by l^s pulses of

465nm laser radiation at 150/is after irradiation; from

Prince, 1986 [76] ...... 28

6 Normalized photoacoustic signals for human aorta as a function of

incident fluence of the 308nm XeCl laser with optical pulse duration

of 7ns and 300ns; from Singleton, 1987 [92] ...... 34

7 The effect of fluences on crater formation with XeCl excimer irra

diation at 308nm and a 5ns pulse with constant total accumulated

energy; from Singleton, 1987 [92] ...... 36

vii 8 Crater diameters produced during perpendicular lasing in varying

concentrations of blood/saline mixtures; from Fenech, 1985 [27]. . 37

9 Waveband of preferential atheroma absorbance and absorption spec

tra of lipophilic chromophores extracted from atheroma and normal

aorta from Prince, 1986 [75] ...... 39

10 Photoacoustic spectrum of normal artery wall, plaque covered with

intima, and plaque with intima removed; from Singleton, 1986 [91]. 41

11 Optical spectra of atherosclerotic plaque; from reference 49]. . . . 42

12 (A)Spectrophotometric scan of freshly formed thrombus, from Lee,

1983 [58]; (B)Optical spectrum of whole human blood, from Kaminow,

1984 [49] 43

13 Spectral properties of human hemoglobin as oxy, carbon monoxide,

and deoxy derivatives; from Antonini [8] ...... 44

14 Fluorescence excitation and emission spectra of hematoporpyrin

derivative; from [78] ...... 47

15 Absorption spectrum of HPD; from Singleton, 1987 [92] ...... 49

16 Threshold fluences for 308nm XeCl and 351nm XeF lasers of normal

and atherosclerotic swine arterial wall after HPD injection; from

Singleton, 1987 [92] ...... 49

17 The absorptive spectra of tetracycline solution and a solubilized

sample of tetracycline-treated atheroma; from Murphy-Chutorian

[67]...... 51

18 Fluorescence spectra of normal and atherosclerotic arterial wall with

excitation wavelength = 480ram and cutoff filter at 520nm; from

Kittrell, 1985 [51] ...... 53

viii 19 Fluorescence spectra of normal and atherosclerotic arterial wall with

excitation wavelength = 337nm; from Andersson, 1987 [6] ...... 55

20 Fluorescence spectra from normal and calcified atherosclerotic hu

man arterial tissue with excitation wavelength = 458nm and cutoff

filter at 470nm; from Sartori, 1987 [85] ...... 56

21 Fluorescence spectra of normal swine arterial wall excited at 222 nm

(KrF) for a fresh specimen, and one after 9000 pulses; from Single

ton, 1987 [92] ...... 57

22 Laser Raman scattering (514nm laser excitation) observed over the

500-1200cm-1 region from a powdered sample of calcium hydrox-

yapatite and a calcified segment of human coronary artery; from

Clarke, 1987 [14] ...... 59

23 Edges of Crater Produced by 3 W, 1000ms with Inner Crater Egde

and Severe Injury Boundary Lines E n tered ...... 74

24 Low Resolution Image Demonstrating the Complete Severe Injury

Boundary of the Crater from Figure 23 75

25 Low Resolution Image of Crater Produced at 1.5 W, 1000ms with

High Resolution Image of Crater with Inner Crater Edge, Severe

Injury Boundary, and Base of Crater Segments Entered ...... 76

26 High Resolution Image Demonstrating the Entry of the Reference

Bar Edge...... 77

27 Injury Parameter Means as a Function of Energy in Atherosclerotic

T is s u e ...... 82

28 Injury Parameter Means as a Function of Power in Atherosclerotic

T is s u e ...... 83

IX 29 Injury Parameter Means as a Function of Exposure Duration in

Atherosclerotic T issue ...... 84

30 Injury Parameter Means for Constant

Energy = 0 .6 J ...... 86

31 Injury Parameter Means for Constant

Energy = 1 .5 J ...... 88

32 Injury Parameter Means for Constant

Power = 3.0 I T ...... 90

33 Injury Parameter Means for Constant

Power = 2.0IT ...... 92

34 Injury Parameter Means for Constant

Exposure = 1000ms ...... 94

35 Injury Parameter Means for Constant

Exposure = 500ms ...... 96

36 Injury Parameter Means for Constant

Power = 3IT for Atherosclerotic and Normal Tissue Injuries .... 98

37 Geometry of discrete nodes in a cylindrical coordinate system of a

finite-difference model ...... 103

38 The Effect of Scatter With Beam Broadening and W ithout Beam

Broadening, at the Surface and at Two Tissue D epths ...... 110

39 Experimentally Measured Thermal Conductivity and Thermal Dif-

fusivity, from Welch, et al. [103] ...... 115

40 Calculated Values of Thermal Conductivity and Thermal Diffusiv-

ity, Adapted for Simulation' from [ 1 0 3 ...... 116

x 41 Thermal Conductivity-Dominent Region of Vaporization, and La

tent Heat-Dominent Region of Vaporization ...... 120

42 Onset of Ablation vs Incident Power for Simulation Data ...... 122

43 Onset of Ablation vs Absorbed Power, predicted by Ready equation

[80] 124

44 Time Evolution of Injury for 7.51V and a 200ms P ulse ...... 130

45 Time Evolution of Injury for 1.5IV and a 1000ms P u lse ...... 131

46 Ablation Time Contours for 7.51V and a 200ms P u l s e ...... 132

47 Ablation Time Contours for 1.51V and a 1000ms Pulse ...... 133

48 Ablated Area vs Total Energy for Entire Simulation Data Set . . . 136

49 Ablated Area vs Total Energy for Entire Experimental DataSet . 137

50 Crater Center Produced at 31V, 500ms ...... 141

51 Section 70 fim from Crater Center and Section 95/im from Crater

C e n te r ...... 142

52 Crater Center Produced at 31V, 500ms and Section 100/zm from

Crater Center ...... 143

53 Crater Center Produced at 31V, 500ms and Section 70 fj,m from

Crater Center ...... 144

54 Ablated Depth vs Number of Iterations for 31V, 200ms and 31V,

1 0 0 m s...... 148

55 Ablated Width vs Number of Iterations for 31V, 200ms and 31V,

100ms 149

56 Ablated Area vs Number of Iterations for 31V, 200ms and 31V,

100ms 150

xi 57 Onset of Ablation vs Number of Iterations for 3W, 200ms and 3 W,

1 0 0 m s ...... 151

58 Distance Increment vs Number of Iterations for 31E, 200ms and

3 W, 1 0 0 m s ...... 152

59 Time Increment, vs Number of Iterations for 3D\ 200ms and

3W, 1 0 0 m s ...... 153

60 Depth of Crater vs Incident Power for. Constant Energy = 1.5J in

Simulation D a ta ...... 155

61 Width of Crater vs Incident Power for Constant Energy = 1.5J in

Simulation D a ta ...... 156

62 Ablated Area vs Incident Power for Constant Energy = 1.5J in

Simulation D a ta ...... 157

63 Crater Shape vs Incident Power for Constant Energy = 1.5J in

Simulation D a ta ...... 158

64 Depth of Crater vs Incident Power for Constant Energy = 0.6J in

Simulation D a ta ...... 159

65 Width of Crater vs Incident Power for Constant Energy = 0.6.7 in

Simulation D a ta ...... 160

66 Ablated Area vs Incident Power for Constant Energy = 0.6.7 in

Simulation D a ta ...... 161

67 Crater Shape vs Incident Power for Constant Energy = 0.6.7 in

Simulation D a ta ...... 162

68 Depth of Crater vs Incident Power for Constant Energy = 0.25J in

Simulation D a ta ...... 163

xii 69 Width of Crater vs Incident Power for Constant Energy = 0.25J in

Simulation D a ta ...... 164

70 Ablated Area vs Incident Power for Constant Energy = 0.25J in

Simulation D a ta ...... 165

71 Crater Shape vs Incident Power for Constant Energy = 0.25 J in

Simulation D a ta ...... 166

72 Crater Depth vs Pulse Duration for Three Values of Constant Power

in Simulation D a t a ...... 168

73 Crater Width vs Pulse Duration for Three Values of Constant Power

in Simulation D a t a ...... 169

74 Ablated Area vs Pulse Duration for Three Values of Constant Power

in Simulation D a t a ...... 170

75 Crater Shape vs Pulse Duration for Three Values of Constant Power

in Simulation D a t a ...... 171

76 Depth of Crater vs Incident Power for Simulation Data

with Constant Pulse Duration = 100m s ...... 173

77 W’idth of Crater vs Incident Power for Simulation Data

with Constant Pulse Duration = 100m s ...... 174

78 Ablated Area vs Incident Power for Simulation Data

with Constant Pulse Duration = 100m s ...... 175

79 Crater Shape vs Incident Power for Simulation Data

with Data Constant Pulse Duration = 1 0 0 m s ...... 176

80 Depth of Crater vs Incident Power for Simulation Data

with Constant Pulse Duration = 200m s ...... 177

xiii 81 Width of Crater vs Incident Power for Simulation Data

with Constant Pulse Duration = 2 0 0 m s ......

82 Ablated Area vs Incident Power for Simulation Data

with Constant Pulse Duration = 200m s ......

83 Crater Shape vs Incident Power for Simulation Data

with Constant Pulse Duration = 200m s ......

84 Depth of Crater vs Incident Power for Simulation Data

with Constant Pulse Duration = 500m s ......

85 Width of Crater vs Incident Power for Simulation Data

with Constant Pulse Duration = 500m s ......

86 Ablated Area vs Incident Power for Simulation Data

with Constant Pulse Duration = 500m s ......

87 Crater Shape vs Incident Power for Simulation Data

with Constant Pulse Duration = 100m s ......

88 Depth of Crater vs Incident Power for Simulation Data

with Constant Pulse Duration = 1000ms ......

89 Width of Crater vs Incident Power for Simulation Data

with Constant Pulse Duration = 1000ms ......

90 Ablated Area vs Incident Power for Simulation Data

with Constant Pulse Duration = 1000ms ......

91 Crater Shape vs Incident Power for Simulation Data

with Constant Pulse Duration = 1000ms ......

xiv LIST OF TABLES

1 Thermal Tissue Effects, from Anderson, 1983 [4], and

Parrish, 1984 [73] ...... 18

2 Thermal Tissue Response, from Anderson, 1983 [41 ...... 18

3 Attenuation coefficients, thermal diffusion times and limiting repetion

rates for 7 wavelengths, from Furzikov [29] ...... 20

4 Mass spectrometer analysis of disintegration products of thrombus

and plaque; from Kaminow, 1984 [49] 27

5 Energy profile and tissue injury: Continuous and pulsed laser irra

diation; from Deckelbaum, 1985 [21] ...... 31

6 Results of COo laser irradiation according to energy profile; from

Deckelbaum, 1986 [22] ...... 32

7 Effect of peak power density on tissue injury; from Deckelbaum,

1986 [22]...... 33

8 XeCl laser photoacoustic ablation thresholds of normal aorta; from

Taylor, 1987 [98] ...... 35

9 Summary of attenuation coefficients obtained for vascular tissue

with pulsed photothermal radiometry; from Long, 1987 [64] ...... 40

10 Absorption (A) and scattering (S) coefficients for vessel wall and

plaque; from van Gemert, 1985 [1001 ...... 41

11 Summary of selective ablation at 465nm; from Prince, 1986 [76]. . 45

xv 12 Ablation thresholds for calcified atheroma and normal arterial tissue

under 290ram, 482nm, and 658nm irradiation; from [77] ...... 45

13 Ablation Thresholds for Vascular Tissue Compiled from Several Au

thors ...... 63

14 Number of Injuries per Power, Pulse and Energy Group for Atheroscle

rotic, and Normal Tissue ...... 78

15 Results of Three Multiple Regression Analyses, One for Each Laser

Parameter with Entire Atherosclerotic Injury Data S et ...... 80

16 Results of Analysis of Variance for Tissue Injury Parameters for

Atherosclerotic T issue ...... 81

17 Analysis of Variance for Injury Parameters with Constant

Energy = 0.67, for Atherosclerotic Tissue Injuries ...... 87

18 Analysis of Variance for Injury Parameters with Constant

Energy = 1.57, for Atherosclerotic Tissue Injuries ...... 89

19 Analysis of Variance for Injury Parameters with Constant

Power = 3.0IV for Atherosclerotic Tissue Injuries ...... 91

20 Analysis of Variance for Injury Parameters with Constant

Power = 2.0 W for Atherosclerotic Tissue Injuries ...... 93

21 Analysis of Variance for Injury Parameters with Constant

Exposure = 1000ms for Atherosclerotic Tissue Injuries ...... 93

22 Analysis of Variance For Injury Parameters with Constant

Exposure = 500ms for Atherosclerotic Tissue Injuries ...... 95

23 Analysis of Variance for Injury Parameters with Constant

Power = 3 W for Atherosclerotic and Normal Tissue Injuries .... 97

xvi 24 Definitions of Indicators of Injury ...... 112

25 Simulation Parameters ...... 113

26 Percent of Pulse Duration Before Onset of Ablation for Constant

Energy ...... 126

27 Transition Pulse Duration at which Injury becomes Deeper than is

is Wide for Constant P o w e r ...... 127

28 Transition Power for Constant Pulse where Injury becomes Deeper

than it is Wide ...... 128

29 Extent of Injury for High and Low Thermal Conductivity, k, for 3 W

and lOOms ...... 134

30 Input Parameters and Simulation R esults ...... 147

xvii C H A P T E R I

Introduction

Atherosclerosis and the resulting direct complications comprise the most com mon cause of death in the United States, in the form of ischemic heart disease and cerebovascular disease [70]. In addition, debilitating physical conditions, such as angina in the case of atherosclerotic heart disease, and functional deficits in the case of cerebrovascular disease, make the scope of the problem much broader than a simple death rate. Current therapuetic interventions may slow the progression, circumvent or morphologically alter a local obstruction, or treat only the symp toms, but are not adequate in terms of long term, asymptomatic survival. The significance of this problem to the health of the general population makes it of great importance to the medical, scientific, and industrial communities. Several innova tive technologies with the potential for successful intervention in the atherosclerotic process are currently under investigation. One of the most exciting is the use of laser energy to ablate lesions. However, the available literature describing the use of direct laser angioplasty, though voluminous, is lacking in basic studies of laser-tissue interactions, which are necessary to understand and thus develop the procedure.

The purpose of this dissertation is to address the need for basic research in laser-tissue interactions in the arterial wall. This will be accomplished by quanti fying the extent of laser-induced injury in the arterial wall using computer-assisted

1 techniques, as a function of an identified, isolated lasing parameter, both exper imentally and theoretically. Prior to describing the techniques involved in this study, current and experimental therapies for atherosclerotic heart disease will be described in the remainder of Chapter I, and the available literature concerning direct laser angioplasty will be thoroughly reviewed in Chapter II.

1.1 Accepted Treatment Modalities for Atherosclerotic Heart Disease:

Low Cholesterol Diet

Multiple studies have shown that lowering serum cholesterol levels will sig nificantly reduce the risk of coronary heart disease [86]. Thus, patients at risk are often advised by medical professionals to reduce dietary intake of cholesterol in an effort to control serum cholesterol. At best, however, this intervention may reduce the collective risk. No studies exist or even suggest that the disease may be eliminated by diet alone, although diet is important in any treatment program.

Percutaneous Transluminal Coronary Angioplasty — PTCA

This procedure, commonly referred to as balloon angioplasty, involves the insertion of a balloon catheter into an atherosclerotically-narrowed vessel lumen while the balloon is deflated, and then inflating the balloon to crush the lesion and widen the lumen. It may be done under local anesthesia, and has a short hospital course if uncomplicated. The success rate in terms of increased lumen diameter at the time of the procedure has been over 85 percent [95]. However, in 25 to 40 percent of the vessels, restenosis occurs within approximately six months [23].

Coronary Artery Bypass Graft — CABG

With surgical intervention, blood flow is routed around a local coronary ar terial obstruction via a vascular graft, usually either saphenous vein or internal

2 mammary artery, in a widely performed procedure referred to as the CABG, or coronary artery bypass graft. This is an open chest operation requiring general anesthesia and total cardiopulmonary bypass. A finite lifetime exists for graft pa tency, however, with reports of as many as 30 percent of saphenous vein grafts occluded within one year of surgery [25], 50 to 60 percent occluded at ten years, and as high as 71 percent occluded at twelve years [36].

1.2 Emerging Technologies for the Treatment of Atherosclerosis:

Dietary Supplements, Fish Oil

It has been suggested that fish oil supplements in the diet may inhibit atheroscle rosis [20,100]. Also, a nonblinded study recently reported a reduction in the restenosis rate following PTCA from 36 percent in the control group, to 16 percent in the experimental group, who were given n-3 fatty acid therapy for seven days prior to the procedure and for six months follow-up [23]. However, other studies exist reporting an adverse effect on lipid/lipoprotein levels [24,98], in contradiction to the reported beneficial effect [42,73,85,88]. Based on the evidence presented to date, further studies are indicated.

Lipid Lowering Pharmocologic Agents

Studies in animals have shown that not only can the progression of early atherosclerosis be halted, but actual regression of lesions is possible if serum choles terol is lowered far enough [86]. The Cholesterol-Lowering Atherosclerosis Study

(CLAS) demonstrated a 26 percent reduction in total plasma cholesterol, a 43 percent reduction in low-density lipoprotein cholesterol, and a 37 percent eleva tion of high-density lipoprotein cholesterol, in nonsmoking men who received com bined Colestipol-Niacin therapy [9]. This was associated with a beneficial effect

3 on atherosclerosis, with regression in some cases. However, side effects includ ing extreme elevation of liver enzymes, were encountered in the treatment group.

This type of therapy must be carefully evaluated for risk versus benefit, over the long-term. Many new pharmocologic agents are currently under clinical study.

Coronary Endoprothesis

Coronary arterial stenting has been proposed as an adjunct to PTCA in or der to maintain arterial patency and thus reduce the incidence of restenosis. The endoprosthesis consists of a self-expanding stainless steel mesh that has been im planted in patients following PTCA [78,87]. Earlier animal studies have shown that complete reendothelialization of the stent occurs without thrombus forma tion. Clinical studies have shown low complication rates and patency for up to nine months. Additional studies are in progress [78,87].

Rotational Endarterectomy

In vivo endarterectomy using a mechanical, rotating, abrasive-tipped catheter has been studied in the atherosclerotic rabbit (n=8) [40], normal canine (n=ll)

[39], cadaver coronary heterografts implanted in canines (n=13) [52], and cadaver coronary segments (n=21) [89]. It has been concluded that this is safe and ef fective for use in coronary arteries. However, the numbers have been small and more extensive studies are needed prior to drawing any such conclusions. Several potential problem areas have not yet been addressed. These include the question of embolization from debris produced during the procedure, long-term studies of healing response after this type of injury, and analysis of the perforation rate after a greater number of procedures have been performed.

4 Laser “Thermal” Angioplasty

Multiple investigators are studying the use of a metal-tipped optical fiber, coupled to a laser, for the treatment of stenotic or occluded periperal [18,28] and coronary [19,53,82] lesions. Laser energy is converted to heat at the metal tip, which is advanced through the vessel while burning a wider lumen. This proce dure is also used in conjunction with PTCA, where the laser probe opens an initial channel for subsequent balloon dilation in lesions which would not otherwise be appropriate candidates [18,19,82]. Complications include perforation, carboniza tion and tissue adherence at the metal tip, reocclusion, and thrombus formation

[81]. Animal studies [50,81], as well as clinical cases [17,18,19,28,53,82] have been documented, although minimal long-term follow-up is recorded. Sapphire contact probes have also been studied in place of the metal contact probes with similar results [33].

1.3 Direct Laser Angioplasty

The use of direct laser energy as a stand-alone method to ablate vascular lesions is receiving wide attention. The intuitive advantages of this procedure over others discussed is in actual lesion removal, rather than just lesion compres sion with PTCA, or bypass with a CABG. Another advantage it has over the

CABG is that direct laser angioplasty could be performed as a percutaneous pro cedure, without surgical intervention. Also, with detailed knowledge of the laser- tissue interactions involved, the potential exists for selective removal of disease, rather than nonspecific burning as in laser thermal angioplasty. Overall, direct laser angioplasty has great potential as an alternative therapy in the treatment of atherosclerosis. Chapter II is dedicated to the detailed discussion of research in this area.

5 C H A P T E R II

Direct Laser Angioplasty: Review of Current Literature

2.1 Introduction

Since the first U.S. published report of direct laser dissolution of cadaver coronary atherosclerotic occlusions by Lee, et al. in 1981 [56], a large quantity of literature has been produced. Many early investigators simply tried their hand at this novel procedure with whatever equipment was available. Everything from calcified lesions to fatty streaks and thrombus have been irradiated. Wavelengths

(A) have ranged from the far ultraviolet (UV) at .193 nanometers (nm), to the infrared (IR) at 10,600nm. Pulse durations have ranged from continuous wave

(CW) all the way down to the nanosecond ( ns) regime. Incident energies have also ranged over several orders of magnitude. Delivery modes have included everything from in vivo, fiber optic application of energy, to excised vessel, dry field, direct exposure. Disease models are quite varied: rats, rabbits, thrombosed dogs or dogs with implanted human plaques, pigs, monkeys, and human — both in vivo and post mortem. Multiple reviews have been written [1,3,7,43,48,44,59,55,64,65,67].

Unacceptably high complication rates have been encountered, with inadvertent vessel wall perforation emerging as the biggest obstacle preventing laser angioplasty from becoming a viable clinical treatment alternative [47].

It is currently accepted that laser energy is capable of ablating atherosclerotic lesions and thrombus. However, research continues with the goal of producing

6 controlled, selective, noncomplicated destruction. The only clear conclusion which

can be drawn from previous work is that successful ablation is dependent on a

complex interaction of lasing parameters including wavelength, pulse duration and

repetition rate, laser fluence (energy per unit area, Joules/ cm?), lasing medium,

delivery system, and others. Bits and pieces of this interaction process have come

out, but the complete picture has yet to be determined.

The literature will be reviewed by first looking at papers which have demon

strated the feasibility of laser angioplasty, followed by a more detailed examination of the basic research that has been published on laser-tissue interactions, optical

and thermal properties of normal and atherosclerotic tissue, damage mechanisms, and reports of selective lesion ablation. An attempt will be made at the conclusion to compile and organize existing results, as well as to identify areas where further research is necessary.

2.2 Feasibility of Laser Angioplasty

Early Studies

Early studies utilized available lasers in a variety of disease models to exam ine the feasibility of laser angioplasty. Most consisted of short reports without pertinent details on lasing parameters and energy delivery. The results are thus difficult to interpret, except in the broadest sense. Since CW lasers were readily accessable at the time, they were the instruments employed intitially.

In 1981, Lee, et al. [56], demonstrated the ability of CW argon ion, Nd-YAG, and CO 2 irradiation to ablate fibrous, lipoid, and calcified plaque in post-mortem human coronary arteries, sectioned transversely in a dry field. In a later report in 1982, Lee, et al. [54], demonstrated the feasibility of in vivo transluminal Nd-

YAG laser angioplasty by inserting a flexible fiberoptic scope into the subclavian

7 artery of open chest dogs in order to irradiate areas in the right iliac. Both reports

simply stated that the procedures were done, without reporting details such as

lasing parameters, the number of arteries injured, or the number of dogs. No

analysis was presented in either paper.

Choy, et al. [12,13], also demonstrated the capability of performing translu

minal angioplasty in 1982, using 2 thrombosed dog femorals in vivo, a thrombosed

rabbit aorta in vivo, and 16 human cadaver coronaries, all with argon ion laser

irradiation. A fiberoptic catheter, designed by Choy, was used for energy delivery.

Tissue Response: Acute and Chronic

Almost every report of laser-induced injury to the arterial wall has included

some histologic analysis of the acute effects. Consistent observations have been

made by various investigators. There is general agreement that CW irradiation

produces a central crater due to tissue vaporization, which is surrounded by areas

of residual thermal and acoustic injury. Charring may or may not be present along

the rim of the crater. Thermal coagulation necrosis often extends into surrounding

tissue where temperatures are achieved below those necessary for vaporization, yet

high enough to adversely affect the structures in the arterial wall. Areas of vacuole

formation and diffuse tissue disruption bordering the coagulation necrosis have also

been observed by multiple authors. This has been attributed to shock or acoustic injury from the physical ablation process [2].

In contrast to the many histologic reports describing the acute appearance of the arterial wall following a laser insult, very few papers have examined the response to laser injury beyond the immediate post-lasing period. No one has looked at the long term healing response beyond 8-9 weeks. Since consistent acute findings have been described, only one paper will be specifically covered dealing

8 with these effects. However, since studies of the short term healing response are

few, these papers will be addressed in greater detail.

Abela, et al. [2] (1982), described the immediate post-lasing effects of CW irra diation by three lasers: CO 2 (10,600ram) with a 0.2mm spot, Nd-YAG (l,064nm) via a 0.5mm silica fiber, and Argon ion (488nm,514nm) via a 0.5mm silica fiber.

Power was varied to 9 W, and exposure to I 6 O5. Postmortem human coronary seg ments (n = 25) with calcified and noncalcified plaques were successfully ablated by all lasers with qualitatively similar types of injuries. Three zones of tissue dam age were identified. Zone 1 consisted of a crater attributed to tissue vaporization.

Zone 2 consisted of an area of coagulation necrosis; and zone 3 consisted of a dif fuse area of tissue disruption from acoustic or shock injury. The results presented were descriptive in nature as either penetrating the plaque or not penetrating the plaque, without measurements of ablated volume. Total energy delivered was the laser parameter found to correlate best with qualitative estimates of magnitude of damage, as opposed to power or exposure duration.

A limited study by Choy, et al. [12] (1982), looked at acute (n = 2) and 5 days post-lasing (n = 1) effects of CW argon ion irradiation on totally occlusive throm bus created by injecting human blood mixed with thrombin into both femorals of a single dog and a single rabbit aorta. No lasing parameters were reported for the in vivo, transluminal procedures, other than 3 W measured at the catheter tip. Intimal necrosis and loss of elastic tissue were observed in the acute experi ments following tangential exposure to laser irradiation. In the 5 days post-lasing specimen, focal medial damage was present without thrombus formation. It was also reported that at 5 days, “the intima was completely repaired,” although no description was provided.

Gerrity, et al. [31] (1983), investigated the effects of CW, nonfocused CO2 irradiation on hypercholesterolemic swine which had been fed an atherogenic chow

diet for 15 to 20 weeks. Examination occured immediately after laser-induced in

jury to the aorta, and at 2 days, 2 weeks, and 8 weeks following the procedure.

Laser energy was delivered perpendicular to the arterial wall in a dry field en

vironment. Parameters evaluated were tissue damage, thrombosis, and healing.

Total energy levels were varied from 1-40J for the immediate examination groups,

and maintained at < 10J for the short term follow up groups, with from 1-20IT

and 0.1-0.5s exposure times. It was demonstrated in the immediate examination group that total energy was the only parameter that correlated well to both di

ameter and depth of the laser-induced crater (Figure 1). These observations are similar to Abela’s findings. None of the other parameters, including variable power at constant exposure, nor variable exposure at constant power, produced consis tent, predictive results. Tissue was evaluated by light microscopy and scanning

(SEM) and transmission (TEM) electron microscopy. Examination of the laser- induced craters demonstrated findings consistent with other authors. A crater was produced in the arterial wall, with areas of thermal injury and tissue disruption extending laterally from the crater. In some areas, which had received higher lev els of energy, a necrotic core was observed in the media. Short term follow up produced no differences in the healing process between normal and atherosclerotic tissue. The observed healing response is characterized by rapid reendothelialization with low thrombogenicity and without enhanced lipid accumulation. This is an extremely significant finding in demonstrating that laser-induced injury pro duces a nondeleterious arterial wall healing response, at least in the initial 8 weeks following injury in the pig.

Necrosis, char, and thermal injury with rapid reendothelialization were con firmed by Lee, et al. [58] (1984), in atherosclerotic rabbits over 1-14 days following

1 0 3000

2800

2400

2200

2 0 0 0

- 1800

2 ieoo

1400

1200

1000

800 . Burn dlamatar • Burn dapth 800

400

200

1 2 3 4 8 10 18 20 2830 38 40

E n a r g y ( Jo uI a a )

Figure 1: Relationship between laser burn dimensions and total laser energy in swine aorta under CW CO 2 irradiation; from Gerrity, 1983 [31 j.

11 CW argon ion laser exposure. Total energy delivered varied from 3-6 J (1-21F, 3s

exposures), and was delivered tangentially to the wall of the artery.

The only study to compare chronic tissue response to CW and pulsed ir

radiation was done by Singleton, et al. [91] (1987), who compared the effects of

CW argon irradiation (1-4.7, l-2s exposure), and pulsed XeCl irradiation (308nm,

16mJ per 30ns pulse, 20 Hz), in adult hypercholesterolemic swine over a 9 week

post-lasing healing period. Similar results as those of Gerrity were observed at

the end of the 9 week period: no acceleration of atherosclerosis and low throm-

bogenicity. The cellular response was similar with the two lasers, except for the

presence of char in the argon-irradiated samples. The CW exposure caused resid

ual damage in areas removed from the ablation site. At 48 hours, thermal and

' coagulation necrosis extended beyond the crater edge, and at 3 weeks and 9 weeks,

a broad band of damage persisted with the presence of char debris. The excimer

laser produced no signs of damage beyond the crater margin at any point in the

healing process.

For obvious reasons, the human arterial wall repair response is difficult to

evaluate. However, Geschwind, et al. [32] (1986), have been able to examine the

short term response in two patients following CW Nd-YAG laser irradiation of

peripheral vessels (12 W, multiple 30s exposures). A diluted blood perfusate was

infused at 30 m l/m in while lasing. To reduce the probability of perforation, en

ergy was delivered coaxially without moving the catheter tip, thus an unknown

distance to the target produced inconsistent fluences. One specimen was obtained

through amputation of the ischemic limb, 2 weeks after unsuccessfully attem pt

ing to recanalize the popliteal artery, despite 10 exposures of 121'F, 30s duration.

The other was obtained at autopsy (cause of death: pneumonia), 4 weeks after a

successful recanalization. Histologic evidence of thermal injury without thrombus

1 2 formation was observed in both specimens, corroborating the findings of previous animal studies. Coagulation necrosis and carbonization had nearly resolved in the 4 week post-lasing specimen. Reendothelialization was also noted in areas of noncalcified plaques. A relatively benign healing process after thermal injury was observed in this very small human population, without structural weakening or other complications.

Complications

Short term healing response has been shown to be relatively benign, as just discussed. However, the actual energy delivery process in an in vivo situation presents some significant problems. Complications have been encountered by mul tiple investigators, the most severe centering around inadvertent laser injury to normal tissue surrounding the target. This results in the potential for vascular perforation, loss of structural integrity with anuerysm formation, and other forms of arterial wall injury beyond the desired site of destruction [32,74].

Lee, et al. [58] (1984), studied in vivo acute (to = 3) and chronic (to = 4) vascular responses to CW argon ion irradiation in atherosclerotic rabbit aortae.

Total energy delivered ranged from 3-6J (1-2 W, 3s exposure), delivered through a quartz fiber without direct visualization. Rabbits studied acutely demonstrated the characteristic crater surrounded by necrosis and areas of thermal injury. In

2/4 rabbits studied chronically, one at 24 hours and one at 14 days, an aortic aneurysm was present with damage extending into the medial layer. The remaining

2 rabbits did not develop complications.

Isner, et al. [47] (1985), performed laser coronary angioplasty in 17 post mortem hearts at 53 sites using Argon ion irradiation at 201V with multiple 2-5s exposure bursts. Vascular perforation resulted in 33/53 cases. Perforation sites

13 were characterized by extensive calcific deposits, the origin of a side branch, and/or

tortuous coronary segments. It was concluded that inadverent perforation repre

sents the “rate-limiting” complication of coronary laser angioplasty.

These results were substantiated by Crea, et al. [16] (1986), who studied

in vivo transluminal angioplasty in five anesthetized dogs. A total of 45 sites were

irradiated in 8 separate coronary arteries, using a CW argon ion laser at 1-2 W

with multiple Is exposures. Perforation resulted in 5/8 of these arteries, followed

by cardiac tamponade and death in 3 dogs. The actual number of perforated sites

out of the 45 total was not reported.

Clinical Studies

Ginsburg, et al. [35] (1984), reported the first case of percutaneous translumi

nal angioplasty in the U.S. on a patient suffering severe claudication and rest pain

of the left leg resulting from a totally occluded superficial femoral artery and a

95% occluded deep femoral artery. The technique used was two stage in nature, to

reduce the possibility of perforation. A fiber was passed through the occlusion un

der relatively low power (21U) CW argon ion laser irradiation from an antegrade

approach and then withdrawn under relatively high power irradiation (7 W) to

enlarge the lumen. Successful recanalization was reported without complication.

This case report was followed-up by a compiled report of peripheral CW argon laser angioplasties on 16 patients [34] (1985). Improved lumen diameter, evaluated

qualitatively, was reported in 8/16 cases. However, the lumen diameters achieved were “not significant by established angiographic criteria”, and were followed by balloon angioplasty. Direct complications of the laser angioplasty included pain

(7/16), spasm (4/16), and perforation (3/16; 2 thermal, 1 mechanical).

Choy [11] (1984) reported successful recanalization of 7/9 human coronary ar

14 teries in patients undergoing bypass surgery of those vessels. However, all vessels

were occluded at three months. Choy hypothesized that platelet aggregation and

thrombus formation may have contributed to the reocclusion, as well as decreased

flow velocity due to competitive flow from the vein grafts. This report of throm

bus formation contradicts the tissue response studies previously discussed that

demonstrated low thrombogenicity after laser injury of primary vessels in animal

models.

2.3 Laser-Tissue Interaction

In the time since the initial feasibility papers, it has been recognized that de

tailed knowledge of the optical and thermal properties of arterial tissue, as well as

knowledge of the basic mechanisms of tissue removal, is necessary to understand the relevant laser-tissue interactions and allow for the optimization of ablation conditions. This is important in order to prevent damage to normal tissue under lying and surrounding the lesion which might lead to structrual weakness and/or perforation of the arterial wall.

The ultimate goal of laser angioplasty is to selectively ablate the atheroscle rotic plaque, in a controlled manner, without affecting normal tissue. To acheive this, spatial confinement of the energy deposition, as well as the subsequent thermomechanical or photochemical effects is required, either through selective absorbtion of exogenous agents that modify the optical and thermal properties of the target tissue, or by optimization of the energy delivery profile. This process involves complex functions of incident spot size, wavelength-dependent absoption, scatter ing within the tissue, pulse duration, incident energy, and thermal conductivity, all of which determine damage mode. In other words, target-specific ablation re quires energy absoption within the target and minimal thermomechanical effects

15 transferred to the surrounding tissue. This is complicated by the fact that in liv ing tissue, any photophysical or photothermal process, which might be short in duration, is followed by a biological response, which may take months or years to be fully realized.

2.3.1 Tissue Response to Light

Light incident on biologic tissue undergoes diffuse and/or Fresnel reflections, or enters the tissue. When light enters the tissue, the photons are either absorbed within the tissue, scattered, or transmitted through the tissue [101 ]. All of these processes are wavelength-dependent. In the ultraviolet and visible region of the spectrum, wavelength is inversely proportional to absorption and scatter, while at the same time, it is directly proportional to depth of penetration. [4,72]

Transmission, absorption and scatter may be analyzed by several methods.

Beer’s Law is a simple model for describing light propagation through absorbing media which does not account for scatter [94]. The mathmatical relation is given in equation (2.1)

/, = / 0 10- “' (2.1) where It =transmitted intensity, Iq =incident intensity, a =absorptivity, and

I =material thickness. Experimentally, the absorption may be determined by mea suring the incident and transmitted light. This model is valid only where scatter is small com pred to absorption [75].

The Kubelka-Munk model for light propagation in turbid and absorbing media is more complex and defines separate absorption and scatter coefficients. The analysis is based on the following first order differential equations describing light flux into and out of a specified material thickness.

16 = -SI - Al + SJ ( 2 . = SJ + AJ - SI where I represents the transmitting light traveling in the forward direction of prop agation, J represents the scattered light traveling in the backward direction, 5 and

.4 represent the scattering and absorption coefficients, respectively, and dX rep resents the differential spatial variable across the thickness of the material. These equations may be solved by specifying the boundary conditions. Experimentally, the absorption and scattering coefficients are calculated from measured values of remittance, transmittance, and thickness [75] (1986).

Scattered and transmitted light is useless for ablative purposes. Tissue ab lation requires absorption, where the electromagnetic photon energy may be con verted to heat [72]; or may result in a photophysical event such as plasma formation if the peak power is high enough and the pulse duration short enough; or may result in a photochemical reaction if the photon energy is high enough [72].

Selective absorption and thus preferential ablation, therefore, might be acheived if the target tissue has greater optical absorption at the lasing wavelength than the surrounding tissue. This may be through endogenous tissue chromophores present with greater concentration in the target or through the introduction of exogenous chromophores which accumulate preferentially in the target and thus alter its absorptive properties.

2.3.2 Thermal/Mechanical Mechanisms

The focal effects of heat generation are not wavelength-specific. Wavelength influences the depth of photon penetration and thus the region of energy deposi tion, but the resultant thermal damage is due to the same nonspecific mechanisms

[72]. Low temperature biological effects, such as inflammation, are reversible in

17 nature. Higher temperatures cause irreversible changes in structure and function

[4,72]. Tissue effects over various temperature ranges are given in Table 1, and the subsequent tissue responses are summarized in Table 2.

Table 1: Thermal Tissue Effects, from Anderson, 1983 [4], and Parrish, 1984 [72]

42°-65°C; some proteins are denatured 60°-70°C; structural proteins, including collagens, are denatured 70°-80°C'; nucleic acids are denatured, membranes become permeable 80°-85°C; DNA denatures

Table 2: Thermal Tissue Response, from Anderson, 1983 [4]

70°-100°C; coagulation necrosis and cell death > 100°C; vaporization of tissue water carbonization of remaining dry mass

Depending on the magnitude and rate of energy deposition, two basic physical phase changes are possible. Slow energy deposition with low temperatures will produce ‘melting’, and heat will be retained within the tissue. Once the tempera ture reaches 100°C, the boiling point of water, the process of vaporization begins, and excess energy is carried away from the surface. With rapid energy deposition, the vaporization temperature is quickly achieved. A third phase change is actually possible, and that is plasma formation. This only occurs with extremely short pulses and high peak powers.

The definitive conclusion to be drawn is that substantial thermal damage can and will occur at temperatures below those necessary for vaporization and tissue removal. Whether this thermal injury will adversely affect long-term tissue healing is unknown. However, on the assumption that residual thermal damage is unde sirable, temperature flow to areas surrounding an ablative target volume should be maintained at low levels to avoid nonspecific, irreversible thermal damage, or uncontrolled damage outside the target volume. The transition from specific, or confined to the target volume, to nonspecific thermal damage, according to Ander son [4] (1983), occurs when the laser pulse width exceeds the thermal relaxation time of the tissue. This is defined as f#, the time required for the central tem perature of a gaussian temperature distribution with a width equal to the target diameter to decrease by 50 percent. By reducing the pulse width below tft, heat flow to surrounding areas can be minimized, and thermal damage confined to the target volume. The thermal relaxation time is a function of the size of the target volume and the thermal diffusivity, £, of the target tissue. The size of the irradiated tissue volume is important since smaller volumes are able to dissapate heat more readily than larger ones. According to Anderson, the calculations translate into the nanosecond time domain for subcellular organelle targets, microseconds on the cell specific scale, and milliseconds for noncapillary vessels and small structures.

(£ = 1.3xl0_3cra2/s)

Furzikov [29] has a slightly different, but analogous interpretation of tissue heating, which accounts for wavelength variability of effect. In this theory, tissue heating and destruction may be either continuous or pulsed based on the char acteristic thermal diffusion time, t . This is defined by the relation: r = ^2/4£, where ( is the thermal diffusivity, and £ is the characteristic linear dimension of the tissue volume being heated. The value, £, is a function of the wavelength- dependent attenuation coefficient of the tissue. To acheive the thermal effects of purely pulsed mode delivery, tp

Also, to produce purely pulsed mode delivery for each pulse of an extended train,

19 Table 3: Attenuation coefficients, thermal diffusion times and limiting repetion rates for 7 wavelengths, from Furzikov, 1987 [29].

Laser Wavelength Attenuation Coefficient Thermal Diffusion Time Limiting Repetition Rate nm c m -1 a Hz K rF 249 650 4.5 x 10-4 2.2 x 10J XeCl 308 200 4.8 x 1 0 - 3 2.1 x 102 Dye(plaque) 465 54 7 x 10-2 14 Dye(wall) 465 26 8 x 10-2 12 Ar+ 514.5 32 8 x 10~2 12 Nd:YAG 1064 7.2 8 x 10~2 12 E r3+ 2940 5000 7.7 x 1 0 -° 1.3 x 105 C 0 2 10600 500 7.7 x 10“ 4 1.3 x 103

It is evident from this discussion that thermal considerations dictate a short laser pulse length. However, other thermomechanical effects are more pronounced with the high peak powers and rapid local heating associated with shorter pulses.

As laser energy is absorbed, the internal energy of the target volume increases causing thermal expansion. If the time duration is very short, and the flux density high, a pressure wave is generated due to the rapid thermal expansion. Compres sive shock waves result which travel through the tissue causing mechanical damage at sites removed from the target volume. Acoustic transients may also be gener ated during the process of tissue vaporization. Volume expansion and physical separation with recoil of material causes motion of the target as a whole. This process is also potentiated by a rapid time course and high peak powers. [4,79]

2 0 2.3.3 Ablative Photodecomposition and the Excimer Laser

Studies of UV irradiation of solid organic polymers lead to a theory termed

“ablative photodecomposition” [Srinivasan, 1982], [96] to describe the process of precise, controlled UV laser etching that produces clean, smooth crater edges with out detectable thermal damage. The etch depth per pulse is a function of the wavelength, pulse width and laser fluence. Weak intramolecular bonds are broken by absorption of UV photons through a photochemical reaction pathway [94]. The exact nature of the reactions involved is not well understood. It is known, how ever, that material is ejected from the surface at supersonic velocities, and consists of fragmentation products such as atoms, diatomics, small molecules, and small fragments of the polymer chain [96]. Microscopic models for the process have been proposed [30], but the specific m echanism rem ains unclear.

Use of the excimer laser for ablation of arterial tissue initially appeared quite attractive since it was thought to remove tissue by a fundamentally different mech anism than the visible and IR lasers. High energy UV photons were postulated to produce a photochemical reaction, similar to that described for organic poly mers, rather than a photothermal reaction [61]. Ablation would result from direct * intramolecular bond breaking, rather than diffuse vaporization. Evidence of this effect was the absence of the unpredictable thermal destruction and the elimina tion of characteristic signs of thermal injury surrounding the laser-induced crater.

Despite this, the existence of a photochemical ablative mechanism in the arterial wall remains controversial. In addition, the major advantage of UV ablation is based on the assumption that nonthermal injury will produce an overall less com plicated healing course. This assumption is currently unsupported by experimental evidence.

2 1 Linsker, et al. [61] (1934), reported histologically “sharp and cleanly defined

boundaries at light-microscopic resolution” of human arterial wall trenches pro

duced by 193nm irradiation from an ArF excimer laser. The fluence was 0.2-

0.3J / cm? with a 14ns pulse width and a repetition rate of 3-10 Hz. No thermal

effects were observed. This was compared to the nonuniform crater with sur

rounding zones of thermal injury produced by visible 532 nm irradiation. Higher

fluences were required at this longer wavelength to produce adequate ablation (0.2-

1.0J/cm^), 10Hz, unknown pulse duration). However, the UV laser was unable

to ablate calcified material. It was concluded that the excimer laser could pro

duce precisely controllable ablation of noncalcified lesions with a fixed depth per

pulse, consistent with a photochemical process. However, as will be discussed in

Section 2.3.5, similarly sharp and cleanly-defined craters with 532 nm irradiation

have been reported 21], using short, high energy pulses. Thus, the question of the

actual process of ablation in arterial tissue at UV wavelengths, remains open.

In contrast to Linsker’s group, Isner, et al. [46], reported successful ablation of calcified aortic valve leaflets and calcified atherosclerotic lesions with 248 nm light from a KrF excimer laser. However, much higher fluences were used, 2.2-

33 Jj cm?' with a 15ns pulse duration at 2-200 Hz. A lack of thermal injury was also reported, with two significant exceptions. Charring was observed under pro longed laser irradiation of heavily calcified aortic valves, even though focal calcified deposits in coronary arteries were readily ablated without thermal injury. Also, charring occurred when the excimer beam was unfocus'ed, resulting in a lower en ergy density at the tissue site. Isner hypothesized that the lack of thermal injury might be the result of combining a high fluence with short pulse duration, optimiz ing thermal diffusion factors, rather than a photochemical, wavelength-dependent phenomenon. The mechanism for removal of calcified tissue was not discussed. Farrell, et al. [26] (1986), demonstrated ablation without thermal injury, eval uated under light and electron microscopy, for three excimer wavelengths: 249nm

(KrF), 308nm (XeCl), and 351nm (XeF), including successful ablation of heav ily calcified lesions. Although it was concluded that depth of ablation correlated directly with energy density, no fluences were reported, so results can not be com pared with other authors.

Slightly different results were obtained by Grundfest, et al. [38] (1985), in comparing the effects of CW irradiation at 1060nra, 514nm. and 488nm, to pulsed irradiation at 1060nra, 532nm, 355nm, 308nm, and 266nm. It was concluded that all wavelengths longer than 308nm produced uncontrolled ablation and thermal injury, including the UV wavelength, 355 nm. Only 266nm and 308nm pulsed lasers produced craters with clean edges and no gross evidence of thermal injury.

The depth of penetration at 308nm was found to be directly proportional to the number of pulses. This confirmed results of an earlier study by the same group in which a linear relationship was demonstrated between depth of penetration and number of pulses at 308nm [37], (Figure 2). In other words, the process is precisely controllable through the number of pulses delivered. It was stated that ablation at

266nm and 308nm is the result of “a substantially different process” than at longer wavelengths. It is difficult to interpret the data and conclusions of Grundfest, et al. since important laser parameters such as fluence and spot size were inconsistent, absent, or conflictingly reported.

A detailed study by Murphy-Chutorian, et al. [68] (1986), examining laser- tissue interactions in normal and atherosclerotic aorta at 351 ram (XeF), concluded that excimer laser ablation is predominately a photothermal process, and that it is the manner in which energy is delivered, not the wavelength, that determines the type of residual injury observed. Pulse length and spot size were kept constant

23 2 .0 PERFORATION 1.6

1.2

0.8 CRATER WIDTH CRATER DEPTH r«-.01« r*.Q70 p»N3 p<.00t 0.4

20 40 60 80 100 120 PULSES

Figure 2: Relationship Between Crater Width, Crater Depth and Number of XeCl pulses at 308nm, 10.6J/cm^, (10-50i/z) and 10ns; from G rundfest,1985 [37]. at 10ns and 1mm , respectively. Pulse energy and repetition rate were varied to determine the effect of each on tissue ablation. A nonlinear relationship between number of pulses and depth of penetration was reported, conflicting with earlier results by several other investigators (Figure 3). However, several differences in laser parameters exist between this result and that of Grundfest, most significantly, the laser fluence. Murphy-Chutorian used a fluence less than half that of Grundfest.

This lower fluence may be very near threshold for this wavelength, since the depth of penetration is reported as 0.0 for less than 150 pulses. In fact, Singleton, et al, calculated a threshold fluence of 4.27/cm ^ for the XeF excimer line. Thus, the saturation effect may be a function of near-threshold conditions, or the result of extended lasing since it occurs beyond a total of 600 pulses. Changes in thermal and optical properties of the tissue under these conditions may allow an equilibrium to be reached between energy deposition and heat dissipation.

Murphy-Chutorian [68] (1986), also reported a nonlinear relationship between depth of penetration and energy per pulse. Since spot size was held constant,

24 0.4

| 0.3

X H 0.2 Q. UJ O 0.1

0.0 ■— 0 150 300 600 900 1200 NUMBER OF PULSES Figure 3: Nonlinear Relationship Between Depth of Penetration and Number of XeF Pulses at 351nm, 5 J/cm?/pulse, lOns, and 10 Hz\ from Murphy-Chutorian, 1986 [68]

this may be interpreted as a nonlinear relationship between depth of penetration

and fluence, rather than simply pulse energy. In other words, volume of ablated

material during a single pulse is not proportional to incident laser fluence. As

laser fluence is increased, a much larger penetration depth per pulse is produced.

Calcified plaque was found to be resistant to ablation, but at the given fluences, irradiation was probably subthreshold for calcified lesions. Pulse repetition rate was found to be a significant parameter at this wavelength. It was determined that 10-20 tfz was optimal to produce histologically clean edges. At 75 Hz, lateral extension of injury was seen with histologic evidence of thermal injury. This was the basis for the conclusion that ablation is predominately a thermal process, even in the ultraviolet range, and that the absence of thermal injury is indicitive of an adequate thermal relaxation time, which prevents excessive heat diffusion.

2.3.4 Debris and Photoproduct Formation

The question of distal embolization by particulate debris and/or thrombus formation following laser angioplasty has generated multiple investigations into the events of the immediate post-lasing period. Contradictions have resulted, with

25 reports of both the presence and absence of particulate debris. In addition, exam

ination of ablative photoproducts may give additional insight into the mechanisms

of tissue removal, whether thermal or photochemical.

In early work, Choy [12] (1982) described “thousands of microscopic bubbles

that rapidly disappeared in solution” when vaporizing artificial clots in saline under

CW argon ion irradiation. No analysis was performed. Abela, et al. [2] (1982),

also observed that “small bubbles were produced during lasing” with CW CO2

irradiation under saline solution. Several authors have since performed analysis of

these gaseous photoproducts.

Isner, et al. [45] (1985), examined the photoproducts liberated under CW

argon ion irradiation by atherosclerotic plaque (n = 10), myocardium (n = 12),

and calcified aortic valve leaflets (n = 6), with analysis by gas chromatography,

gas chromatography-mass spectrometry, and absorbance spectroscopy. Gas phase

products included light hydrocarbon fragments, carbon monoxide, and water va

por, which are consistent with protein and porphyrin pyrolysis. Products in solu

tion included protein fragments and nitrogen heterocyclic ring fragments, which are

also consistent with thermal degradation of proteins and porphryrins. No particu late products were observed, even with ablation of heavily calcified atherosclerotic lesions. This is in contradiction to other studies to be discussed later in this sec tion. It was concluded that CW irradiation ablates tissue through a purely thermal mechanism without formation of particulate debris.

A similar analysis by Kaminow, et al. [49] (1984), using mass spectrome try to analyze the gaseous photoproducts of human thrombus and cadaver aorta atheroma under CW argon ion irradiation, showed results consistent with Isner

(Table 4). The largest component was identified as water vapor which could not be measured quantitatively. A subset of the same investigative group [11], lased

26 technetium labeled thrombi in two rabbits and one human cadaver aorta. Lack

of distal embolization was evidenced by the absence of radioactivity in the distal

vasculature after lasing and profusion with saline.

Table 4: Mass spectrometer analysis of disintegration products of thrombus and plaque; from Kaminow, 1984 [49]

Constituent Concentration (% by volume) ______Thrombus______Plaque Nitrogen 17 24 Oxygen 1 3.5 Argon 0 0.1 Carbon Dioxide 50+ 30 Hydrogen 15 15 Methane 3 13.5 Ethane 1.5 2 Ethylene 6 5 Propane 1 2 Propylene 3.5 4 Cf hydrocarbons 0.7 1 Aromatic hydrocarbons 0.1 -

Conversely, two groups within the same laboratory have demonstrated posi

tive formation of particulate debris following laser ablation under pulsed, visible

irradiation [75,76]. At 465nm, 18J/cm 2, with a 1 (is pulse, ablation debris from

human fibrofatty atheromas was collected by placing a microscope slide 2cm in

front of the specimen in the path of the incoming beam [75]. Debris consisted of

whole and fragmented cholesterol crystals, small pieces of'calcific material, and fibers that appeared shredded. Particles were generally under 100 fim in size, with some as large as 300/im, shown in Figure 4. High-speed flash photography at 150/is post-lasing, produced evidence of “a mist of fine particles ” moving at a velocity of 300m/s coming from the target site, shown in Figure 5. It was stated that this provides strong evidence that ablation is “due not only to vaporization but also to liquefaction and mechanical failure accompanied by ejection of bulk material”.

At 482nm, 50-100.7/cm2, with a 1 [is pulse, ablation debris from calcified human plaque under saline consisted of fibrous and particulate tissue fragments

27 Figure 4: (A)Intact and shattered cholesterol crystals.(Bar=100/zra) (B)Collagen fragments and small bits of calcific material(Bar=200//m); from Prince, 1986 [75]. with fragmented cholesterol crystals [76]. Fragments were generally less than 20 fim in size, with a few over 100 fim. Plasma formation was verified spectroscopically during calcific tissue removal. The plasma formation with ejection of particulate debris was interpreted as evidence for a mechanical removal process under the given conditions.

Figure 5: High-speed flash photograph of atheroma ablation by 1 fis pulses of 465nm laser radiation at 150/^5 after irradiation; from Prince, 1986 [75]. Several authors have examined ablative photoproducts of excimer laser irra diation to determine if evidence of a photochemical reaction could be produced.

Clarke, et al. [15] (1987), used gas-chromatography to analyze the gas phase prod ucts of pulsed excimer laser irradiation of myocardium and atherosclerotic coronary arteries (193nm and 351ram, 3.2-16J/cm 2, pulse duration not identified). They found similar vapor phase photoproducts during excimer irradiation as those pro duced under visible CW irradiation, as well as those produced by simply flame torching the myocardium: methane acetylene, ethylene, ethane, propyne, allene, propylene, propane, and butene. It was concluded that despite the absence of thermal injury under excimer irradiation, the predominent destructive mechanism involves a thermal process. It was pointed out, however, that the photoprod ucts identified in this study may not represent all of those formed. Nonvolatile, greater mass products may also be present. Additional minor peaks were observed with gas chromatography under conditions of maximum gain that may be the result of a wavelength-dependent photochemical side process (radicals or radical- recombination products).

Qualitatively similar results were observed by Singleton, et al. [90] (1987), with five different excimer wavelengths (193nm, 222nm, 249nm, 308nm, and 350nm) for both calcified and nonclacified plaque. Photoproducts were identified as hy drogen, carbon monoxide, methane, ethylene, low molecular weight hydrocarbons, and traces of acetaldehyde. Contrary to Isner, however, Singleton supports the nonthermal ablative photodecomposition mechanism, as opposed to the thermal destruction mechanism. Thus, the question of destruction mechanism under UV irrradiation remains open. This is an important area for additional study.

29 2.3.5 Effects of Pulse Duration and Laser Fluence

As mentioned briefly in the Thermal/Mechanical Mechanisms Section, laser pulse duration plays a vital role in determining the ablative destruction mode.

Regardless of wavelength, poorly confined damage will probably result if the ex posure is beyond the thermal relaxation time of the tissue. The lack of thermal injury under excimer irradiation was initially thought to be due to a nonthermal photodecomposition. However, more recent studies indicate the possibility that it is merely a function of the inherently short pulse durations and higher ener gies characteristic of the excimer laser, since qualitatively similar results can be obtained at longer wavelengths where photodecomposition is impossible.

Deckelbaum, et al. [21] (1985), were able to reproduce ablation without the t usual signs of thermal injury under visible irradiation by using pulsed mode output with high-laser fluences and low repetition rates. Pulse duration ranged between

0.2-358ns, which was also compared to continuous wave. Repetition rates ranged from 1 Hz-256 MHz, and pulse energies from 2mJ-370mJ. Six discrete wave lengths were investigated, from UV to IR: 248nm (excimer), 35onm (tripled Nd-

YAG), 51471771 (Argon), 522nm (doubled Nd-YAG), 10647im (Nd-YAG), 10,6007itti

(CW C 0 2). Grossly visible signs of thermal injury and charring of myocardial slices were observed both under CW irradiation, and with pulsed repetion rates greater than 2 kHz combined with low pulse energies of less than 3mJ. O n the other hand, with repetition rates less than 200 Hz and pulse energies greater than

IO771J, neither gross signs of charring nor histologic signs of thermal injury were seen. This is summarized in Table 5, with the fluences calculated from the reported information. It was concluded that thermal injury of cardiovascular tissue may be eliminated with an appropriate pulsed energy profile. It was also noted that the

30 energies required in this study cannot be coupled to fiberoptics, but they may be

useful during intraoperative, open chest procedures.

Table 5: Energy profile and tissue injury: Continuous laser irradiation (top); and Pulsed laser irradiation (bottom); from Deckelbaum, 1985 [21].

X . Power Exposure Energy (J) No. of Laser . (nm) (W) (sec) (mean ± SEM) Spec. TC Argon* 48B-515 1-3 42-100 98 ± 6 10 + Nd-YAG* 1064 4-38 6-62 205 ± 26 11 + co2t 10,600 5-24 3-24 110 db 12 7 + • Fiber. f Focused beam. Nd-YAG = neodymhim-yttrlunvalumlnum-gamet; SEM = standard error of the mean; Spec. ’ 1 specimens; TC = tissue charring; + = present; X = wavelength.

Pow*r (W) Spot Enaryy (J) NO. Of Fluence* Sit# X Rap. Rat* PA PO Expotur* (■nM Luar (nm) (Hi) (rrvn (n») Path Avg (••cl (maan ± SEM) Spae. TC Argon* S1S 256 X 10* 2-5 X 10“* 0.2 10-23 0.5-1.2 21-181 55 ± 7 11 + — —— NO-YAO’ 532 2-10 X 10* 0.1-0.5 86-180 0.7-5 X 10* 1-1.8 11-82 47 ± 7 15 + n . 0 1 3 - 0 .0 3 0.8 Nd-YAQl 532 2-10 X 10* 0.1-0.S 86-180 0.7-5 X 10* 1-1.5 2-18 10 ± 2 14 + 0.05-0.75 0.3 Nd-YAO* 1,064 2-10 X 10* 1-2.7 140-356 3-18 X 10* 2-10.5 15-63 403 * 68 6 + 0.13-0.14 0.8 Excimar* 248 1-200 10-370 15 0.7-25 X 10* 0.5-37 1-68 2 2 * 3 18 0 5-115 0.7 Nd-YAO* 355 2-10 •0-86 20 3-4 X 10* 0.1-0.8 6-108 14 * 4 8 0 30-44 0.7 Nd-YAG* 532 2-10 60-180 20 3-8 X 10* 04-1.8 7-74 12* 1 31 0 30-95 0.3 Nd>YAQ‘ 1.064 10 180-250 20 8-12 X 10* 1.8-2.S 6-26 2 4 * 3 13 0 95-135 0.3 ’ Ffcar. ' Dtraci tfrnn. * Focusad Nam. Avg*» avaraga; n» ■ nanoaaconda (10** »*oontfcfc PA * put** amplltuda; PO ■ puUa dilation; Rap. Raia ■ rapatltion rata; 0 ■ at*ant

ariucnces calculated by C. Roberta from qiven lnform.itIon

It is not clear from the data, however, if the optimal values were determined,

or even if parameters were sufficiently isolated to draw conclusions. A large gap

exists between the fluences which resulted in thermal injury and those that did

not. For example, at 532nm, the highest fluence which produced thermal injury

was 0.25 J /c tti2 , and the lowest fluence which did not result in thermal injury was

30 J/cm 2. A range that covers two orders of magnitude was not reported. In addi

tion, 0.25 J/cm 2 is probably significantly subthreshold for this wavelength based on

data of Prince, et al. [75], to be discussed in Section 2.3.8. Thus, the thermal injury

may be a result of extended lasing under subthreshold ablation conditions. Further

investigations in this area are required to determine fluence thresholds for thermal

31 injury, and compare them to thresholds that initiate ablation. Also, if the data is

broken down according to pulse duration, one finds that 15-20ns pulses did not

result in thermal injury, and 96-190n$ pulses did produce signs of thermal damage.

This paper provided valuable evidence that longer wavelength, visible irradiation

with an appropriate energy profile is able to produce clean craters without residual

thermal injury. However, the lasing parameters must be more carefully isolated

before definitive conclusions can be drawn about the optimal lasing conditions.

An additional study by Deckelbaum, et al. [22] (1986), examined pulsed de

livery of a CO 2 laser at 10,600nm over multiple power levels and pulse ranges to

determine if thermal injury could be prevented with an appropriate energy pro

file, even with infrared irradiation. It was demonstrated that only with high pulse

energies greater than 80 m J, peak powers greater than 80 kW ,and power densities

greater than OOkW/mm,2, could all signs of thermal injury be eliminated. Peak

powers less than 500Wr consistently produced thermal injury. Results are summa

rized in Table 6 and Table 7. Careful examination of the data, however, allows

Table 6: Results of C O 2 laser irradiation according to energy profile; from D eckelbaum , 1986 [22].

^ P u l s e .. , * , n Po**f

CW 20 0 3 — — 4 in 22 4 10 22 36 * 6 ♦ ------Chopped II 01 I 7tn22 w 10* 7 10 22 2 1 0 II 1 0 * 7 ♦ 100-500 2K-7K PultfJ* 34 04 .VliiiWI • m 11 Mlolll t it* 27 22 * 1 4 0 .1 - 0 .9 2 0 -8 .3 Puluilt 36 01 30 in W0 I0lo40 17 lu 233 I to 31 1 * 04 4 0 .1 - 0 .9 10-40 Puliedl______42______06____ 2 to 10 10 to 100 ______1 10 10 » 10* 0.6io3______14 * 2______0 Q.QQl 13-50 *Cooper 250Z; (Cooper 300Z; ITxhiiio Symm 333. Avg ■ average; CW ■ conunwout wave; ♦ m prcMM; 0 ■ abicat.

aFlucnces calculated by C. Hobortn from qlven information

for some additional interpretations. One must remember that shorter pulses are inherently associated with higher peak powers. The investigators concluded that

the lack of thermal injury at 80&W was a result of the higher peak power. Yet,

the pulse duration at this level was at least two orders of magnitude shorter than

32 Table 7: Effect of peak power density on tissue injury; from Deckelbaum, 1986 [22].

Spot Silt No. of Repetition W o r»»-n Enrrg, III ITO TK.ee Fluence® |mflt:l Speeimewi Rue IHlI EncrgplmJI Peak tkW| A.g |W| I mean £ SEMI IkW/mnr’) Chairing (J/cm) 0 6 6 10 IN 110 I I 3 £ | 316 f 0 I.] I 10 110 110 I I 9 1 1 130 0 1 5 2.3 5 10 123 213 1.) 16 1 1 90 0 9 . 0 3 1 6 10 IW IMI | | 42 1 4 31 4 5 .6 4 2 « 10 110 IN | | 39 * 7 42 4 4 .] 71 3 10 110 110 1.1 DNBT 23 4 j c ■Tachiuo Spmtn 333. DNBT • 4M not bora throegk tiiaue; p ro • peak power demitp

■Fluence* calculated by C. Roberta from qlven Information

at any other level. In fact, all other pulse lengths are at or much larger than the

characteristic thermal diffusion time of 0.77ms, calculated by Furzikov for this

wavelength. Also, much higher repetition rates were used with the longer pulse lengths, which further exacerbates the problem. Table 6 may simply demonstrate

that reducing pulse duration below the thermal diffusion time eliminates thermal injury. The investigators also concluded that a peak power density of greater than

60 kW /mm? is required to prevent thermal injury, based on the information in

Table 7. An additional column has been added to this table. Laser fluences were calculated from the given information. As spot size was increased, fluence dropped accordingly. It may be that the investigators determined a critical fluence below which thermal injury occurs, rather than power density. Also, spot size alone, i may have contributed to the observed effects. Defocused energy delivery may re sult in thermal injury by creating a larger target volume, not solely by reducing the incident fluence and power density.

The only study to critically evaluate the difference between fluence and peak power density by comparing the effects of two pulse durations, 7 ns and 300ns, over a wide range of laser fluences, was performed by Taylor, Singleton, and

Paraskevopoulos [97] (1987), with XeCl excimer laser irradiation (308nm). Ab lation threshold fluence was determined by measuring photoacoustic spectra of

33 normal human aorta. It was defined as the fluence where a dramatic rise in the photoacoustic signal occured, which signifies the sudden ejection of molecules from the surface of the tissue, as illustrated in Figure 6. Spot size was verified to have

m c3

A) u to r c 3 U. V. to < 0.

0 4 6 a to Flusnce (J/cmJ)

Figure 6: Normalized photoacoustic signals for human aorta as a function of incident fluence of the 308nm XeCl laser with optical pulse durations of 7ns (o) and 300ns (•) showing the onset of ablation near 2 J / c m from Singleton, 1987 [91]. no effect since etch depth at constant fluence was independent of spot size, at least from 0.6-1.8mm. It was determined that although the shorter, higher en ergy pulse did produce a small decrease in threshold fluence, the magnitude of the decrease was insignificant (Table 8). A 400% increase in the intensity produced only about a 20% decrease in the ablation fluence threshold. It was concluded that ablative photodecomposition of solid organic material is a fluence dependent, not an intensity dependent, process.

Singleton, et al. [91] (1987), examined the effect of fluence per pulse on the quality of the laser cut in the tissue. In previous work with XeCl excimer ir radiation, threshold fluence based on photoacousic spectra was calculated to be

1.4J/cm2 and measured to be 5J/cm 2. From this data, three fluences were cho sen above and below threshold to investigate the result of repetitive 308nm, bns

34 Table 8: XeCl laser photoacoustic ablation thresholds of normal aorta; from Taylor, 1987 [97].

Pulse Duration Threshold Fluence ns m J /cm? 7 TMO 300 2200 pulses, with constant total energy in each case. The effects of subthreshold fluence at 1.1 J/ cm?, superthreshold fluence at 4.1 J/cm 2, and excessivly superthreshold fluence at 22 J/ cm? on postmortem atherosclerotic human aorta indicate an opti mal fluence does exist for obtaining high-quality cuts, as shown in Figure 7. Poor quality cuts were seen at both subthreshold and excessively superthreshold flu ences. With TlJ/crr? , deep acoustic damage, disruption of the surface layer, and a ragged crater floor result. It was concluded that for XeCl, 5 ns excimer pulses, the range 2-15 J/cm? is appropriate for optimal ablation conditions.

2.3.6 Lasing Medium

Absorption of the laser energy by the medium surrounding a target is an important factor to consider in determing the optimal lasing parameters and pro cedure. A detailed study by Fenech, et al. [27] (1985), compared the differnces in lasing medium using saline, whole blood, and various blood-saline dilutions, on the nature and extent of arterial wall injury produced with changing power densities under CW argon ion irradiation. Energy was delivered through a fiber at varying distances from the target, both in a perpendicular manner and tangentially. It was found that increasing concentrations of blood increased the beam divergence an gle (15° in saline to 30° in 1:64 blood-saline dilution), reduced the forward beam projection (down by 30% in 1:64 blood-saline dilution), and widened the crater produced in the arterial wall (Figure 8). Crater depth was not quantified. Also,

35 Figure 7: The effect of fluences on crater formation with XeCl excimer irradiation at 308nm and a 5ns pulse with constant total accumulated energy. (A)l.17/cm2; (B)4.1J/cm2; (C)227/cra2; from Singleton, 1987 [91]. 36 even though forward projection in blood was reduced, damage could be produced

at greater distances from the target than under saline. Lasing in a tangential

1S00 • (MEAN + S.E.M.)

14 0 0

1 3 0 0 • * P < 0 .0 1 ^ V com pind to • alln* •* P < 0 .0 0 1 W 1200- ■ 2 w att*. io s a c . oz a: i 1 0 0 ■ • 2 walla, S aac. o p<0.05 25 iooo z 000 cc UJ h soo Ul 2 7 0 0 o cc— «00 UJ H S00 oc p»NS o 4 0 0

3 0 0

200

1:32 1:10 1:8 1:4 whola blood MEDIUM Figure 8: Crater diameters produced during perpendicular lasing in varying concentrations of blood/saline mixtures; from Fenech, 1985 [27]; NS=not significant; S.E.M.=standard error of the mean. manner did not produce any damage to the arterial wall under saline, while a wide crater was produced under blood. It was hypothesized that “blood may act as an efficient heat conductor and therefore transmit energy over a larger area and for a greater distance”. Although there is greater damage under blood, the extent of damage is not predictable. Also noted was the lack of a flowing medium which might affect the results.

Other authors have observed similar differences in lasing through blood and

37 saline, but have not quantified the results. Abela, et al. [2] (1982), observed

enhanced absorption requiring less total energy for ablation in blood as opposed

to saline.

2.3.7 Wavelength-Dependent Tissue Absorption

Prince, et al. [74] (1986), used two techniques to evaluate tissue absorption in

human cadaver aorta. A spectrophotometer fitted with an integrating sphere and

a tunable-dye laser-based spectrophotometer. Data obtained by each techinique

were analyzed with two methods. A straight Beer’s Law analysis was done which is

valid only where scattering is small compared to absorption. Also, a Kubelka-Munk

formalism was done in which absorption and scattering are separate components.

The data from both methods indicate preferential absorbance in fatty atheromas

between 420nm and 530nm, with a peak at 470nm. The average atheroma aborp-

tion is > 1.7 times greater than that of normal artery over the waveband 450ram-

500nm. This is illustrated in Figure 9A. Lipophilic pigments were extracted from

the atheromas by thin layer chromatography, which were shown to be consistent

with several carotenoids known to be present in human atheromas. In particular,

/3-carotene, has an absorption spectrum which overlaps the band of preferential atheroma absorption. (Figure 9B)

A separate study from the same laboratory [63] (1987), used pulsed photothermal radiometry (PPTR) to examine absorption properties by measuring the optical attenuation coeffients at 4 discrete wavelengths, 308n.m, 351nm, 488nm,

532nm. PPTR is a noncontact technique which uses a pulsed light source to pro duce localized transient surface heating of the artery. The time depencence of the infrared black body emission is then used to measure the optical and thermal properties. The results of the study corroborated the earlier work by showing a

38 25

I >» o • a 20 C \a 9 o »» 2 O o uo < c o Q. X3 < 4 0 0 450 50 0 600 0.5 350 400 500300 550 600 Wavelength (nm) Figure 9: (A)Waveband of preferential atheroma absorbance: the ratio of atheroma absorption to normal aorta absorption for two measuring techniques; (B)Absorption spectra of lipophilic chromophores extracted from atheroma and normal aorta from Prince, 1986 [74]. two-fold greater attenuation in fibro-fatty plaque over normal artery at 488 nm.

Greater attenuation persisted at 532 nm, but not to as great an extent. Calcific plaque showed higher absorption than normal artery only at 488nm of the four wavelengths tested. No significant differences were observed in fibrofatty or cal cified plaque vs normal tissue at 308nm and 351nm (Table 9). Greater overall absorption was shown in the UV region.

Singleton, et al [90] (1986), measured the photoacoustic spectra of normal and diseased human femoral tissue under 193nm (ArF), 222 nm (KrCl), 249nm (KrF),

308nm (XeCl), and 350nm (XeF), excimer laser lines (small n, unidentified) The photoacoustic signal produced is assumed to be proportional to the linear optical absorption coefficient. No significant differences were demonstrated in absorption between normal artery and plaque at any wavelength tested. These results sub stantiate the work of Prince and Long previously discussed, which showed no dif ferences in absorption between plaque and normal tissue in the UV region. Greater overall absorption at shorter wavelengths was also demonstrated, consistent with

39 Table 9: Summary of attenuation coefficients obtained for vascular tissue with pulsed photothermal radiometry; from Long, 1987 [63].

TISSUE TYPE WAVELENGTH

1 308nm. 3S1nm. 4B8nm. 532nm j N Avg.ist. error N Avg.tst. error N Avg. ist. erro N Avg.ist erron (cm-1) (cm-1) (cm-l) (cm t) 1

Normal 3 180116 4 14518 16 3214.4 8 30i1.8 |

* Mm. Diseased 8 108H7 7 116111 7 25l3.7 6 37i4 5

Plaque 3 120i21 5 114116 8 5919.1 12 4614.9

Calcific Plaque 4 137133 2 118117 10 4217.9 9 3413.7

Toiai 18 18 41 35

known trends (Figure 10).

Similar results were also obtained by vanGemert, et al. [99] (1985), in a limited study with small sample sizes. The same wavelength-dependent absorption trends were shown. Three discrete A’s were used, 514.5nm (Argon), 633nm (HeNe), and

1060nm (Filtered Xe-arc lamp). A Kubelka-Munk analysis of the data was done.

At 514.5nm, which is within the preferential band identified by Prince, greater absorption was shown in plaque (n = 1) over normal tissue (n = 4). No differences were shown at the red or infrared lines (Table 10).

Kaminow, et al. [49] (1984), measured transmission in a Cary-14 spectrometer over a 300nm-1200nm range in three samples of human aorta which they classified as yellow-white, yellow, and red-yellow. Optical Density was calculated based on a Beer’s Law formulation. The yellow-white had the least absorption at 488nm and 514nm (~ 4 QD/cm); the yellow and red-yellow plaques showed stronger ab sorption (15-30 OD/cm). If it is assumed the yellow white plaque is the closet to normal, then the results are consistent with other studies discussed. However, no

40 r —O

-A

200 250300 350 Wavelength (nm) Figure 10: Photoacoustic spectrum of normal artery wall(A), of plaque covered with intima (o), and of plaque with intima removed (□); from Singleton, 1986 [90].

Table 10: Absorption (A) and scattering (S) coefficients for vessel wall and plaque; from van Gemert, 1985 [99]

514.5nm 633nm 1,06071771

Tissue A (cm *) S(cm *) A(cm-1) S(cm- *) A(C771- 1 ) S(C771- 1 )

Vessel wall 11.1(2.7) 11.0(0.8) 1.8(0.9) 6.3(1.4) 0.9(0.3) 2.8(2)

Plaque 18 19 2 12 1.4 2.3

Standard deviations in parentheses when possible normal tissue was tested, so comparisons cannot be conclusive (Figure 11).

Existing evidence indicates photoradiation between 420nm-530nm, centered around 470nm is the optimal wavelength to achieve preferential absorption by plaque over normal artery. However, no author has examined absorption beyond

1300nm. Further studies are needed to cover more of the IR spectral region and produce a complete picture.

Several authors have reported spectrophotometric data of human blood or blood components. Lee, et al. [57] (1983), reported a scan of freshly formed

41 120

g 100 PLAQUE g > 0 0

(S> ARGON 5 60 LASER o _j 40 < u R-Y 20 Y-W

300 300 700 900 1100 WAVELENGTH - nm Figure 11: Optical spectra of atherosclerotic plaque: Y-W, yellow white; Y, yellow; R-Y, red-yellow; from reference [49]. thrombus created by mixing human blood with thrombin, shown in Figure 12A.

The blood was permitted to clot and dry for 15-20 hours. Kaminow [49] 1984, reported an optical spectrum of whole human blood, shown in Figure 12B. Both show similar spectral characteristics, although Lee’s lineshape appears blunted, consistent with the characteristic bands of hemoglobin: the alpha band 550nm-

570nm, the beta band 530nm-550ram, and the soret band 390nm-420nm [8,74], illustrated in Figure 13. Though the preferential absorption band identified for plaque (420nm-530nm) is off the major peaks of blood and thrombus, both still show significant absorption in that region.

2.3.8 Preferential Energy Absorption: Selective Ablation

Based on previous evidence of preferential energy absorption in plaques, Prince, et al. [75] (1986), demonstrated selective ablation at 465ram with a 1 fxs pulse length.

Threshold fluence is a function of optical absorbtion. Therefore, greater absorp tion means lower threshold. Energy was delivered above the threshold fluence that was determined for plaque, yet at or near the threshold determined for normal tissue. Ablation threshold in this study was defined as the fluence required to

“roughen the tissue surface” of human cadaver aortas in regions of yellow plaques

42 (A) 1000 HUMAN WHOLE BOO BLOOD OE >• 6 0 0 «/> z OUJ -j 4 0 0 ARGON u< LASER & 200

200 400 600 BOO 1000 1200 1400 WAVELENGTH - nm

• 00 (B)

sm 2

5 "

.20

400 SOO •00 WAVELENGTH(nm)

Figure 12: (A)Spectrophotometric scan of freshly formed thrombus, from Lee, 1983 [57]; (B)Optical spectrum of whole human blood, from Kaminow, 1984 49].

43 lOO

E mM

75 15-

50 lOO 10 -

25 5-

250 3 00350 40 0 450 50 0 550 000 0 5 0 X (nm)

Figure 13: Spectral properties of human hemoglobin as oxy (—), carbon monoxide (— • — • —), and deoxy ( ------) derivatives; pH 7, 20°C; from A ntonini [8].

44 and normal tissue. Normal tissue was found to have a 2.6 greater threshold fluence than plaque which is consistent with the two fold greater absorption that has been demonstrated in plaque at this wavelength (Table 11). Preferential ablation was verified at 18J/cm 2 and 1 Hz by measuring 2-5.7 times greater ablated mass in plaque than in normal tissue.

Table 11: Summary of selective ablation at 465nm; from Prince, 1986 [75].

Atheroma Normal Aorta Ratio

Absorption (cm *) at 470nm 54± 12 26± 4 2.2

Threshold fluence (J/cm 2) 6.8± 2.0 15.9± 2.2 2.6

A group from the same laboratory have also demonstrated preferential abla tion of clacified plaques with plasma formation (verified by characteristic emission spectrum), at 482nm with a 1 fj.s pulse duration [76] (1987). At this wavelength, ablation thresholds were found to be 2.3-2.4 times greater for normal tissue than for calcified plaque (Table 12). Noncalcified atheromas were not studied. Prefer-

Table 12: Ablation thresholds for calcified atheroma and normal arterial tissue under 290nm, 482nm, and 658nm irradiation; from [76].

(A)-Calcified (B)-Normal Significance

Plaque (mJ) A rtery (m J ) B/A (p value)

290nm air 3.2± 0.7 3.1± 0.6 0.9 0.27

saline 3.6± 0.6 3.2± 0.7 0.9 0.14

482nm air 34± 5 81± 13 2.4 6.5(10-6)

saline 35± 6 79± 9 2.3 1.2(10~6)

658nm saline 102± 15 >237 >2.3

45 ential ablation was verified by a 1.7-12.0 times greater ablated mass in calcified plaque over normal tissue at various pulse energies. Threshold was defined as the energy at which “50 percent of 20 separate exposures produced observable tissue ablation”. This definition is different than that in the previous study, and may account for the difference in measured ablation thresholds for normal tissue (Ta bles 11 and 12). It is also important to note that two other wavelengths were tested, 290nm and 658nm. Only 658nm produced distinctly different ablation thresholds for normal and calcified tissue. However, the higher energies required damaged the delivery fiber, so this wavelength could not be adequately evaluated.

The shorter wavelength did produce lower overall thresholds in both normal and calcified tissue than the longer wavelengths, consistent with the known inverse relationship between absorbance and wavelength.

Preferential absorption in the 420nm-550nm band has been attributed to the presence of carotenoids in atheromas. It has been further suggested by Prince, et al.

[74], that preferential energy absorption might be further enhanced through the administration of oral doses of /?-carotene. This is based on evidence by Blanken- horn that carotenoid content in xanthomas could be increased by as much as 30% after administration of /3-carotene. Further studies are needed in this important area.

2.3.9 Exogenous Agents Hematoporphyrin Derivative: Photodynamic Therapy

Hematoporphyrin Derivative (HPD) or Photofrin II (trade name, Quadra

Logic Technologies, Inc. ) has been used in the treatment of endstage cancer ous tumors [41] by a mechanism termed ‘photodynamic therapy’. In this process, the photofrin II concentrates in a tumor cell. On exposure to low power light, the

46 photons are absorbed by the HPD leading to an excited state of the molecule. The

energy is transferred to ambient oxygen causing the formation of an electronically

excited state, termed singlet oxygen. This is still molecular C> 2 ; however, an elec

tron exists in a higher energy o rb ital [71]. Singlet O 2 can be highly reactive, where

ground state O 2 is inert. The singlet O 2 is cytotoxic causing tumor cell destruc

tion. HPD also exhibits fluorescence under ultraviolet excitation (Figure 14). This property, along with the photosensitiviy, has generated interest among investiga tors in the possibility of causing selective regression of atherosclerotic lesions with photodynamic therapy. The advantage is that the laser energy is not destructive; it serves only to photosensitize the dye.

100

(B) •0

(A) HpO in Y*79 C tlU UJ UUJ 2 L UJ S s» u 3 UJ > 2 5 UJ wK c 4U

WAVELENGTH (nm |

WAVELENGTH

Figure 14: (A)Fluorescence excitation and (B)fluorescence emission spectra of hematoporpyrin derivative; from Profio, 1984 [77].

In light of the success in cancer therapy, Spears, et al. [93] (1983), examined the possibility that HPD might also selectively concentrate in atherosclerotic plaques.

Preferential absorption of HPD by atheromas was shown in atherosclerotic rabbits

(n = 4) and a patas monkey (n = 1). The plaques were identified by the char-

47 aeteristic fluorescence of HPD. No plaque free areas exhibited gross fluroescence.

Transverse sections revealed gross fluorescence only in the lesion. No fluorescence

was seen in the underlying arterial wall. A control hypercholseterolemic rabbit,

not given HPD, did not demonstrate fluorescence at the sites of lesions. It was

concluded that HPD localizes within atheromatous lesions.

Results were substantiated by Litvack, et al. [62] (1985), in a study of 15

atherosclerotic rabbits. Ten recieved HPD, and five did not. In all rabbits that

received HPD, regions of fluorescence corresponded to regions of gross atheroma.

No untreated rabbits exhibited fluorescent atheroma. Histologically, the fluores

cent intensity diminished gradually from luminal surface to media. Under light

microscopy, the fluorescence was present within the intercellular matrix and the cellular matter of the intima. It was concluded that HPD selectively accumulates in atherosclerotic lesions with a diminishing concentration gradient from lumen to m edia.

Neave, et al. [69] (1986), also confirm preferential accumulation of porphyrin in the plaque of rabbits.In addition, plaque dissolution after photodynamic therapy was reported, evaluated 6 weeks after the procedure. No mechanism was identified.

Singleton, et al. [91] (1987), examined the effects of HPD accumulation on the possibility of allowing preferential absorption of destructive energy in plaque over normal arterial wall, which is a fundamentally different process than the photodynamic therapy. Increased absorption should lower ablation thresholds.

The absorption spectrum of HPD, illustrated in Figure 15, shows a strong peak very near the wavelength of the XeF excimer laser (351nm, 30ns), and slightly off that of the XeCl excimer laser (308nm, 7ns). Since both plaque and normal artery show similar absorption in the UV, Singleton examined the possibility of

HPD accumulation enhancing plaque absorption at these two wavelengths in HPD-

48 200 400 600 Wavelength (nml

Figure 15: Absorption spectrum of HPD, diluted to 3.7x10 ~^mg/mL] Absorbance = -/o<7io(transmittance); from Singleton, 1987 [91]. treated swine, based on photoacoustic spectra. It was found that the threshold fluences for normal arterial wall and for plaque are not significantly different at either wavelength, although 308nm irradiation does produce lower thresholds for both normal and plaque, as expected, due to the higher optical absorption at that wavelength. This is illustrated in Figure 16.

Fluence Figure 16: Threshold fluences for 308nm XeCl and 351 nm XeF lasers of normal and atherosclerotic swine arterial wall after HPD injection; (o) normal, 308nm; (•) plaque, 308nm; (□) normal, 351nm; (■) plaque, 351nm; from Singleton, 1987 [91].

Tetracycline: Preferential Absorption and Ablation

It is posssible to change the absorptive properties of atherosclerotic tissue by introducing an exogenous chromophore with the desired absorption band, which

49 shows selective uptake in the target tissue. Tetracycline has been shown to have an

affinity for human atherosclerotic lesions. Work done by Lindgren and Raekallio

[60] (1966), over 20 years ago, demonstrated that tetracycline deposition in post

mortem human aortas of patients who had received therapuetic doses during the

last few days of life, correlated well to the location of acid mucopolysaccharides and

areas of calcium salts in atheromas. Tetracycline was identified by its characteristic

fluorescence.

More recently, Murphy-Chutorian, et al. [66] (1985), also showed preferential

accumulation of tetracycline in plaque by 3 methods, using post-mortem human

aorta. Absorbtive spectrometry showed an absorbtive peak at 355nm, which corre

sponds to tetracycline, in treated human aortas that was absent in treated normal

vessels, illustrated in Figure 17. Treatment consisted of a 2 hour bath in a solution

containing 1 6fig/ml tetracycline. Ultraviolet microscopy revealed that tetracy

cline (identified by fluorescence) was localized within plaque and not present in normal tissue. Histologically, tetracycline occured near, but not within, choles

terol crystals. Also, gross fluorescence was observed in lesions of excised vessels from patients undergoing vascular surgery who had received tetracycline preoper- atively. A final method showed a 4-fold greater uptake of radiolabeled tetracycline in atheroma over normal vessel. To study the potential enhanced absorbtion of ultraviolet light, third harmonic YAG at 355nm was used to deliver equal amounts of energy to treated plaque (n = 7), untreated plaque (n = 5), untreated normal vessel (n = 6), and treated normal vessel (n = 7). Ablation was twice as ex tensive, measured by depth of penetration, in treated plaque (2.2 ± 0.25m m ) vs nontreated plaque (1.3 ± 0.55mm) with P < 0.017 in a 2-tailed student t test for unpaired means. Also, significantly greater ablation was found in treated plaque

(2.2 ± 0.25mm) vs treated normal vessel (1.2 ± 0.29mm withP < 0.0001), and vs

50 (A) (B) TETRACYCLINE HEMOGLOBIN

ATHEROMA TETRACYCLINE

UJ UJ U o z < z 03 4 CC CO 8 CC a 038 < <

300 350 400 450 500 300 350 400 450 500 WAVELENGTH fnml WAVELENGTH |nm|

Figure 17: (A)The absorptive spectrum of tetracycline solution which shows a peak at 355nm; (B)The absorptive spectrum from a solubilized sample of tetracycline-treated atheroma which shows the same peak at 355nm; from M urphy-C hutorian [66]. untreated normal vessel (1.0 ± 0.8mm withP < 0.0001). It was concluded that tetracycline administration allows enhanced destruction of atherosclerotic plaque by ultraviolet irradiation. The problem with this technique, however, is that al though plaque destruction is almost twice that of normal tissue after tetracycline administration, the process is not totally selective. Normal tissue is still ablated, just to a lesser extent. It may be possible to overcome this problem by choosing lasing conditions which are subthreshold for normal tissue, yet superthreshold for tetracycline-treated plaque. Additional studies are needed in this area.

Other Exogenous Agents: Enhanced Absorption

Two additional exogenous agents have been examined in an extremely limited manner to determine if they impart preferential absorbtion to atherosclerotic le sions. They are sudan black and cardiogreen. Abela, et al. [2] (1982), determined the total energy required for plaque perforation under CW Nd-YAG irradiation at 1064nm in human cadaver coronaries. It was concluded that sudan black does

51 enhance absorption, verified by less total energy required for plaque perforation than in nontreated vessels. Sudan black, however, is not appropriate for injection due to toxicicty, and is therefore not a viable choice for the purposes of enhanced ablation. Though cardiogreen is a nontoxic agent, it was found to have no effect on the energy required for ablation. No spectroscopic measurements were made on the dyes themselves to determine characteristic absorption bands, and no other ablative wavelengths were tested. It is not known whether 1064nm is even within an absorbtive region of the dyes. No tissue uptake studies were done. Also, no comparisons were made to normal vessels, and lasing parameters are impossible to determine from the report. The fiber tip was placed parallel to the arterial wall, and spot size at the actual surface was not reported. Therefore, a more care ful study is needed before definitive conclusions can be drawn about the effect of cardiogreen on the ablative process.

2.3.10 Photoemission Properties Fluorescence

Over 30 years ago, investigators were examining microfluorescence of athero mas in an attempt to identify the location of characteristic lipophilic substances within the lesion to help further understanding of the disease process. It was con cluded by Blankenhom, et al [1956], that carotenoids accumulate in human aortic atheroscerotic lesions in direct proportion to the extent and relative age of the lesion. It was also known that carotenoids exhibit a pale green fluorescence under ultraviolet light. In a follow-up study, Blankenhom, et al. [10] (1958), examined the microscopic fluorescence of atherosclerotic lesions in various stages of devel opment; then extracted the lipophilic substances responsible for the fluorescence, and finally identified carotenoids as the source. The lesions were found to exhibit

52 NORMAL ATHEROSCLEROTIC VI ARTERY l>c ARTERY c oV c ua> VI « w O3

500 600 700 500 600 700 wavelength (nm) wavelength (nm)

Figure 18: Fluorescence spectra of normal and atherosclerotic arterial wall with excitation wavelength = 480nm and cutoff filter at 520nm; from K ittrell, 1985 [51]. greater amounts of green fluorescence as they developed which correlated with an increasing concentration of carotenoids. These results have been recently corrob orated by Prince, et al. [74] (1986), who identified carotenoids as the lipophilic chromophores extracted from fibrofatty plaques and not present in normal tissue.

A resurgence of work aimed at examining fluorescence properties of the arterial wall' has occured to determine if in vivo spectral discrimination of atheromas is feasible for providing selectivity in the lasing process. Many groups are studying this, with inconsistent results. A problem may be in the differing measurment techniques, including excitation wavelength. Many reports are in the form of abstracts without clear details of experimental procedure or results.

Kittrell, et al. [51] (1985), described two spectral peaks at 550nm and 600nm with an excitation at 480nm, which were present in both normal and atheroscle rotic human cadaver coronaries, as illustrated in Figure 18. In normal tissue, both peaks had approximately equal magnitude, and in plaque, the 550nm peak had greater relative magnitude than the 600nm peak. It is interesting to note that although 550nm is yellow-green in color, and may be consistent with the fluores cence observed by Blankenhom, the 600nm peak is red-orange and definately not

53 attributable to carotenoids. A contrast ratio was defined as 72 = /(600)//(580), where 7(A) represents the fluorescence intensity at the arguement wavelength. The value 7(580) corresponds to the valley between peaks. The mean value of 72, cal culated from the values reported, is 1.88 for normal and 1.05 for atherosclerotic artery. A t test comparing the R's measured for normal (n = 3) and atheroma

(n = 3) was reported to yield P < 0.01. It was concluded that spectral discrimina tion of atheromas is indeed feasible, based on a total of six data points. Though the technique is interesting, more data is needed before this can be a valid conclusion.

The shorter excitation wavelength used by Andersson, et al. [5,6] (1987), pro duced different spectra of normal and atherosclerotic arteries. With an excitation wavelength at 337nm, two peaks were present at 395 nm and 480nm, in both nor mal and diseased tissue (Figure 19). In normal tissue the second peak was larger than the first. In atheroma, the first was larger than the second. It is interest ing to note in this study that 395 nm corresponds to deep violet or ultraviolet, just beyond the edge of the visible region, and 480nm is blue. Neither is consis tent with the fluroescence pattern of carotenoids. However, blunted structure is present in these spectra at 550nm and 600nm, which is consistent with the loca tion of the prominent peaks of Kittrell produced at longer wavelength excitation.

Andersson defined five different dimensionless contrast functions to discriminate between normal and diseased tissue as follows:

F\ = 7(395) 7(450)/7(420) 7(480) Di = 1.8,0.6

F2 = 7(395) 7(450)/7(480)2 D2 = 5.8,1.8

F3 = 7(395)/7(480) D3 = 7.3,1.8 (2.4)

FA = 7(395) 7(420)/7(450) 7(480) DA = 2.1,2.5

Fb = 7(450)/7(480) D5 = 4.4,1.6

54 tJ

% o 0.4

r 0. 2 -

ATHEROSCLEROTIC PLAQUE

0 .0 .

NORMAL AORTIC ARCH

0.0 490900400 690

Figure 19: Fluorescence spectra of normal and atherosclerotic arterial wall with excitation wavelength = 337nm; from Andersson, 1987 [6]. where /(A) represents the intensity at the identified wavelength, and D represents the discrimination power determined by eight samples and is defined as the dif ference in the mean values for the two types of tissue divided by the square root of the sum of the standard deviations of the means, D = (xp — xn)/(a-p + o-2)1/ 2.

In other words, a larger value for D indicates that the function was better able to differentiate between normal and diseased tissue. The first column of D's was calculated for samples that were classified into normal and atherosclerotic areas histologically, and the second was for macrospopically examined samples. The histologically classified samples demonstrated larger D values, indicating better discrimination than the macroscopically examined samples. The discrimination criteria used were not identified in either case. It was concluded that spectral dis crimination is a viable technique. No attempt was made to identify the responsible chromophores, though studies are currently in progress to that end.

The previous two papers dealt with examining differences in fluorescence line

55 5« SSI M ESi sa sai M NMOCTBS

Figure 20: Autofluorescence spectra from (A)normal and (B)calcified atherosclerotic human arterial tissue with excitation wavelengtn = 458nm and cutoff filter at 470nm; from Sartori, 1987 [84J.

shapes produced by normal and diseased tissue. An alternate approach was taken

by Sartori, et al. [84] (1987), in which differences in absolute fluorescence intensity

between calcified and noncalcified tissue were compared. It was found that cal

cified tissue produced over four times greater fluorescence intensity in vitro th an

nonclacified atheroma or normal tissue in the range 480nm-630nm. Other param

eters such as excitation intensity and distance from fiber tip, were kept constant

(Figure 20). Computer-generated maps were produced which correlated well with

grossly evident calcified regions of artery. Practically, however, it is difficult to have

confidence in a method which relies soley on absolute intensity discrimination over

an irregular surface in the blood filled, moving environment of the coronary ar

teries. Measurements of absolute fluorescence intensity in such a system would be affected by fiber distance from the arterial wall, angle of the fiber face with the wall, and the presence of blood between the fiber and the wall.

It is interesting to compare the spectra of Sartori and Kittrell. Sartori used

458 nm excitation, close to the 480ram excitation used by Kittrell. Although they

56 2 5 0 3 5 04 5 0 550 650 Wavelength (nm) Figure 21: Fluorescence spectra of normal swine arterial wall excited at 222 nrri (KrF) for a fresh specimen (solid line), and one after 9000 pulses (dashed line); from Singleton, 1987 [91].

appear different, Sartori’s spectra actually are close to those of Kittrell, upon closer

examination. The same spectral peaks at 550nm and 600nm are present with the

same intensity ratios between normal and diseased tissue. However, Sartori’s spec

tra exhibit an additional peak at 520nm, not present in Kittrell’s. The difference

is in the filters used. Kittrell’s cutoff right at 520ram, eliminating that peak, and

Sartori’s cutoff at 470nm which allowed expression of that peak.

Singleton, et al. [91] (1987), used 222nm excitation to examine fluorescence

properties of normal swine arterial wall in air under prolonged exposure (Fig

ure 21). The maximum at 310nm is probably from scattered light at the 222 nm

excitation peak that has been blocked by the cutoff filter and thus may represent

an artifact of the cutoff filter. Increasing duration of exposure to excitation ra

diation (5 mJ/cm?) resulted in a decay of the intensity of fluorescence, indicated

by the dashed line in Figure 21. The authors suggest the possibility that tissue from which a layer has been removed by laser ablation may have different fluores cence characteristics, making discrimination between plaque and normal arterial wall more difficult. It should also be noted that although this spectrum appears

57 different than that of Andersson (Figure 19), the absissa has been compressed to

cover a wider range of emission wavelengths. The peak that Singleton discusses at

450nm may indeed be a merging of the two peaks Andersson identified at 395 nm

and 450nm, due to the compressed axis. This is substantiated by the doubled-

humped structure of the wide 450nm peak identified by Singleton. Therefore, the

results of these two authors may be consistent.

Raman Spectroscopy

One study by Clarke, et al. [14] (1987) has been published looking at Raman

spectroscopy of formalin fixed calcified atherosclerotic human coronary tissue. The

Raman spectrum produced by powdered calcium hydroxvapatite was compared to

that of calcified coronary tissue (Figure 22). Similar spectral features were observed

in both. When the spectrum was run on normal tissue, no Raman features were

observed, even in conditions of maximum gain. It was concluded that Raman

spectroscopy could identify significant mineralization in arterial tissue. No attem pt

was made to examine noncalcified atherosclerotic regions.

2.4 Conclusions drawn From Current Literature

The literature reviewed indicates that laser angioplasty is a feasible technique

for removing vascular obstructions. However, the details regarding the appro

priate lasing parameters that will optimize laser-tissue interactions, as well as

methods of providing selectivity or control, are not yet completely understood.

The three major lasing parameters which have provided the most definitive results

thus far are laser fluence, pulse duration, and wavelength. Effects of fluence and pulse duration are closely related in determining the actual damage mechanism, as well as whether residual thermal injury will result from the ablation process.

58 (.M *1

1.3X IS

in c (D +• C

SH.W tSl.M IM.M Ramon shift (cm'1)

Figure 22: Laser Raman scattering observed over the 500-1200cm- * region (514nm laser excitation) from (A) a powdered sample of calcium hydroxy apatite and (B) a calcified segment of human coronary artery with background fluorescence subtracted out; from Clarke, 1987 [14].

Wavelength-dependent tissue absorbtion determines depth of penetration and is a critical consideration in the potential development of a selective process. Thermal S tissue properties are a function of both temperature and wavelength. Approriate choices of lasing parameters for ablation should therefore depend on a thorough understanding of ail the contributing factors and interactions. Conclusions drawn from the literature will be briefly summarized and areas where additional studies are needed will be identified.

59 2.4.1 Optimal Lasing Parameters, Tissue Properties

Due to the wide variablity in experimental conditions and the lack of lasing parameter isolation in the available literature, it is difficult to compare the results of the various investigators conclusively, even when a particular parameter such as wavelength is held constant. Only general trends can be extracted from the mass of data that has been published. The complex interactions involved make deter mination of the optimal lasing parameters from the existing literature extremely difficult.

Wavelength and Tissue Asorption

The literature indicates that normal arterial wall and fibrofatty atheromas have similar optical absorption in the UV, which gradually decreases with longer wavelengths through the visible and near-IR regions. The only consistent signifi cant differences that have been shown to exist are in the blue-green waveband from

420nm-530nm. In this range, the atheroma has approximately twice the optical absorption of normal artery. Although no spectra have been measured on calcified plaque, it has been shown that calcified lesions have higher absorption than normal tissue at the single discrete wavelength of 488 nm. These data indicate that the optimal lasing wavelength is in the center of the band 420nm-530Tim. As a direct consequence of the greater absorption, plaque has also been shown to have lower ablation thresholds than normal arterial wall in this same band. By delivering en ergy above the threshold for plaque which is below the threshold for normal tissue, selective ablation has been accomplished.

Some investigators favor excimer irradiation due to the clean ablation craters produced. In addition, it has been claimed that the overall greater absorption in the UV, and the subsequently smaller depth of penetration, would permit better

60 operator control of the ablation process [91]. However, it has been shown that visible irradiation can produce qualitativley the same type of clean crater without residual thermal injury simply by using an appropriate energy profile. Also, no conclusive in vivo evidence exists suppporting the premise that a nonthermal ab lation has any advantage over thermal ablation. Other factors to consider include

UV irradiation from excimer lasers is difficult to couple to fibers, has a poten tially carcinogeneic effect, and has no selective absorption in atheromas. In view of these facts, the best choice for optimal lasing wavelength is most likely in the blue-green range discussed above. An argon ion laser or tunable dye laser would be appropriate choices in this wavelength range.

Pulse Width

Pusled energy delivery is the temporal profile of choice, if one accepts the premise that the absence of residual thermal injury provides the optimal condition for an appropriate arterial wall healing response. As previously discussed, however, this premise is unsupported by evidence in the literature. An additional argument is that pulsed energy delivery allows greater operator control over the ablation process by limiting unpredictable cumulative thermal effects. However, until the healing response of laser-irradiated tissue is examined to compare the outcome of injuries with and without residual thermal injury, definitive conclusions can not be drawn.

Ablation Thresholds

Although multiple authors have reported “thresholds” for ablation, careful examination of the methods will reveal that what was reported was simply suc cessful ablation over a particular range, not a true threshold. A few investigators, however, have indeed reported true ablation thresholds where a range of fluences

61 was swept to identify the level at which tissue ablation was initiated. The problem which arises in comparing the results is that inconsistent definitions of threshold were used, even by the same authors in different papers. Table 13 is a compilation of the results of several careful studies to measure threshold fluences for ablation.

One can easily deduce the trend for increasing thresholds with longer wavelengths.

This is consistent with the known trend for greater optical absorption with shorter wavelengths. The conclusion is that threshold fluence for ablation is proportional to wavelength. Note there is quite a disparity in the measured values for normal tissue thresholds at 465nm and 482nm. The difference in wavelength is not enough to account for a jump from 6.8 J/cm 2 to 101J/cm2. However, two other differences in experimental conditions may indeed explain the discrepancy. Threshold defini tions were not totally consistent, and spot size was almost an order of magnitude different between the two measurements. The smaller spot size may allow more efficient heat flow out of the target volume which would result in higher threshold requirements.

Delivery Techniques

An additional factor which must be considered in determining the optimal ablation fluence is the suitability of the fiber optic delivery system that must be used in the in vivo situation. Fluences necessary for nonthermal ablation processes may be greater than the damage thresholds of the fibers which must transmit the energy to the target. Ultimately, the fluence may be limited by the transmission characteristics of available optical fibers.

Many delivery techniques have been attempted in the clinical situation to reduce the possible occurence of arterial wall perforation. These include: advance ment of the catheter through the obstruction under low power and withdrawl under

62 Table 13: Ablation Thresholds for Vascular Tissue Compiled from Several A uthors

Laser , "A normal tissue thresholds fibrofatty calcified (nm) (7 /c m 2) (J /cm?) (J/cm^) ArF 193 a .i3 0.4 KrCl 222 0.22 K rF 249 0.35 0.45 dye 290 3.9 4.0 XeCl 308 1.4 1.6 XeF 350 4.2 4.2 dye 465 6.8 15.9 dye 482 101 42 dye 658 > 295 >127 spot diameter: l-2mm l-2mm l-2mm 1mm 320fim 1mm 320fim threshold method: # i #2 #3 #4 #5 #4 #5 Methods of Defining Ablation Threshold: #1: calculated photoacoustic ablation threshold from [90]. #2: measured photoecoustic ablation threshold from [90]. #3: microscopically observed ablation threshold from [90]. #4: grossly observed ablation threshold to "roughen the tissue surface" from [75], #5: grossly noticable ablation for "50 percent of 20 separate exposures" from [76].

high power; stationary lasing with an inflated balloon to maintain coaxial energy

delivery with tiny interim advancements; and using a fiber much smaller than the

vessel diameter, followed by balloon dilation. Variable success rates have resulted.

2.4.2 Areas of Further Study Isolation of Lasing Parameter Effects

The effects of each of the major lasing parameters on tissue ablation must be carefully isolated in any study. Fluence, power density, and pulse duration are all closely related, since power is simply a rate of energy delivery. It is therefore difficult to separate them without a very carefully controlled study. Some authors report power density without fluence, and others report the reverse. An important question that has yet to be answered is whether ablation is an energy-dependent or a power-dependent phenomenon. Intuitively, one might choose energy-dependence, since energy is actually absorbed, not power. However, it would not explain why

63 higher fluences are needed to prevent residual thermal injury when pulse width is

constant. In fact, a pure energy absorption model would predict the exact opposite

— a higher fluence with greater energy deposition should result in increased heat

production and thus be more likely to cause residual thermal injury. One must

then consider power density to resolve this seeming conflict. An increased rate of

energy delivery might prevent thermal effects by causing ablation to occur faster

than heat conduction into the surrounding tissue.

Spot size is also important in determining damage. Equal fluences with differ

ent spot sizes may not produce the same results since there is greater relative heat

loss from a smaller target volume. This would explain the high fluence require

ment to prevent thermal damage, if the higher fluence were obtained by focusing

the beam down to a smaller spot. Heat flow from the resulting smaller target vol

ume woqJd_.be more efficient., hinder^Qgjthe development of high temperatures and

residual thermal injury. Therefore, the effects of fluence and peak power density

should be determined by varying the actual pulse energy with a constant pulse

width and spot size, not by simply defocusing the beam. Also, the effects of spot

size over a wide range of values need to be evaluated at constant fluence to de

termine if this is a significant factor. Then studies comparing fluence vs power

density can be done. Since these two parameters are related simply by the pulse

duration, the studies may be conducted by varying the pulse length while holding either fluence or power density constant.

Intuitively, one might still hypothesize that fluence, rather than power density, is the more definitive of the two parameters. Scientific evidence does exist to support this hypothesis. Early studies of CW lasers demonstrated that total energy correlated best with extent of injury, rather than power or exposure duration [31].

Also, one study has been done in the UV range for a pulsed laser, examining

64 the effect of power at constant fluence [97] for two separate pulse widths (See section 2.3.5). It was concluded that ablation is a fluence-dependent phenomenon, at least for a wavelength of 308nm. This type of study needs to be extended over a broader wavelength range. The experimental design did include a limited evaluation of spot size at constant fluence from 0.6mm-1.8mm diameter. It was concluded that in this range, spot size had no effect. This study needs to be extended over a much wider range of spot sizes and a much broader waveband.

Ablation and Destruction Thresholds

Ablation thresholds across the spectrum need to be determined with consistent definition of the threshold condition. To date, only the UV and several discrete wavelengths in the visible range have been studied, and those with inconsistent definition of threshold. Studies need to be repeated on lesions of varying composi tion, since atherosclerotic tissue is extremely heterogeneous in composition, even in lesions which appear grossly similar. Also, the characteristics of the laser injury as a function of superthreshold fluence across the spectrum need to be studied. Only one study has been conducted in the UV range dealing with this aspect which found an optimal range of ablation fluences for producing “high quality cuts” with the smoothest healing course potential [91], as discussed in Section 2.3.5.

Optical and Thermal Properties

The absorption spectrum of the arterial wall across the entire UV, visible, and near-IR to IR ranges must be well characterized before knowledgable decisions regarding the optimal wavelength for ablation can be made. Thus far, spectra have been measured over most of the UV and visible regions for fibrofatty plaques, but only out to 1300nm in the IR, and very little has been done on calcified lesions.

65 The next step is to examine thermal tissue parameters such as thermal diffu sion and thermal conductivity as a function of temperature and wavelength. Lim ited studies in this area have been done. This information could allow accurate predictions of extent of damage based on the lasing parameters chosen.

Tissue Response

Extended studies of tissue response and repair are needed to determine long term healing effects of various types of arterial wall injury as a function of the var ious lasing parameters. Investigators have been trying to determine a method of energy delivery that does not produce residual thermal injury, such as using high laser fluence and short pulse width. However, it has not been shown that thermal injury is necessarily deleterious. One potential problem that has been suggested by Singleton [91] is that residual thermal effects do not allow an accurate assess ment 6f the extent of damage to be made at the time of the procedure. It was hypothesized that unrecognized structural injury may increase the possibility of late complications such as anuerysm. However, studies of the “hot tip” probe do not support this hypothesis. This is a technique in which laser energy is used to heat a metal or sapphire-capped fiber, resulting in purely thermal destruction.

Sanborn, et al. [83] (1988), reported a 77% one year patency rate in 99 successfully treated femoropopliteal stenoses and occlusions. Treatment consisted of laser ther mal angioplasty followed by conventional balloon angioplasty. When the lesions were grouped by severity, one year patency rates were reported as 95% in 21 steno sis, 93% in 17 short occlusions(< 4cm), 76% in occlusions from 4-7cm in length, and 58% in occlusion greater than 7 cm. No late complications were reported. An interesting observation reported for the those lesions with recurrence and repeat angiography was that the lesion did not always occur in the laser-treated segment,_

66 but elsewhere in the vessel. The clinical success of this procedure, which relies on thermal destructive mechanisms, emphasizes the need for careful investigation into the healing response of arterial tissue before conclusions may be drawn about the preferred destruction mode for direct laser-induced injuries.

Photoemission Properties

It is clear from the literature that the fluorescent emission spectra of normal arterial wall and atheroma have qualitatively similar lineshapes. The same emis sion peaks are present in both, when excitation wavelength is constant. The only differences are in the relative intensities of the given peaks. This makes discrimi nation more difficult since some type of mathmatical analysis with comparison of the detected intensities is necessary. One cannot simply look for the presence or absence of a particular peak. Therefore, extensive in vivo studies must be done with reliable results if this technique is to be used as a diagnostic tool. There is some promise, however, in using Raman spectroscopy to identify calcified lesions, since this produces a spectral spike not present in noncalcied normal tissue. Fur ther studies are needed to compare these results with noncalcified atherosclerotic lesions.

Although it may prove that fluorescent discrimination is not appropriate for the in vivo situation, or at least difficult to implement, it may be an effective tech nique in the more easily controlled in vitro environment for the purpose of mapping arterial disease quantitatively. Few researchers are investigating the arterial wall emission properties for this purpose. Computer-based image processing systems could be used to generate valuable 2-D maps of disease occurence.

67 Exogenous Chromophores

Conclusive evidence of the selective uptake of tetracycline in atheromas has

been reported. This has been shown to enhance photoabsorption in a particular

waveband in the UV region of the spectrum. Since tetracycline has a characteristic

fluorescence, it would be interesting to examine the effect of tetracycline adminis

tration on the fluorescent emission spectra of normal and diseased arterial tissue.

Only examination of gross fluorescence has been done thus far.

More detailed studies of other tissue chromophores, such as cardiogreen and carotenoids are needed to determine if the absorptive or emissive properties of atherosclerotic tissue can be altered sufficiently when compared to normal tissue.

Also, more definitive studies of atheroma regression after adminsistration of HPD with photoactivation are needed. HPD has been shown to accumulate selectively in atheromas in addition to exhibiting a characteristic fluorescence. Therefore, it should alter the fluorescent emission spectra of treated atherosclerotic tissue.

These data have not yet been published.

2.4.3 Additional Considerations

It must be remembered, as pointed out be Lee [55] and Singleton [91], that de spite attempts to characterize the optical ancf thermal properties of atherosclerotic lesions, a large variability in measured parameters, such as cutting rate per pulse, will still exist due the heterogeneous composition of plaques. In addition, these properties may change as ablation progresses. Predicting tissue damage becomes even more difficult.

68 CHAPTER III

Experimental Materials and Methods

3.1 Tissue Preparation

Post-mortem human aorta, harvested within 24 hours of death, frozen and stored at -80°C, was thawed at room temperature in a saline bath for approxi mately 1 hour before use. Fatty lesions were grossly identified by their charac teristic yellow color, and raised appearance. Areas of normal arterial wall were also grossly identified. Each aorta was numbered and photographed prior to laser injury.

3.2 Laser Injury

The saline was drained from the aorta and injuries were made in a dry field environment, although the vessels were flushed with saline periodically to prevent the tissue from drying out. A continuous-wave, Cooper Sonics, argon-pumped, tunable dye laser with the dye cell bypassed was used to injure the tissue with the broadband output of the argon ion laser. The beam was focused to produce a 600/im spot at the level of a petri dish placed on a microtranslation stage, in which the aortas were placed. Spot size was determined using thermal paper, and maintained constant throughout. A Newport mechanical shutter/iris, model 830, was used to chop the beam at discrete time intervals of 1/100, 1/50, 1/10, 1/5,

1/2, and 1 second. Power was measured using a Newport digital power meter,

69 model 815.

After injury, each aorta was photographed and then fixed in 10% buffered

formalin for a minimum of 24 hours before further processing. The aorta was then grossly sectioned to include from one to three injuries with the same energy delivery profile per histologic specimen. The specimen was placed in a tissue cassette with a positioning sponge to produce the correct orientation for embedding.

3.3 Histology

Each specimen was embedded in parafin and serially sectioned at 5/zm, pick ing up every third section, producing 15 fim spacing between mounted sections.

Approximately 36 sections per injury were mounted. The same technician per formed all of the cutting to provide consistency. Special procedures were used in specimen processing, as recommended by Histology Services, to prevent stretching or wrinkling of the sections, which might artificially alter the crater dimensions.

These procedures are listed below.

• The parafin block was cut at room temperature without cooling.

• The temperature of the bath was maintained at a constant, monitored level.

• The slide was dried at room temperature, without heating.

For each injury, the unstained serial sections were examined microscopically to identify the section corresponding to the crater center. Under the assumption that the crater is symmetric and conical in shape, two criteria were used to make this judgement, maximal crater width and depth. The slide containing the crater center was returned to Histology Services for Masson’s trichrome staining. This method will stain the areas of coagulation necrosis bordering the crater edge a bright to

70 a deep red. Collagen stains blue, producing an easily identifiable boundary for severe thermal injury. Minor thermal injury may or may not stain a light pink, making its classification more difficult.

3.4 Image Processing

Histologic slides were placed on a Zeiss microscope to provide magnication for scanning. An Eikonix 78/99 digital scanner was used to capture full color images at IK x IK x 8 bit resolution, by scanning the stained section with a 1mm reference bar 3 times, once each through a red, green, and blue colored filter. Images were then stored on disk for subsequent processing.

The full color image was displayed using a Gould IP8400 image processing system. The boundaries between the crater and the areas of thermal injury were manually traced on the full resolution image using a digitizing tablet. The edges of the reference bar were identified in the same manner. Six separate lines segments were entered: scale 1, scale 2, the inner crater edge, the boundary of severe injury, the boundary of minor injury and a short segment at the base of the crater. Criteria used for identification are as follows:

• Inner Crater Edge

1. The initial point is entered where the intima is first disrupted.

2. The line entered traces the boundary between ablated area, which is

white, and tissue, which is either red or blue.

3. If the crater walls are smooth or slightly jagged, the actual boundary is

closely followed in tracing.

71 4. If diffuse tissue disruption is present, with areas of separation extending

into the crater, the line segment entered will cross the white areas of

separation.

5. The endpoint is where the intima transitions back to an intact state.

• Severe Injury Boundary

1. The area enclosed between the crater edge and the severe boundary is

dark to bright red in color, or follows the inner crater edge across areas

of tissue separation.

2. If the red-stained areas are clumped together with blue areas in between,

the general red outline is followed, as illustrated in Figures 23 and 24.

• Minor Injury Boundary

1. The initial point is entered where thermal expansion causes tissue to

protrude above the level of the noninjured surface.

2. The area enclosed includes that which stains light pink in color, as well

as areas of tissue disruption, and thermal expansion.

■ Base of Crater

1. A short line segment is entered which intersects the inner crater edge

at its deepest point. This is illustrated in Figure 25.

2. If the floor of the crater is flat, the base of crater segment is entered at

the center of the crater floor.

72 • Scale 1

— A line segment is entered which traces one edge of the reference bar on

the high resolution image. This is illustrated in Figure 26.

• Scale 2

- A line segment is entered tracing the second edge of the reference bar.

Image analysis involved calculation of the crater width, crater depth, ablated

area, severe injury area, and minor injury area, all with the 1mm bar as reference.

Crater width is defined as the length of the straight line segment which connects

the endpoints of the inner crater edge. Crater depth is defined as the length of

the straight line which connects the midpoint of the crater width segment with

the intersection point of the base of crater segment and the inner crater edge. The

ablated area is defined as the area of the region bounded by the inner crater edge

and the crater width segment. The severe injury area is defined as the area of

that region bounded by the severe injury boundary segment and the inner crater

edge, with their respective endpoints connected in straight lines. The minor injury

area is defined as the area of that region bounded by the minor injury boundary

segment and the severe injury boundary segment, with their respective endpoints

connected in straight lines. An additional quantity, crater shape, is defined as

crater depth/crater width. Therefore, after image analysis, each injury has six

parameters associated with it, all of which have been determined on the 5 fim

section at the center of the injury. They are crater diameter in mm, crater depth in mm, crater shape which is dimensionless, ablated area in mm2, area of severe

• • 0 thermal injury in mm~, and area of minor thermal injury in mm . These values are then used in a quantitative comparison of the tissue effects produced as a function

73 r, U - " V'l,'/*,: • 1 / . > i..; f y 1 1 r I i 'I ' II I V '

Figure 23: Edges of Crater Produced by 3IF, 1000m.s with Inner Crater Egde and Severe Injury Boundary Lines Entered

74 Figure 24: Low Resolution Image Demonstrating the Complete Severe Injury Boundary of the Crater from Figure 23 of the lasing parameters. Illustrations of low resolution images once analysis has been completed are given in Figures 24 and 25, with the minor injury boundary removed. A total of 63 injuries, 44 of which were identified as atherosclerotic and

19 of which were identified as normal, were analyzed.

3.5 Analysis

The data was subdivided into groups of constant energy, constant power, and constant pulse for analysis purposes. These groups are summarized in Table 14 with the number of injuries listed for each power, pulse and energy combina tion. Two constant power groups were formed, 2W and 3 IT, which are repre sented by horizontal rows. Two constant pulse groups were formed, 500ms and

1000ms, which are represented by vertical columns. Two constant energy groups were formed, 0.6J and 1.5J. Constant energy groups are represented by psuedo- Figure 25: Low Resolution Image of Crater Produced at 1.5 IV, 1000ms (top). High Resolution Image of Crater with Inner Crater Edge, Severe Injury Boundary, and Base of Crater Segments Entered (bottom).

76 Figure 26: High Resolution Image Demonstrating the Entry of the Reference Bar Edge. diagonals with positve slope. Normal and atherosclerotic comparison groups were formed at constant power = 3 W. All statistical analysis was performed using the software packages, SAS and SAS/GRAPH, Version 5 Editions.

77 Table 14: Number of Injuries per Power, Pulse and Energy Group for Atherosclerotic (A), and Normal (N) Tissue

Power Pulse in ms

IV 100 200 500 1000

0.6 i n=2(A) i' + i + 0.67

j 1.2 n=4(A) i * ; 0.67 + 1 i 1.5 . ! n=6(A)

+ • | + 1.57

2.0 n=3(A) n=3(A) n=3( A) n=4(A) 1 0.2 7 0.47 1.07 2.07

3.0 n=2(A) n=3(A) j n=10(A) n=4(A)

n=4(N) n=3(N) n=5(N) n=7(N)

0.37 0.6./ | 1.57 3.07

* No discernable arterial injury

+ Not included

78 C H A P T E R IV

Experimental Results

The literature revealed five laser parameters to be important in determin ing arterial wall damage: wavelength, energy, pulse length or exposure duration, power, and spot size. In this study, both spot size and wavelength were held con stant. Power, exposure duration, and thus energy were varied. Effects of these three parameters are difficult to isolate since they are not mutually independent.

All are related by the equation: Total Power x Exposure = Energy. Only one may be held constant at a time, while two must vary. Data will therefore be presented in the first section of this chapter exploring the relationships and isolating the effects of these three parameters.

A comparison of tissue response to the same set of laser parameters between atherosclerotic and normal arterial wall will be presented in the second section of this chapter, and will be followed by a discussion of possible sources of error.

Finally, a summary of the conclusions that may be drawn and the supporting evidence will be given.

Six dependent tissue injury parameters were identified from image analysis: ablated area (ablated), severe tissue injury area (severe), minor injury area (mi nor), crater width (width), crater depth (depth), and crater shape (shape). Minor injury area was later excluded from the final analysis due to ambiguities in the identification criteria encountered during the manual tracing portion of the study.

79 Therefore, results presented will be based on five dependent tissue injury parame

ters.

4.1 Isolating the Effects of Power, Exposure, and Energy

Before separating the data into groups based on a constant lasing parameter,

the entire atherosclerotic data set was analyzed to establish baseline information.

Data from the 44 atherosclerotic injuries were compiled into a SAS data set and

multiple regression analysis was performed three times, once each for power, ex

posure, and energy, using all five injury parameters. Results are presented in

Table 15. The model with the highest R2 and highest level of significance was the energy model, as expected from trends reported in the literature.

Table 15: Results of Three Multiple Regression Analyses, One for Each Laser Parameter with Entire Atherosclerotic Injury Data Set

j______R2 P > F______|j j Energy j0.60 0.0001 n=44 j

i \. Power !0.39 0.0017 n=44 :

Pulse |0.29 0.0211 n=44 |!

The next step involved performing separate analysis of variance based on a model of the means for each independent lasing parameter with each dependent injury parameter, to determine which of the five tissue injury parameters demon strated significant differences as separate functions of energy, power, and pulse.

These results are presented in Table 16. The analysis of variance supports the regression in demonstrating that the means of the injury parameters show the most significant levels of differences with the highest R2 values as a function of energy, as opposed to power or exposure. Bar charts of the means of the significant

80 Table 16: Results of Analysis of Variance for Tissue Injury Parameters for Atherosclerotic Tissue

Independent Variable: ENERGY

Parameter 1 R2 P>F Significance

; Ablated j 0.69 0.0001 yes 11 = 44 : 3 II ' Severe 1 0.64 0.0001 yes II 4> * & . . , Width ! 0.28 0.0775 no 3

Depth , 0.69 0.0001 yes n=44

j Shape 1 0.59 0.0001 yes n=44

I ji Independent Variable: POW ER

It 1 9 i Parameter ! R P>F Significance

! Ablated 0.35 0.0014 yes n=44 i -}< c ; Severe ! 0.24 0.0292 yes II

; Width 0.40 0.0005 yes n=44 II Depth i 0.26 0.0173 yes rt< 3 Shape | 0.16 0.1282 no II ' ____i Independent Variable: EXPOSURE DURATION

Parameter R2 P > F Significance

; j j Ablated 0.23 0.0140 yes n=44 I 3 Severe 0.20 0.0265 yes II

Width 0.10 0.2233 no n=44

, Depth 0.21 0.0189 yes n=44

Shape 0.20 0.0284 yes n=44

81 n = 3 (U.052) n=4 (0.060)

n=3 (0.019)

n=2 n=3 (0.007 )(0.011) D07' n=^ „ n=9 (0.013) n=2 o o» (vvgjxo.ose; (0.009) 0.05 • 888 R55ijS 0,04 ■ $9$ 9w 0.03- S88{ XXX 0 0?- XXX 885 0 0' • 888 888 o.oo idomdo X. 0.? 0.) 0.4 0.1 1.0 1.5 1.0 5.0 n=3 (0.083)

n—4 (0.08S)

n=3 (0.027)

01 0.) 0 1 01 10 1.5 1.0 30 cucicr Figure 27: Injury Parameter Means as a Function of Energy in Atherosclerotic Tissue (n=44)

82 n = 19 (0.027) (0.138) fOltl (0.014) 0.004 0.1 12 15 0.1 20 JO [0095^> 0 0- 0 (0.005 83 Tissue (n=44) n=19 (0.094) n - u n=19 (0.397)(0-287) ft 0.194) (0.108) POWE POWE 0.1 11 5.0 15 0.1 2.0 n=2 n=4 0.029)(0.042 NV3H Hldio Figure 28: Injury Parameter Means as a Function of Power in Atherosclerotic 100 700 S00 1 000 100 700 500 1 000

PUL SC 0 . * n=17 n=16 PUL SC 1.7- n = l 6 (0.663)

0 . 5

0 . 4

0 . J

n =6 (0.211)

0 I

0 . 0 0.0 * 100 700 500 1000 100 700 500 1000 puisr PUL SC Figure 29: Injury Parameter Means as a Function of Exposure Duration in Atherosclerotic Tissue (n=44)

84 dependent variables as a function of the three separate independent variables are given in Figures 27, 28, and 29.

Although the regression analyses indicate significance, close examination of the injury parameter means reveals two regions, one with lower levels of injury and one with higher levels of injury, with an apparent discontinuity between re gions for energy, power, and to a lesser degree, pulse. This indicates that regression might not be an appropriate tool for analysis. The critical ranges in which the non- linearities occur are 0.6-1.0.7 for energy, 1.2-1.5IF for power, and 200ms-500ms for exposure duration. To examine and isolate the effects of the three individ ual lasing parameters with respect to each other and the apparent discontinuity in response, the atherosclerotic data was further broken down into subgroups of constant energy, constant power, and constant exposure duration.

Constant Energy Subgroup

Two constant energy levels were examined, 0.6.7, on the edge of the critical region and 1.57, outside of the critical region. In the 0.67 group (n=9), three power levels with three corresponding pulse durations were included, 0.61F at

1000ms (n=2), 1.2IF at 500ms (n=4), and 3.01F at 200ms (n = 3). First, an analysis of variance was performed for each injury parameter to determine which were significantly different, as a function of power or pulse. Results indicate that both ablated area and severe injury area are significant parameters with p<0.05

(Table 17). Examination of the bar charts for these parameters shows a dramatic jump in both parameters between 1.2IF and 3.OIF, which also corresponds to

500ms and 200ms, respectively (Figure 30). However, only the difference in power can lead to a definitive conclusion, since the increase in the level of the injury parameters is in the wrong direction for exposure duration. This indicates that a

85 n=3 0 . 1 2 n 0.024 (0.005)

0.023 0.11-

o.io-

0. 09 -

• 0. 06 -

0. 07 -

0. 0 6 -

0. 05 -

0 . 0 4 -

n=2 0. 03 - (0.029) "=4 (0.042)

0 . 0 2 -

0 . 0 1 -

0 .00 0 .000 0.6 1.2 3.0 0.6 1.2 3.0

POWER POWER

Figure 30: Injury Parameter Means for Constant Energy = 0.6J (n=9), standard deviations in parentheses

86 Table 17: Analysis of Variance for Injury Parameters with Constant Energy = 0.67, for Atherosclerotic Tissue Injuries (n=9)

Parameter R2 P > F Signicance

Ablated 0.70 0.0262 yes

Severe 0.79 0.0083 yes

Width 0.51 0.1198 no

Depth 0.55 0.0864 no

Shape 0.33 0.2950 no

nonlinearity in response to power does exist. In other words, the rate of energy delivery is important, independent of the total energy delivered, and the exposure duration. A factor of 2.5 increase in power produced a factor of 4.3 greater ablated area.

In the 1.57 group (n=16), two power levels with two corresponding exposure durations were included, 1.5H’ at 1000ms (n=6), and 3.0W at 500ms (n = 10).

Analysis of variance of each of the injury parameters demonstrated that only ab lated area shows significant differences as a function of power or pulse. (Table 18).

However, the R2 values are much lower than in the previous group, and the bar charts are much less dramatic (Figure 31). The effect of power in this higher energy group is therefore present, but more subtle.

Constant Power Subgroup

Two constant power levels were examined, 3W and 2 W, both outside the region of interest in terms of power. In the 3IV group (n=19), four energy levels with four corresponding exposure durations were included, 37 at 1000ms (n=4),

1.57 at 500ms (n=10), 0.67 at 200ms (n=3), and 0.37 at 100ms(n=2). An analysis

87 n=10 0.27 i (0.046)

0.26

0.25

0.24

0 . 2 3 0.22 0.21 0.20

0.19

0.16 . n=6 (0.048)

A 0.14

£ 0.12

0.10-

0 . 09 -

0 . 08 -

0 . 07 -

0 . 0 6 -

0 . 05 -

0 . 0 4 -

0 . 03 -

0 . 0 2 - 0.01- 0.00- 1.5 3.0

POWER

Figure 31: Injury Parameter Means for Constant Energy = 1.5J (n=16), standard deviations in parentheses

88 Table 18: Analysis of Variance for Injury Parameters with Constant Energy = 1.57, for Atherosclerotic Tissue Injuries (n=16)

Parameter R2 P > F Signicance

Ablated 0.57 0.0007 yes

Severe 0.14 0.1476 no

Width 0.22 0.0671 no

Depth 0.24 0.0550 no

Shape 0.02 0.6372 no of variance of the tissue injury parameters determined that all five show significant differences as a function of energy or pulse (Table 19). Examination of the bar charts of the means (Figure 32), reveals a general increasing trend with increasing energy and pulse for all parameters except width. The discontinuity is not as apparent in this constant power subgroup, although ablated area and depth show a slightly larger increase between 0.6.7 and 1.57, which also corresponds to 200ms and 500ms, respectively, than between other levels. A factor of 2.5 increase in either energy or pulse duration produced a factor of 2.4 increase in ablated area.

The extent of injury also tends to level off at high pulse/energy.

The second constant power group at 2 W (n=13), also included four energy levels with four corresponding exposures, 2 7 at 1000ms (n=4), 17 at 500ms (n=3),

0.47 at 200ms (n=3), and 0.27 at 100ms (n=3). The analysis of variance of the tissue injury parameters, however, showed that only four demonstrated significant differences (Table 20). Examination of the bar charts of the means (Figure 33) shows a general increasing trend, as in the 3W group, except that the level of injury falls off at the highest energy/pulse value. This is probably the result

89 n= 4 n=4 (0.060) (0.025)

n =2 0.01 (0.056)

0 00 ■ -

n -10 (0.184)

0.4- n =2 0.138)

n=3 (0.086)

i m i c t t me * c r Figure 32: Injury Parameter Means for Constant Power = 3.OIF (n=19), standard deviations in parentheses

90 Table 19: Analysis of Variance for Injury Parameters with Constant Power = 3.01V for Atherosclerotic Tissue Injuries (n = 19)

Parameter R2 P > F Signicance

Ablated 0.79 0.0001 yes

Severe 0.55 0.0067 yes

Width 0.45 0.0277 yes

Depth 0.72 0.0002 yes

Shape 0.56 0.0052 yes

of experimental variability due to tissue heterogeneity, or other sources of error

discussed in Section 4.4. Also, the same large increase in ablated area exists

between 200ms and 500ms, which corresponds to 0.4,7 and 1.0J, respectively.

This additional data lends evidence to the conclusion that this is an exposure

phenomenon, and not energy-related when power is held constant. A factor of

2.5 increase in exposure duration or energy produced a factor of 2.2 increase in

ablated area. This is very close to the factor of 2.4 calculated at 3 W for the

exact same range of exposure durations, but a different range of energies. The

definitive conclusion to be drawn is that, like power, some type of threshold exists

for exposure duration between 200 and 500ms.

Constant Exposure Duration Subgroup

The last subgroup to be examined is that of constant exposure duration. Two

exposures were examined, 1000ms and 500ms. In the 1000ms group (n=16), four

energy levels with four corresponding power levels were included, 3 J at 3IV (n=4),

2J at 21V (n=4), 1.5J at 1.51V (n=6), and 0.6J at 0.6IV (n=2). The analysis of variance indicates that four of the five tissue injury parameters demonstrate sig-

91 n=3 (0.0S2)

n=3 (0.011)

n = 3 n=3 (0.163) . n=3 (0.083) (0.003)

E NE « CV CNCKCr

n=3 (0 .212) n=3 (0.027)

(H(«C1 C Nf»cr

Figure 33: Injury Parameter Means for Constant Power = 2.0 W (n=13), standard deviations in parentheses

92 Table 20: Analysis of Variance for Injury Parameters with Constant Power = 2.01V for Atherosclerotic Tissue Injuries (n=13)

Parameter R2 P > F Signicance

Ablated 0.69 0.0117 yes

Severe 0.75 0.0044 yes

Width 0.23 0.4887 no

Depth 0.69 0.0116 yes

Shape 0.62 0.0261 yes nificant differences as a function of energy or power (Table 21). The bar charts of the means (Figure 34) demonstrate a general increasing trend with the exception

Table 21: Analysis of Variance for Injury Parameters with Constant Exposure = 1000ms for Atherosclerotic Tissue Injuries (n=16)

Parameter R2 P > F Signicance

Ablated 0.70 0.0018 yes

Severe 0.69 0.0021 yes

Width 0.57 0.0150 yes

Depth 0.50 0.0346 yes

Shape 0.28 0.2508 no

of width. Close examination of the ablated area means reveal an apparent discon tinuity in response from 0.6J to 1.5.7, which also corresponds to 0.61V to 1.5VV.

A factor of 2.5 increase in power or energy resulted in a factor of 6.2 increase in ablated area. From the data presented thus far, this dramatic increase is probably due to a nonlinearity in response to power, not energy.

93 n=4 (0.025)

n=6 (0.048)

n=4 o S' ■ n=2 (0.085) 0 . Cl (0.029) o oi ■ R0w

C MC R C T

n=6 (0.194)

n=2 [0.095)

08151010 0.1151010 CNCOOY (»i«cr

Figure 34: Injury Parameter Means for Constant Exposure = lOOOms (n=16), standard deviations in parentheses Table 22: Analysis of Variance For Injury Parameters with Constant Exposure = 500ms for Atherosclerotic Tissue Injuries (n=17)

Parameter R2 P > F Signicance

Ablated 0.87 0.0001 yes

Severe 0.51 0.0066 yes

Width 0.57 0.0034 yes

Depth 0.84 0.0001 yes

Shape 0.77 0.0001 yes

In the 500ms (n=17) group, three energy levels with three corresponding power levels were included, 1.5,7 at 3 W (n=10), 1.0.7 at 2 W (n=3), and 0.6,7 at

1.2W (n=4). The analysis of variance indicates that all five tissue injury param eters show significant differences as a function of power or energy (Table 22). Bar charts of the means demonstrate the same dramatic increase in injury parameters between 1.2 W and 2.0 W, which also corresponds to 0.6,7 and 1.0J (Figure 35).

However, the jump in ablated area is much larger than for any other subgroup.

A factor of 1.67 increase in power or energy produced a factor of 12.9 increase in ablated area.

4.2 Comparison of Normal and Atherosclerotic Tissue Injuries

Normal (n=19) and Atherosclerotic (athero) (n=19) tissue injuries were com pared at constant power =3IV. Four energy levels with four corresponding expo sures were included for both types of tissue, 3 J at 1000ms (n=7 for normal, n=4 for athero), 1.5.7 at 500ms (n=5 for normal, n=10 for athero), 0.6,7 at 200ms

(n=3 for normal, n=3 for athero), and 0.3J at 100ms (n=4 for normal, n=2 for athero). An analysis of variance based on two independent variables, energy and

95 0 .OS n=3 (0.019)

n=3 (0.083)

CHCitcr

ENCRCT

0 . 5

0.3' n=4 (0.331) 0.3

0 . J 0 7

n=4 (0.064)

0.0

Figure 35: Injury Parameter Means for Constant Exposure = 500ms (n=17), standard deviations in parentheses

96 type (normal vs athero), demonstrated significant differences in four dependent

tissue injury parameters based on both energy and type (Table 23). The bar

Table 23: Analysis of Variance for Injury Parameters with Constant Power = 31V for Atherosclerotic (n=19) and Normal (n=19) Tissue Injuries

Energy Typ' e

Parameter R2 P > F Sig P > F Sig

Ablated 0.77 0.0001 yes 0.0001 yes

Severe 0.62 0.0001 yes 0.0010 yes

Width 0.74 0.0001 yes 0.1186 no

Depth 0.69 0.0001 yes 0.0003 yes

Shape 0.47 0.0106 yes 0.0079 yes charts of the means of the significant tissue injury parameters illustrate the differ ence in normal vs atherosclerotic tissue (Figure 36). Normal tissue demonstrated significantly lower levels of tissure injury over all energy levels than atherosclerotic tissue at the same energy levels. This is consistent with the greater optical absorp tion for atherosclerotic lesions in this wavelength region that has been reported in the literature.

4.3 Conclusions

The results presented in this study support the conclusion that a nonlinear tissue response to incident power exists in the range of 1.21V to 1.51V, at the wavelengths produced by an argon ion laser and the given spot size. (Power den sity or Flux is actually the parameter of interest, which in this study is linearly related to power.) Results also suppport the conclusion that response to energy is probably linear once ablation has been initiated. (Fluence or J/cm 2 is actually

97 ) 021 . n=7 0 (0.565) for W (0.2UH0.155) (0.001X0.001) n=4 (0.025) 2 (0.259) 0.) 0.1 1.a JO 1.a CNEDCr 1.0 0.1 1.0 0.) 0.1 0.J [0.007 ■ 08 . 0 tor 98 t H I 0.364) (0.118) (0.063)

deviations in parentheses ° 0 2 ) 0 E2Q )( (0.0301(0.018) 002 . 0 ( n=4 (0.060) n = n lO (0.046) ) 010 . n=3 0 ( 0.1 0.1 1.0 J.O 0 J 0.1 1.0 J.O ENCKCr 04 01 15 ENCKCr 10 J.O J.O 1.0 J 0.1 1.0 14 0 0.1 40 B'1 °'4 0.1 I,Mt' =2 0.J 0.1 10 J.O 10 J.O 0.1 0.J II 0.) 0.0 1.0 n Figure 36: Injury Parameter Means for Constant Power = 3 XXX 0 8 0 s g x m .4 (0.056

D . 1 . D 0 0 7 0 0 . 0 . 0 0 0 0 - ■ ■ ‘ 1 ft 1 1 ■ 1 1 tft - tft 1 4 • 4 1 J 1 1 1 OS 04 os ■ 01 00 2? 2? ■ J 2 0 07 0 Oft 0 0 0 0 02 0 0 0 0 10 009 - 0 01 0 IS 0 0 ■ 0 12 0 2ft 0 0 2ft 0 2 ■ 0 24 0 0 22 1 0 2 0 20 0 19 0 0 - 0 1ft

NV3ft 0 31V 19 V Atherosclerotic (A) (n=19) and Normal (N) (n=19) Tissue Injuries, standard the parameter of interest, which in this study is linearly related to energy.) This is

evidenced not only in the subgroups examined, but also in the multiple regression

analysis performed on the entire atherosclerotic data set. The parameter, energy,

produced the highest R2 value and highest level of significance for a linear model, as opposed to either power or pulse.

The source of the nonlinearity in tissue response is related to the thermal properties of the tissue. As discussed in the literature review. Furzikov [29j the orized that for wavelengths in the visible region, the millisecond time domain for pulse length would be short enough not to exceed the thermal diffusion time of the tissue. Beyond this region, both optical and thermal effects would become important. Results of the current study provide supporting data for Furzikov’s theory in terms of exposure duration. In addition, however, evidence is provided that power, independent of pulse duration, also induces a nonlinear response over a critical region. Since power is a rate of energy delivery, or a time-related pa rameter, this response may also be explained in terms of thermal tissue properties.

When the rate of energy deposition exceeds the capacity of the surrounding tissue to dissipate the excess heat generation, ablation will result from secondary thermal effects, in addition to the primary effects of photon absorption.

Results of the comparison of normal tissue response to atherosclerotic tissue response supports evidence in the literature of an almost two-fold greater photon absorption in atherosclerotic tissue vs normal tissue, reported by Prince, et al. [75].

The average ablated area mean for the atherosclerotic group in the current study was a factor of 1.8 greater than the average mean for the normal group.

Attempts at quantification of laser tissue injury in the literature have included measurements of crater depth, crater width, and weight of ablated volume, as well as crude qualitative estimates of the amount of damage. Estimates of ablated

99 volume have also been made from models of crater shape using actual width and

depth measurements. The current study provides true measurements of ablated

area at the crater center. Ablated area as a tissue injury parameter was the

only parameter to be significant in every subgroup examined. Crater width was

the parameter which most frequently demonstrated no signigicant differences as a

function of the independent parameters.

4.4 Sources of Error

Unavoidable sources of error were introduced at several points in the study

procedure, bdth in tissue injury and injury analysis. The human arterial tissue

used, though collected within 24 hours of death, had been frozen 14 to 18 months

before being thawed for laser injury. The optical and thermal tissue properties,

and thus response, may have been altered with such a long freezing time. Also,

the power output of the laser was variable up to 10%. The ideal experimental

arrangement would be to make an actual power measurement at the same time as

the tissue injury to insure accuracy.

Histology services was used for sectioning, mounting, and staining. It was

reported that sections were sometimes lost during the cutting phase, providing

the possibility of inconsistent distances between mounted sections and errors in

choosing the crater center. Also, variability in the intensity of the staining was encountered, due to different batches of staining solution.

Since all of the image analysis and identification of boundaries between areas of injury was done manually, error may have been introduced in the form of inter pretation by the researcher. Some craters had very smooth edges, making tracing quite simple and straight forward. Others had jagged, irregular edges, making consistent tracing more difficult.

100 C H A PT E R V

Model of Light Absoprtion, Heat Conduction, and Ablation

in Laser-Irradiated Tissue

In order to gain insight and increase understanding of the phenomena asso

ciated with tissue removal by laser energy, a mathmatical model was developed.

It was implemented in a computer simulation of light energy absorption and heat

generation with subsequent heat transfer to surrounding areas and/or tissue ab

lation. The predictions of the model were then used to allow additional, guided

interpretation of the experimental data disscussed in the previous chapter.

The accuracy of any model of this kind is dependent upon the accuracy of

the model parameters and assumptions. However, the thermal and optical proper

ties of normal and atherosclerotic arterial tissue are not well characterized in the

literature. Atherosclerotic tissue presents a unique additional problem due to its

extremely heterogeneous structure. The few studies that do exist report widely

varying parameters. Therefore, the purpose of this model will not be to determine

exact predictions of ablated area and ablation depth. Rather, the goal will be to

determine interaction relationships of power, exposure duration, and total energy,

based on a fixed set of input parameters and a homogeneous structure. Then,

the thermal and optical properties will be varied independently to determine the effect of each on the interaction process, within a fixed set of lasing parameters.

Once this has been accomplished, the variability in the experimental results may

101 be separated into that which can be accounted for soley by the differences in lasing parameters, and that which must be attributed to other causes.

5.1 Development of the Model

The model began as the simple one-dimensional case of light absorption with a temperature gradient produced only in the direction of the optical axis, normal to the tissue surface. This was based on a program by R. J. Rice !81J which modelled laser activation of glassy carbon electrode surfaces. It quickly became apparent, however, that several assumptions Rice made for glassy carbon were not valid for arterial tissue. The most significant was the criterion for one dimensional heat transfer — that the dimensions of the heated surface were large compared to the penetration depth of the light. This assumption breaks down for the several millimeters penetration depth of visible light into arterial tissue. Therefore, a two-dimensional model was developed in cylindrical coordinates, for temperature gradients produced in the radial and axial directions.

Heat transfer in any medium may be described by the heat conduction equa tion, which is given by equation (5.1) in cylindrical coordinates with zero tern- perature gradient in the angular direction (i.e. ^ = 0), since for this model the temperature is assumed to be independent of angular position. The axial direction is defined in terms of the z coordinate, and the radial direction is defined in terms of the r coordinate.

C St rSr V 6r) 6z2 k ^

k where £ = — = thermal diffusivity in pc s

102 W k = thermal conductivity in mK° , . . kg p= density in —* m J T c = heat capacity in kgK° T = temperature

t = time

r = radial distance variable

z = depth or axial distance variable

Qs = rate in W associated with the heat source term

The cylindrical coordinate system was chosen due to the circular cross-sectional area of the source beam, and subsequent cylindrical volume of heated tissue. A finite-difference numerical method was used to approximate the solution to the heat conduction equation. The tissue volume was divided into individual nodes of discrete temperature, based on the cylindrical coordinate system. Each node was located at the center of a local environment with the geometry illustrated in

Figure 37.

\ v h r

Figure 37: Geometry of discrete nodes in a cylindrical coordinate system of a finite-difference model.

103 Heat transfer occurs across the interfaces midway between two adjoining

nodes. The area of the interface in the 2 direction, Az, may be determined by

subtracting the area of the sector defined by the smaller radius, (W ~~ l ) ^ r )25

from the area of the sector defined by the larger radius, w A r)2, where w is the

nodal increment in the radial direction, and A r is the incremental distance. The

reduced formula for area in the 2 direction, the formulas for each of the interface

areas in the r direction, and the elemental volume formula is given in the following

set of equations:

Area of conduction in the z direction:

Az — (w — l/2)Ar2A (5.2a)

Area of conduction at the larger r interface:

Air = (w — l)A rA 2 A^» (5.2b)

Area of conduction at the smaller r interface:

Asr = w Ar A 2 A0 (5.2c)

Volume of each element:

V = (w - l/2)Ar2A2 A<£ (5.2d)

The rate of heat flow between nodes may be described by Fourier’s law of heat

conduction, which is approximated by a finite-difference form [52]:

dT AT q = - k A — ~ -kA — , (5.3) dx Ax x ' where q is the rate of heat flow, A is the area through which it flows, k is the thermal conductivity, and x is the distance. The temperature gradient between

104 nodes is thus assumed to be linear. The equations descibing the nodal temperature

behavior are derived by performing an energy balance on each node:

y-, /i A * rate of internal \ / time rate of change in 1 ('4) ' - (* 5heat generation J 1 internal energy of nodey

Therefore, by conservation of energy in node (j, w), where j is the depth increment,

the following equation is derived:

Qs+ (5-5)

Q{j,w+l)-> (j,w) + = Jt ’ where Qs is defined as the source term and U represents the internal energy.

The rates of heat transfer from the four surrounding nodes in the two-dimensional system, into node (j, w), may be derived by substituting the appropriate values from equations (5.2a)-(5.2d) into the finite-difference form of Fourier’s law, equa tion (5.3).

(5-6a)

9(j-l,»)-.(j»~ k A *

'J't _ ’J't

a,9 0.U )+1)— n /•(j,w) i - — kA, K A lr (O.OCj

j't _ j t q. . , . . . ~ LA______(hw ) ( c C J \

The superscripts on the temperature values represent the appropriate time incre ment, and the subscripts represent the location of the node in space.

The problem under study is one of transient thermalconduction, since the tmperature of each node varies in time as well as space. The time rate of change in internal energy may be approximated by the following:

105 ‘l i M ~ = ycr0>)‘ ^ (5.7) H At H At v ' where (t — At) represents the next time increment and m = mass.

By combining equations (5.5), (5.6a)-(5.6d), and (5.7), the energy balance for node (j,w) may be obtained:

Qs+ + fc.4zr ('j-| '“ )~7'6 » H- (0.8)

rt _Tt pt _Tt rpt+ At _ rpt LA. 0>+l) (j>) | LA 0>-l) 0>) _ y (j,w) {j.w) ^Alr S? ------Sr - P* c ^ ------

Substituting the appropriate areas and volumes, and solving for the temper ature in the next time increment produces a general form of the energy balance:

T^+ $)> <5'9)

I (At /rpt rpt \ + A?^(j-l,u;) ~ 1 (j,w))

+ (u- - 1/2) ” W

! ( ^ ^ / r p t ______r p t \ r p t + A t r p t (iv — 1/2) 0>-i) 0>r ~~ 0>) (J» where ( = ± .

Interior Nodes

By defining the dimensionless Fourier number, Fo =f , and assuming

A r = Az = Ax, the general nodal energy balance equation will reduce to the following for a node located in the interior of the tissue volume:

+ t t K W , - TU <5-10)

+ Fo(Tf■v ,. - 7 1 u,w)' 0 w + (w - 1/2)

I ^ F'nCT't Tt \ rpt + A t rpt (w —1/2) ^ 0>-i) 0»* 0» 0»

106 Surface Nodes

Using a similar energy balance on the nodes at the surface of the tissue volume, the following is obtained:

QsAt Vpc F ° ( T h + <3-u>

+ (u ;-l/ 2 ) Fo(T(j,™+1) T( j ^

I ~ J T n C T t — T t \ _ rpt + A t _ rpt (w - 1/2) 0>-i) 0»' 0>) 0>)

Axial Nodes

For the axial nodes at the center of the cylindrical volume, the following energy balance equation is obtained:

F°(TU « ) - <5' 12>

+ i ^ W ) f °(tU d - t(U) = isr.),- io»

5.1.1 Forms of the Source Term

The attenuation of light due to absorption and scatter as it propagates through tissue in the z direction, may be modeled as a decaying exponential using a mod ified version of Beer’s Law in which the attenuation coefficient, 7 = a -t- /?:

I{z) = I0e~(a+V z (5.13) where a represents the absorption coefficient, and /? represents the scattering coef ficient, both in cm - 1 . The incident intensity is represented by J0, in W /cm 2, and the intensity as a function of depth'is represented by I{z).

107 Radial Spatial Distribution:

The symmetric radial variation in intensity may be modeled as either a uni form distribution, as in equation (5.14a), or a Gaussian distribution, as in equation

(5.15a).

Uniform radial distribution:

I(z,r) = I0e~(a+^ z for r < wQ and 0 elsewhere (5.14a)

where IQ = (5.14b) ITWr

Gaussian spatial distribution:

—2 r 2 I(z,r) — IDe wo e~(a+0)z (5.15a)

where IQ = (5.15b) TTW&

o and w0 is the 1/e radius of the gaussian profile, or is the defined beam radius of the uniform intensity distribution, and P is the total beam power.

Beam Broadening:

According to a purely exponential model of absorption and scatter in a gaus sian spatial distribution, the intensity decay due to scatter is lost to the tissue volume, and does not contribute to heat generation. Also, the beam size remains constant with propagation. However, evidence has shown that beam spreading does occur in laser-irradiated arterial tissue [93]. Motamedi [102] proposed a model which allowed the standard deviation of the gaussian spot to increase as a function of depth. This model was adapted for the current simulation by allowing the 1/e2 beam radius to spread as a function of depth.

— 2 r 2 I(z,r) = e~(a+0)z (516)

108 Given the gaussian distribution of equation (5.16), the 1/e2 radius at 2 = 0 is

now defined by iu2(z). To determine the nature of this function, it is assumed that

scattered light is no longer lost to the tissue volume, but instead causes the spot to

spread. If absorption were zero, then the attenuation would be purely a function

of scatter, and the total beam power at any depth would be equal to that at the

surface. In a similar manner to Motamedi, the powers are equated to determine

the beam spread function.

Total beam power at the surface:

P( 0) = (5.17a)

Total beam power at depth = 2 :

• ,w = ( ,i7b)

By equating the powers and solving for the beam spread function, it is deter

mined that:

w2{z) = w2{ 0)ePz (5.18)

Therefore, the final equation describing the attenuation of a gaussian beam,

with beam broadening, as a function of depth is given by equation (5.19).

—2 r 2 I{z,r) = IQewoe^z e~(a +0)2 (5.19) where wQ is the incident 1/e2 radius. The result of beam broadening on the intensity distribution as a function of depth is illustrated in Figure 38.

Temporal Profile of Energy Deposition:

Two temporal profiles are possible in laser-irradiation of tissue. They are chopped, continuous-wave delivery in the hundreds of milliseconds to seconds

109 4 4 4 4 4 4 4

Surface

x * * * x X X X X ♦ X X * * D epthl K 4 X X 4

^ X X ^

X X 4 4 X x +x X* * • * * +X .* \ *+ k ,* Depth2 *, x $ .* \ S { * * * ‘fX X* T * T « .« * r- * & ..

S m t ' • < Prolila in Arbitrary Units

444 4 4 4 4

4 4 + Surface +

* x***x + X X X X + X X

^ X D epthl X + x x

♦ X X +

+ X X + + X .•*•*•, X ♦ X . * * . X 4 4 * 4 x 4 Depth2 4 x ♦ x • • X ♦ * 4 4 X * * X 4

4 4 4 * 4 4 X * « X ^ . X « « X .

■xw xrt****** IS*______**s»tt*n••'■ * « « XttMMHIISN ...... I ...... I p i i »'» i » I* ...... ' I ...... f r r r i »......

S a • I • s t P r o( iIs in Arbi trsry Units

Figure 38: The Effect of Scatter With Beam Broadening (top) and the Effect of Scatter Without Beam Broadening (bottom), at the Surface and at Two Tissue Depths.

1 1 0 range, and pulsed delivery, usually in the nanosecond, microsecond, or millisec ond range. The chopped pulse may be modeled as a flat temporal profile, and the short pulse may be modeled as a gaussian temporal profile, as in Rice [81].

Chopped Continuous Wave Delivery:

I(z,r,t) = I(z, r)fort < tp and 0 otherwise (5.20)

Pulsed Delivery:

I(z,r,t) = I(z,r)e ^ (5.21) where tp is the pulse width for both, and is defined as the full-width-half-maximum

(FWHM) for the gaussian temporal profile. The 6 value defines the shape of the gaussian pulse based on tp, and 2 defines the peak power point.

Heat Generation due to Light Absorption

Heat generation within the tissue is due solely to photon absorption. Scattered light causes attenuation of the beam without resulting in tissue heating. The rate of change in flux due to absorption as a function of depth, for any of the forms already discussed, is given by equation (5.22):

r,t) (5.22)

Therefore, the rate of heat generation per unit volume of tissue — the source term in the energy balance equation — becomes:

^=a/(z,r,f) (5.23)

111 5.2 Implementation of the Model

The model was implemented in a Fortran program written to run interac tively on the MicroVax II. One version was adapted to run on the Cray X-MP, in batch, for the most CPU-intensive input data sets. The MicroVax-version of the

Fortran program is included in Appendix E. The simulation parameters which are under the control of the user include: number of iterations, constant vs variable thermal properties as a function of tissue type, optical absorption and scattering coeffiecients, wavelength, pulse duration, temporal power profile, spatial irradiance distribution, total beam power, percent of incident irradiation transmitted into the tissue (e), initial temperature, and vaporization temperature.

Each simulation produces a set of five indicators of tissue injury, a list of the simulation parameters which produced that injury, and a number of output files documenting the time evolution of the injury in terms of the indicators, the maximum temperature acheived by each node, and the ablation time of each node within the crater. The five injury indicators are defined in Table 24.

Table 24: Definitions of Indicators of Injury

Indicator Definition

onset of ablation: time of ablation of node (1,1)

ablated depth: maximum depth ablated along axial nodes

ablated width: twice the ablated radius at the surface nodes

ablated area: twice the total dx2 area of ablated nodes

shape: depth/width

The parameters for the current study were chosen to match the experimen tal conditions as closely as possible in order to allow comparisons to be made

112 regarding the interaction process. Exact values of the injury indicators were not analyzed, but the trends produced by varying the lasing parameters were com pared for consistency with experimental results. Therefore, the pulse length, and the total beam power were varied independently, but the parameters listed in Ta ble 25 were constant for all simulation results that will be presented, except when specifically noted.

Table 25: Simulation Parameters

Parameter Simulation Value

Thermal Properties variable, according to Figure 40

Absorption Coefficient* 27cm-1 (fatty), 18cm-1 (normal)

Scattering Coefficient* 18cm-1 (fatty), 12cm-1 (normal)

Wavelength 514.5nm

Temporal Power Profile uniform

Spot Size 0.6mm

Spatial Irradiance gaussian

Beam Broadening yes

To 25°C

Tv 100°C

*: Adapted from spectral data reported by Prince, et al. [75]

Lasing Medium for the Simulation

It was assumed in the model development that the tissue was in air, as was the case for the experimental work. Under these conditions, it was also assumed that no heat transfer occured between the tissue and air medium. In other words, all heat generated in the tissue remained in the tissue. This assumption is supported

113 by the greater than 15:1 ratio between the thermal conductivity used for tissue

and the thermal conductivity of air. However, if any other medium were used,

such as saline, the program would have to be altered since the assumptions would

no longer be valid.

Temperature-Dependent Thermal Parameters

The thermal properties chosen were the temperature-dependent thermal dif-

fusivity and thermal conductivity described by Welch [103!. The parameters were

measured in ranges from 20 - 100od7 for several types of arterial tissue. Welch's

data are given in Figure 39, and the adaptations used in the model under study are

given in Figure 40. The thermal parameters were assumed to be linear functions

of temperature. Therefore, for tissue types which Welch did not measure over the

full range, the given data were extended linearly to cover that range. Distinct

thermal conductivities were calculated for each interface in the tissue volume based

on the average temperature of the two nodes on either side of the interface.

Ablation

The ablation of tissue was modeled as a process similar to the phase transition of water from the liquid to the vapor state. The temperature of each node was allowed to rise until the vaporization temperature, T„, was reached. The tempera ture was then held constant at Tv, and absorbed energy was allowed to accumulate in the nodal environment. When enough energy had accumulated to equal the la tent heat of vaporization, L, for the amount of tissue present, the node and its surrounding environment were removed from the tissue volume and the surface was moved one distance increment into the tissue.

The value chosen for Tv was lOO0^, the vaporization temperature of water.

The value chosen for L was 80% of the latent heat of vaporizaton of water, on

114 Water o: 6 Calcified

...Fibrous

7 t o Normal a 4 o% Fall y

•

t 2 • 20 30 40 50 60 70 0Q 90 1000

TEMPERATURE (°C )

\ >- H ^

_ V)

t o cc2 _o u * X * h- f 20 30 40 50 60 70 80 90 100

Figure 39: Experimentally Measured Thermal Conductivity (top) and Thermal DifFusivity (bottom), from Welch, et al. [103].

115 0 . s 0 . s o e o t o e o. s 0 6 0 6 ,.»♦** Normal 0 S 0 . 5 0.5 0 . 5 o 5 0 - 5 0 . 5 0 . 5 .* 0 . 5 -0.5 ; o. 5 x** -0.4 X* “ 0.4 >0.4 ;:*** Z 0.4 Fibrous •0.4 ° 0.4 - 0 4 e 0.4 ;*•0 o.4 4 - 0.1 0.1 0 .1 0 .1 0 1 0 . 1 xxXxXK Fatty 0.1 0.1 0 . 1 0.2 0.2 0.2 0.2 0 . 2 - 0.2 n’" 10 40 50 10 7 0 10 00 100

Ttftptrtlwft in 0ifr««t Cmli«r«4«

1 ?0C-0 7

I 6 0 E - 0 7

1 5 0 E - 0 7 .t* Normal i.++

1 4 0E- 0 7

e 1 10E-07 ****** ...... **•«

Fibrout

I . 20E-07

XXWOOOOOOOOOOOOOOOOC <000O00O00oo(>o<»oooo< Fatty

1 OOE * 0 7 " I'' rTT-n T 20 5 0 10 70 10 • 0 100

Figure 40: Calculated Values of Thermal Conductivity in Wrn 1K° (top) and Thermal DifFusivity in m 2s -1 (bottom), Adapted for Simulation from [103].

116 the assumption that arterial tissue is nominally ~80% water. The premise of the model is that when the tissue water is vaporized, it carries the solid phase away in the form of debris, through explosive thermal expansion. This is consistent with observations reported in the literature, as illustrated in Figure 5.

5.3 Validation of the Model

Number of Iterations for Accuracy

One source of error present in this model is quantization error due to the technique of allowing discrete tissue volumes to accumulate energy over discrete time intervals until ablation of the entire volume occurs. Variations in both the time increment over which energy is deposited, and the distance increment over which energy is absorbed and diffused, will affect the final result. Since both dx and dt are a function of the number of simulation iterations, the iterations determine the quantization error, if all other input parameters are held constant.

The number of iterations required to produce consistent results was evaluated by varying simulation iterations from 100 to 4000 for two distinct sets of input parameters. The results for 3W, 200ms and 3 W, 100ms, are listed in Table 30, and illustrated graphically in Figures 54-59, all in Appendix A.

The minimum error of the resultant ablated depth is limited by the distance increment, dx, which varied from 0.0369233mm to 0.0041282mm for the iteration ranges chosen. In terms of ablated width, the minimum error is 2 dx, since the width is calculated by multiplying the ablated radius by two. Using a similar analysis, the minimum error of ablated area is 2 dx^. Additional error introduced by the time increment, dt, is in the form of excess energy, beyond that needed for ablation, being deposited during one time interval. The excess energy is lost when

117 the accumulator exceeds its limit. For the given input parameters and range of

iterations chosen, dt varied from 3ms to 0.0375ms.

It should be noted that the final result for all injury values after the maximum

number of iterations is within 0.4% - 6.4% of the largest deviations present. At

1000 iterations, the error is reduced to less than 1% for all values except the width

at 3W, 100ms, which has 2.3% error. The crater width has inherently greater

error than the other resultant injury values for two reasons. The intensity fall-off

in the radial direction is greater than that in the axial direction, by more than

double. Therefore, each incremental distance in the radial direction represents

twice the intensity differential as the same increment in the axial direction. Also,

the direct result of the simulation produces only the crater radius. This value must

be doubled for the crater width, which doubles the limit of accuracy.

5.4 Model Predictions and Comparison to Experimental Results

Before examining the results from the simulation, the hypothesis proposed in

the discussion of the experimental data, that the apparent nonlinear response in

tissue injury over specific ranges of power, pulse duration and energy is a result of the thermal,conductivity, will be addressed in more theoretical detail. The simulation data will then be presented and compared to both experimental results and theoretical explanations.

In terms of the vaporization of metals, Ready [80] observed and mathmatically described an absorbed flux density, Fc, above which vaporization is dominated by the latent heat of vaporization of the material, and below which vaporization is dominated by the thermal conductivity of the material. At relatively low flux densities, heat is efficiently conducted into the material and little is vaporized.

The rate of material removal is relatively low. At higher flux densities, above Fc,

118 the energy is being supplied too fast to allow heat to be conducted into the tissue interior. The rate of material removal is relatively high, and the effect of thermal conductivity is negligible. The absorbed flux density differentiating the two regions \ may be approximated by the the following equation:

1 - i Fc = 2LpOtp 5 (5.24) with all variables as previously defined.

This concept may also be applied to arterial tissue to explain the apparent nonlinearity of tissue response. Equation (5.24) is illustrated graphically by Fig ure 41 for the simulation parameters used in the model under study. Power is plotted, instead of flux density, referenced to a 0.6mm spot size. If a horizontal line is drawn at Power = 11V, it is noted that both 100ms and 200ms fall in the low rate of vaporization region, dominated by thermal conductivity. However, both

500ms and 1000ms are in the high rate of vaporization region, dominated by latent heat. The crossover occurs between 200ms and 500ms, where the nonlinearity in experimental injury parameters also occured, as discussed in the previous chapter.

The only inconsistency with the experimental data is in the power level. This inconsistency may be explained by several factors. Small errors in experimentally measuring the spot size cause larger errors in the calculated flux density. Also, the equation of Ready assumes surface absorption of energy, and does not account for a finite depth of penetration, as is true for arterial tissue. The equation as sumes known thermal properties of the material, which is not the case for arterial tissue. In addition, a significant difference exists between absorbed flux density and incident flux density. The absorbed powers in Figure 41 may be significantly lower than the associated incident powers. The fraction of incident power which is actually transmitted into arterial tissue and absorbed is not well documented

119 . 5 -

. 4 -

. 3 -

. 2 ■

. I •

.0 - Latent Heat Dominent Region k 0 . 9 -

_ 0 .6 »ft o 0 . 7 -

!.,o m JCk "*0.5

0 . 4

0 . 3

0.2- Thermal Conductivity Dominent Region

0.1-

0.0 —i-----1----- 1-----1----->-----1-----1-----1---- '-----1-----1-----1----- 1-----1-----'-----1-----1-----1-----'-----r 0.0 0.2 0.4 0.6 0.6 1.0 1.2 1.4 1.6 1.6 2.0

T i m in Stcondi

Figure 41: Thermal Conductivity-Dominent Region of Vaporization (below curve), and Latent Heat-Dominent Region of Vaporization (above curve), predicted by Ready equation (5.24) [80] for simulation parameters.

120 in the literature. It is dependent on reflection/transmission properties, as well as

scattering and absorption properties. Therefore, as stated in the introduction of

this chapter, the trends will be analyzed and compared, rather than exact values.

This is the only prudent approach due to the dearth of precise experimental data

for many of the requisite parameters. The concept of a region of high rate of va

porization and a region of low rate of vaporization, based on absorbed flux density,

does support the experimental data for constant power.

This concept also offers a possible explanation for the nonlinearity in the

constant energy experimental data. By locating the points for total energy = 0.24 J

on Figure 41, (100ms, 2AW\ 200ms, 1.2W\ 500ms, 0.48IF; 1000ms, 0.24IF), it

can be noted that both 100ms and 200ms are located in the region corresponding

to high rate of vaporization and both 500ms and 1000ms are located in the region

corresponding to low rate of vaporization. This is consistent with the experimental

data, which showed a marked increase in ablated area in moving from 500ms to

200ms, with a corresponding increase in the incident power level.

The discontinuity in the constant pulse experimental data may be explained

by drawing a vertical line at pulse = 1.0 seconds. The crossover into the region of high vaporization occurs at approximately 0.451^. Therefore, powers less than

this value would produce lower ablation rates, and powers above this value would produce higher vaporization rates.

5.4.1 Onset of Ablation

The results of the simulation demonstrate that the onset of ablation is purely a function of power. If dx and dt are independently matched, then all simulations having the same incident power have the same onset of ablation. The data is presented in Figure 42 for dx = 0.0261mm and dt = 1.5ms.

121 1 3 0 0 -

110 0 -

1 000 -

900 -

e C 800 -

e o 700 - o

< 500 - o

Z 500 - !• e o

4 00 -

500 •

700

100 ■

74 5 5

Po*« r in No t1 1

Figure 42: Onset of Ablation in ms vs Incident Power for Simulation Data

1 2 2 The pattern in Figure 42 is consistent with the equation for the time to va

porization temperature that was described by Ready[80], for the case of surface

absorption. This equation defining the onset of vaporization is given below:

= 3 ~ T°>2 (3-25>

where F is the flux density in W/cm?, and all other variables are as previously

defined. The graphical representation of equation (5.25) is illustrated in Figure 43

for the case of arterial tissue. Once again, the actual values do not exactly match

those of Figure 42, even though the trend is the same. This is due to the assump

tions made by Ready of thermal properties that are independent of temperature,

as well as surface absorption. The model under study assumed thermal properties

which vary as a function of temperature, as well as a finite depth of light penetra

tion with significant scattering properties. In addition, the onset of ablation in the

model is defined as the time when node (1,1) ablates. This occurs after the node

reaches vaporization temperature and accumulates energy equivalent to the latent

heat. The onset of vaporization defined by Ready is the time when the surface just

reaches vaporization temperature. This will be shorter than the model prediction.

5.4.2 Constant Energy

It has been hypothesized in the literature that total energy is the most reli able way to predict extent of injury [31]. However, the results of this simulation demonstrate that the energy delivery profile has a significant impact on the resul tant injury, independent of the total energy. All values of constant energy that were evaluated showed the same pattern in the extent of injury as a function of power or pulse. The data produced by three energy values will be reported, 1.5J,

123 3 0 0

200

S K = 0 .5 6 ^ 100

K = 0 .2 8 ^ o 0 i 4 5

Abiorbid P o»« r in Wstti

Figure 43: Onset of Ablation in ms vs Absorbed Power for Two Values of Thermal Conductivity, K, a 0.6mm spot size and simulation parameters, predicted by Ready equation [80].

124 0.6,7, and 0.25 J. Pulse was varied from lOOms - 1000m.s, in 100m.s intervals, with the appropriate power to produce the desired total energy. The results of the sim ulation in terms of the injury indicators is given for 1.5,7 in Figure 60 - Figure 63, for 0.6J in Figure 64 - Figure 67, and for 0.25,7 in Figure 68 - Figure 71.

The data for constant energy clearly show that extent of injury is not consis tent with constant energy. Higher power and lower pulse length result in greater ablated area. This trend matches that observed in the experimental data, as well as the predictions of the latent heat-dominent vs conductivity-dominent equation of Ready. A 75% difference exists between the ablated area at lOOOms and that at 100ms, with total energy of 0.25J. For the 0.6J data, there is a 30% difference between ablated area at 1000ms and ablated area at 100ms. This effect continues to decrease with increasing energy levels. For the 1.5,7 data, the difference is 20% between ablated area at 1000ms and that at 100ms.

Extent of injury increases as the pulse duration decreases. Therefore, the phe nomenon must be an effect of power, since the power increases at the same rate that pulse decreases, in order to maintain constant energy. This may be partially explained by considering several factors. With the lower power levels of the longer pulses, the onset of ablation increases and the rate of ablation decreases. The effect of onset is only slight, however, when the lengthened onset is compared with the lengthened pulse duration. This effect is quantified in Table 26, which provides the percentage of each pulse occupied by the onset of ablation for several values of constant energy. This demonstrates that differences in onset of ablation are not enough to account for the differences in ablated area. The definitive explanation for the differences lies in the transition from the thermal conductivity-dominated re gion to the latent heat-dominated region as power, and thus flux density, increases with shorter pulses. The reason for the decrease in the effect with increasing levels

125 Table 26: Percent of Pulse Duration Before Onset of Ablation for Constant Energy

Energy 100ms 200ms 500ms 1000ms Difference

0.25J 61.5% 63.0% 65.5% 70.5% 9.0%

0.4.7 37.5% 39.0% 40.0% 41.5% 4.0%

0.6J 24.0% 25.5% 26.5% 27.5% 3.5%

1.5J 9.00% 9.75% 10.0% 10.5% 1.5% of constant energy is twofold. Higher energies mean higher overall powers, which means the points are further into the latent heat-dominent region with higher rates of ablation. The differences between powers*become less significant. Also, as noted in Table 26, the differences in onset of ablation become smaller with increasing energy.

5.4.3 Constant Power

Three power levels were evaluated, 3 IT, 1IT, and 0.75PT, in terms of the indicators of injury. Results are given in Figures 72-75, in Appendix C. Ablated depth is shown to be a relatively linear function of pulse or energy. Ablated width, however, levels off to an apparent maximum value at the longer pulse durations, while depth continues to increase. This is probably a function of the gaussian nature of the radial intensity distribution, where there is not enough power in the tails of gaussian to reach threshold. The shape function is defined as crater depth/width. It demonstrates an increasing trend with increasing pulse length, starting with a value less than one. In explanation, the width apparently increases more rapidly than the depth, initially. As the shape factor crosses one, the depth continues to increase, as the width slows its growth. The pulse duration at which

126 this transition occurs shortens considerably with increasing power, as indicated in

Table 27.

Table 27: Transition Pulse Duration at which Injury becomes Deeper than is is Wide for Constant Power

Power: 0.75VF 1.0 W 3IV

Pulse: 600ms 450ms 150ms

One would expect ablated area to show a slow rate of initial growth followed by rapid growth when considering the thermal conductivity-dominent vs latent heat- dominent regions of Ready. However, the data demonstrate a relatively linear function of pulse duration. A possibile explanation for the lack of the effect is that the determining factor for the slow ablation vs rapid ablation regions is the flux density or power. The effect would therefore be more pronounced in comparing data where power is varied, as in the constant energy or constant pulse data.

5.4.4 Constant Pulse Duration

The simulation data for constant pulse will be examined for four different pulse durations, in terms of the injury indicators. All others showed the same trends as those that will be presented. The injury indicators as a function of power and energy for 100ms are given in Figure 76 - Figure 79, for 200ms in

Figure 80 - Figure 83, for 500ms in Figure 84 - Figure 87, and for 1000ms in

Figure 88 - Figure 91, all in Appendix D. These figures demonstrate that depth is a linear function of power, once threshold has been reached. Ablation width, on the other hand, is a saturation-type function of power, once beyond threshold.

Most simulations show saturation levels near 0.6mm, the 1/e2 gaussian radius of the incident beam. At the saturation width, an equilibrium is reached between

127 energy deposition and heat conduction into the interior, and depth will increase

as width remains constant.

The shape factor, which illustrates the relationship between depth and width

of the injury, shows a linearly increasing trend with increasing power for constant

pulse duration. This pattern corroborates the conclusion in the constant power

section that the extent of injury increases faster in the direction of width initially,

and then continues to increase faster in the direction of depth. Table 28 shows the

power levels at which the injury changes from wider to deeper for four values of

constant pulse.

Table 28: Transition Power for Constant Pulse where Injury becomes Deeper than it is Wide.

Pulse: 100ms 200ms 500ms 1000ms

Power: 4.75IT 2.3 W 0.85W 0.45IT

Ablated area demonstrates a nonlinear function of power for constant pulse.

However, close examination of the data reveals two linear portions, one corre

sponding to lower powers, and one to higher powers. The linear function in the

low power region has a shallower slope, and the function in the high power region

has a steeper slope. The regions are identified on the graphs, and are consistent

with the thermal conductivity-dominent with low rate of ablation region, and la

tent heat-dominent with high rate of ablation region described by Ready. The transition between regions in the simulation data occurs at lower power levels with increasing pulse duration. This is also consistent with Ready’s predictions.

128 5.4.5 Time Evolution of Injury

Data in both the sections on constant power and constant pulse, lead to the hypothesis that the time evolution of laser-induced injuries involved an initially more rapid increase in ablation width, followed by a saturation in width and contin ued ablation in terms of depth. This may be dramatically illustrated by examining ablation over time for a specific set of input parameters. Figure 44 demonstrates depth, width, and area ablation over time for 7.5VF and 200m.s. Figure 45 demon strates depth, width, and area ablation over time for 1.5IF and 1000ms. For both sets of input parameters, the onset of ablation results in a linear increase in depth, and an initial rapid increase in width, followed by a leveling-off, as hypothesized.

The ablation rate, in terms of area, begins as a slow linear rate, and increases to a more rapid linear rate for the majority of the pulse.

In order to look at the time evolution of the injuries in space, the time of ablation of each node in the crater was plotted as a function of depth and width.

For the same two sets of input parameters, 7.5W, 200ms and 1.5IT, 1000ms, the ablation time contours are illustrated in Figure 46 and Figure 47, respectively. The temporal contour above which depth excceeds width is given by 0.055s in Figure 46 and 0.275s in Figure 47.

5.4.6 Constant vs. Variable Thermal Properties

In all of the data presented thus far, the thermal properties of the arterial tissue were assumed to be linear functions of temperature. In order to examine the effect of the thermal parameters, the thermal conductivity was held constant at two values for the same set of input parameters and then compared for the changes in the injury indicators. The values of conductivity and diffusivity chosen were those used by Welch [103]. Thermal diffusivity was constant for both runs at

129 60

Depth

Width

0 0 too 200 J00 Tint in n i 1 I i

1000

900

BOO

Area

too

e e

400

J00

100

0 100 200 1 I n « in ft i II j

Figure 44: Time Evolution of Injury for l.bW and a 200ms Pulse

130 to

* Depth

c ♦

e u c

Width

x-a

0 m 400 600600 1000 1700 1400 1600 Tint in mMi tt c o n Ji

1000

900

600

700

600

Area * too c e

400

700

100

0 700 400 600 1000 1100 1400 1600 1 ini in nillittconjt Figure 45: Time Evolution of Injury for \.bW and a 1000ms Pulse

131 IncidentBeam Incremental Units Depth o E p 37 55 73 r I 9 H 00 t 1 ft --- iue4: bain ie otus o 7.5 for Contours Time Ablation 46: Figure ONSE f 0.137 0.029 3.75 Incremental Units ——W idth Units Incremental 160 4 0 . 056 132 0.191 0.083 W n a 0m Pulse 200ms a and

0.110 12.00 ^Surface Incremental Units Depth IncidentBeam 6.00 EPtH 00 50 75 1

ft 00 iue4: bain i Cnor o 1.5 for Contours e Tim Ablation 47: Figure ONSCI 0.665 0.150 .5 .0 9.25 6.50 5.75 nrmna is idth W nits U Incremental 0.619 0 . 265 133 0.955 ------0.417 W n a lOOOms Pulse a and 0.551 1} oo <=Surface 0.128(10_6)m2/s. Thermal conductivity was 0.26W/m°K for the first simulation

and 0.52lV/m°K for the second. The results are given in Table 29 for 3IF and

100ms.

Table 29: Extent of Injury for High and Low Thermal Conductivity, k, for 3Hr and 100ms

k depth width area onset

W /m °K m m m m m m2 ms

.28 1.5244 0.5949 0.5465 24.9

.56 0.2366 0.3505 0.0542 49.95

Thermal Diffusivity = 0.128(10 6)m2/s

The data clearly show that effect of thermal conductivity is significant in the

injury outcome. Reducing the conductivity by half resulted in 10 times greater

ablated area, 6.4 times greater depth, and 1.7 times greater width. The conclusion

to be drawn is that small errors in knowledge of thermal parameters may result in

much larger errors in estimating extent of injury.

5.5 Discussion and Conclusions

The simulation data presented thus far have been separated into distinct groups of energy, power and pulse for analysis purposes. The data may be re combined and the injury indicators plotted against energy for the complete data set, to examine overall trends. The results are given in Figure 48. It can be noted that extent of injury, as a function of energy does lend itself to a linear fit, as has been reported in the literature. This was also seen in the experimental data of the current study, as demonstrated in Figure 49. However, variability in the data for any particular energy level is a function of the energy delivery profile. Therefore,

134 at least part of the variability in experimental data that has been reported may

be explained simply as a result of the lasing parameters.

The results of the current study have important implications in several areas:

influencing the course of future experimental work, guiding future attempts to

model ablation theorectically, as well as influencing the use of laser angioplasty

clinically. The patterns in the experimental injury parameters, as a function of the

individual lasing parameters, were reproduced theoretically, and an explanation

offered in terms of the thermal properties in the tissue. These results should be

verified experimentally over a broader range of lasing parameters to determine

if the relationships still hold. Also, additional trends, which were brought out

in the simulation, should be closely examined experimentally, including the time

evolution of injury data.

Most assessments of injury reported in the literature are confined to measures

of depth or width, since these two parameters are relatively simple to obtain.

However, the results of this study indicate that this is not enough to accurately

evaluate extent of injury. Width tends to reach a maximum value, and depth gives

no indication of radial extension into the interior. Also, the changes in rate of

ablation are not contained in the depth data, since these changes are a result of

differences in heat transfer to the interior. Therefore, it is critical to evaluate the

ablated area, especially in basic studies of laser-tissue interactions.

Another aspect brought out by the simulation is the importance of knowing

the complete energy delivery profile, not just total energy, or just power, or just

pulse. These parameters are all closely tied together in determining the extent of injury. Some of the variability in experimental data may be reduced by more carefully controlling the laser parameters.

Spot size was held constant in this study, and therefore its effects on the out-

135 AREA 0 . B

0 . 7

0.6

0.4

0.3

0.2

0 . 1

0.0

0.0 0.2 0.4 0 . 6 0.6 I .0 1.2 I . 4 1 .6 1 . 6 ENERCr

Figure 48: Ablated Area vs Total Energy for Entire Simulation Data Set

136 . 36 • . 35 . 34 . 33 .32 .31 . 30 .29 .28 .27 .28 .25 .24 .23 .22 .21 .20 . 19 . IB . I 7 . IB . 15 . 1 4 . 13 . 12 . 1 I . 10 . 09 .06 .07 . OB .05 .04 .03 .02 .01- . 00 ■

Emrgy in Joules

Figure 49: Ablated Area vs Total Energy for Entire Experimental Data Set

137 come can not be evaluated. However, the size of the tissue volume being irradiated is significant in terms of heat transfer to the interior. Further studies are needed to document this effect, both experimentally and theorectically.

5.5.1 Implications for Laser Angioplasty

One of the most critical considerations in laser angioplasty is that of con trolling damage to the arterial wall. The results of this study indicate that for relatively low power, shorter pulses, the injury grows most rapidly in the direction of width. If this can be quantified experimentally, it may be one technique of con trolling arterial wall perforation. However, there are many factors which must be examined in some basic studies before definitive conclusions may be drawn. These include the independent effects of spot size, flux density, wavelength, and spatial irradiance distribution. The output of an optical fiber is not spatially gaussian, and would have to be considered for the case of in vivo energy delivery. Also, one consequence of using lower powers that has been reported in the literature is the increase in residual thermal damage. It has been assumed that this is an undesirable outcome in terms of tissue healing, but the healing response has not been well documented. The risk vs benefit of energy delivery profile as it relates to healing is a vital area for future research.

138 CH A PTER VI

Areas of Further Study

The results of this study have demonstrated that the effects of the major lasing

parameters on tissue injury can be isolated and quantified, despite their interde

pendence. The next step for expanded research is to repeat the same study over

several wavelengths and a wider range of energies, power levels, and pulse lengths

in order to examine the nonlinear tissue response to power and pulse duration in

more detail. The image analysis procedure, currently user time-intensive, could

be modified to automate the outlining of the boundaries between areas of tissue

injury, allowing a greater number of injuries to be analyzed in a shorter length

of time. This would also remove the source of error and individual interpretation

introduced by manually tracing the boundaries. In addition, studies comparing

the effects of different lasing media on the resulting tissue injuries, using the tech

niques of the current study, are important in understanding the processes involved

in tissue ablation.

In examining the unstained serial sections to locate the crater center, an inter

esting incidental finding was observed in sections toward the periphery of the crater

for injuries with at least 500ms exposure duration, 1.5 W of power, and a minimum

of 1J of energy. The craters were not conical in shape, nor symmetric, as had been

assumed. In fact, ablated areas were present below the level of an intact surface, or below the intact floor of a crater. Approximately 30% of injuries produced by

139 1J or greater in both atherosclerotic and normal tissue demonstrated this effect.

Figures 50 and 51 illustrate the case of an ablated area below an intact surface.

Figure 50 represents the crater center and Figure 51 represents sections from the same injury at a distance of 70/xm. and 95/zm from crater center. Figures 52 and

53 illustrate the case of an ablated area below an intact crater floor.

A possible explanation for this phenomenon lies in potententially significant spatial differences in thermal tissue properties due to heterogeneous tissue com position. The results of the simulation demonstrate that relatively small changes in thermal conductivity produce relatively large changes in extent of injury. The areas of nonsymmetric ablation may have been areas of low thermal conductiv ity, resulting in greater tissue destruction and a non-symmetric crater of irregular shape. Therefore, tissue injury measurements at the ‘crater center’ may not ac curately reflect the true extent of tissue damage. This can only be determined through three-dimensional reconstruction of the injury to obtain volume measure ments, rather than area, as well as to obtain a true picture of the shape of the crater. For a study of this type, the analysis procedure would require automation to make 3-D reconstruction feasible for a large number of injuries. Serial sections at 5firn produce up to 100 sections or more per injury. This is an important study to be undertaken in the future.

140 Figure 50: Crater Center Produced at 3 W, 500ms

141 •V 'i ' \ a ' # ' 1 7 . w ; ,

Figure 51: Section 70/zra from Crater Center (top) Section 95 fim from Crater Center (bottom)

142 Figure 52: Crater Center Produced at 3 W, 500m.s (top) Section 100/itm from Crater Center (bottom)

143 Figure 53: Crater Center Produced at 3W, 500m.s (top) Section 70 fim from Crater Center (bottom)

144 APPENDICES A P P E N D IX A

Number of Iterations for Accuracy Data

146 Table 30: Input Parameters and Simulation Results

Set 1: 3W and 200ms E p P 0 W 0 N I u 0 E IA NE T L W P D R S R E SE T T E D D EG R E R H HA T X T Y 2 2 2 2 2 2 2 2 2 2

100 200 3 0.664620 0.516927 0.209953 0.0030000 0.0369233 51.0000 0.6 200 200 3 0.652719 0.469958 0.208590 0.0015000 0.0261087 51.0000 0.6 300 200 3 0.660849 0.511625 0.211771 0.0010000 0.0213177 51 .0000 0.6 400 200 3 0.664620 0.480004 0.211998 0.0007500 0.0184617 51.0000 0 .6 500 200 3 0.677018 0.495379 0.211589 0.0006000 0.0165126 50.4000 0.6 600 200 3 0.663251 0.482365 0.211317 0.0005000 0.0150739 50.5000 0.6 700 200 3 0.669874 0.502406 0.210732 0.0004286 0.0139557 50.5714 0.6 800 200 3 0.665773 0.496066 0.211658 0.0003750 0.0130544 50.6250 0.6 900 200 3 0.676928 0.492311 0.210862 0.0003333 0.0123078 50.3330 0 .6 1000 200 3 0.665543 0.490400 0.210771 0.0003000 0.0116762 50.4000 0 .6 1200 200 3 0.671508 0.490307 0.211544 0.0002500 0.0106589 50.2500 0.6 1400 200 3 0.671036 0.493409 0.211122 0.0002143 0.0098682 50.3571 0.6 1600 200 3 0.673851 0.498465 0.211146 0.0001875 0 .009230B 50.2500 0.6 1800 200 3 0.670125 0.487363 0.211165 0.0001667 0.0087029 50.1670 0 .6 2000 200 3 0.668761 0.495379 0.211317 0.0001500 0.0082563 50.1000 0.6 2500 200 3 0.672005 0.487388 0.211153 0.0001200 0.0073847 50.1600 0.6

Set 2: 3W and 100ms i zui P p 0 W o uj

I U 0 E I A N > a: o T L w P 0 R s E SE T T E ODE R E R H H A TXT

100 100 3 0.234979 0.365522 0.0545333 0.0015000 0.0261087 51.0000 0.3 200 100 3 0.240002 0.332310 0.0552150 0.0007500 0.0184617 51.0000 0.3 300 100 3 0.226108 0.361773 0.0540789 0.0005000 0.0150739 50.5000 0.3 400 100 3 0.234979 0.339414 0.0531700 0.0003750 0.0130544 50.6250 0.3 500 100 3 0.233524 0.350286 0.0542607 0.0003000 0.0116762 50.4000 0.3 600 100 3 0.234495 0.341083 0.0538517 0.0002500 0.0106589 50.2500 0.3 700 100 3 0.226968 0.355254 0.0537543 0.0002143 0.0098682 50.3571 0.3 800 100 3 0.230771 0.350772 0.0533404 0.0001875 0.0092308 50.2500 0.3 900 100 3 0.226276 0.3481 17 0.0534730 0.0001667 0.0087029 50.1670 0.3 1000 100 3 0.231177 0.346765 0.0534427 0.0001500 0.0082563 50.1000 0.3 1250 100 3 0.228925 0.354464 0.0534427 0.0001200 0.0073847 50.1600 0.3 1500 100 3 0.229203 0.350545 0.0532609 0.0001000 0.0067412 50.1000 0.3 2000 100 3 0.227686 0.350286 0.0533063 0.0000750 0.0058381 49.9500 0.3 2500 100 3 0.229757 0.355079 0.0532245 0.0000600 0.0052217 49.9200 0.3 3000 100 3 0.228806 0.352742 0.0533063 0.0000500 0.0047668 49.9000 0.3 4000 100 3 0.231177 0.355021 0.0534427 0.0000375 0.0041282 49.8375 0.3

147 DEP f M 0 . 72 70 6 v ■f‘>V v K f ' 2 \ ...... i 6 6 62 X-* bO 4( 4 4 4 40 4 solid line: simulation result dashed line: +dx and — dx 4

4 40 1 1 1 1 10 2 2 2 2

2 ■4 — |- 'I I 1 I* I I I I T I I I I I ' ! | I I1 I I I 1000 2 000 3000 4000 Nuntxi u I I I « f o I ions

Figure 54: Ablated Depth vs Number of Iterations for 3 ^ , 200ms (top) and 3W, 100ms (bottom).

148 WIDTH

solid line: simulation result dashed line: +2dx and —2 dx

0.40

0 1000 2000 5000 4000 Nunbir ol llirolioni

Figure 55: Ablated Width vs Number of Iterations for 3IF, 200ms (top) and 3W, 100ms (bottom).

149 Aft

—if::#..

Alt Dlt 016 Oil 01? Oil 1000 2000 3000 Oil Nwnbt i oI I I • f o I i oAl OKI Oil Oil 01) Oil 0 1 0 solid line: simulation result 010 dashed line: +2d* and —2d* 019 Oil 017 Oil Oil Oil 014 011 012 012 011 010 049 041 041 0<7 041 041 .04 4 044 043 04? 04 I 040 040 2000 4 000 oI I 1t r «I i •«»

Figure 56: Ablated Area vs Number of Iterations for 3fT, 200m.s (top) and 3IV, 100m3 (bottom).

150 ONSET 54 . 0 53.6 53.6 53.4 5 3.2 53 . 0 52.6 52 . 6 52.4 52 . 2 52 . 0 5 1.6 51.6 5 1.4 5 1.2 5 1.0 50 . 6 50 . 6 50 . 4 50.2 50.0 48.6 49.6 49.4 49.2 49.0 46.6 46.6 46.4 46.2 46.0

0 1000 2 000 3 000 4 0 0 0 Nunbtr oI I 1 •r oIi on s

Figure 57: Onset of Ablation vs Number of Iterations for 311’, 200ms (top) and 31F, 100ms (bottom).

151 0 5 7 • 036 - 035 - 0 3 4 ■ 033 032 ■ 031 ■ 030 ■ 029 020 027 026 025 024 023 022 021 020 019 010 017 010 015 0.014 • 0.013 012- 0 1 1 010 009 000 007 000 005 • 00 4 1 —I—i- 1000 2 000 3000 4 000 Nunbir si Itirotiofis

Figure 58: Distance Increment vs Number of Iterations for31V, 200ms (top) and 3VF, 100ms (bottom ).

152 .0030 - .0029 .0020

.002 7

. 002 6 . 002 5 .002 4 .0025 .0022

.002 1 .0020 .0019 .0016 .0017 .0016 0.0015 0.0014 .0015 .0012 .001 1 .0010 .0009 .0006 ■ , 0007 ■ .0006 ' .0005 .0004 ■

. 0005 ■

.0002 -

.000 1 ■ . 0000 ' ' ' I ' 1000 2000 5000 4 00 0

Nunbir o I Itirol.'ons

Figure 59: Time Increment, dt, vs Number of Iterations for W,3 200ms (top) and 3 IV, 100ms (bottom).

153 A P P E N D IX B

Simulation Data for Constant Energy

154 iue 0 Dph fCae v Icdn Pwr o Cntn Eeg = 15 in 1.5J = Energy Constant for Power Incident vs Crater of Depth 60: Figure

D< p1h in nn —« —< —< —i —i —i —i —i —i —i —i —. —. —i r i— |— .— ]— .— |— i— |— i— |— i— |— i— |— i— |— i— i— i— i— i— <— i— <— i— i— «— T— 2 4 5 4 5 2 1 4 4 4 iuain Data Simulation 6 f 9 0 1 2 5 4 IS 14 15 12 11 10 9 ft 7 Povf Veils in r 155 4 4 6 4 4 6 4 3- 6 4 2 - 6 4 1- 610 - 6 3 9 tit 6 3 7 636 - 635 6 3 4 6 3 3 632 631 630 620 626 627 626 626 624 623 622

6 2 1 - 620 6 19 i 6 16 617- 616 6 1 6 6 14 613 612 6 1 1 6 10 609 606 60 7 -1 l —I- —T~ - r- ~r~ - r 1 10 1 1 12 13 14 16 Po»t r in Wo Its

Figure 61: Width of Crater vs Incident Power for Constant Energy = 1.5J in Simulation Data

156 0.77-

0.76

0.75-

0.74-

0.75

0.72

0 . 7 1

0.70

0 . 60

0.66

0.67

0 . 66

0.66

0.64 1---1----- 1-■---1--1---1--■---1--'---1--'---T— 7 6 i 10 11 12 16 14 16

Po»« r in W« I 1

Figure 62: Ablated Area vs Incident Power for Constant Energy = 1.5J in Simulation Data

157 3 09 3 Ot 3 07 3 oe 3 05

3 04 3 03

3 02

3 01

3 00 ■■ w 2 99 c o 2 96 «• c 2 97 m e 2 96

. 2 95 • o. 94 m 2 r- M 2 93

2 92 -

2 91

2 90

2 69

2 66

2 57

2 66

2 65 ■

2 64

1 2 3 4 5 S 7 t 9 10 11 12 13 14 15

Pour in Walts

Figure 63: Crater Shape vs Incident Power for Constant Energy = 1.5J in Simulation Data

158 iue6: et fCae v Icdn Pwr o Cntn Eeg = = Energy Constant for Power Incident vs Crater of Depth 64: Figure

01 p I h in nn 0 . 59 0.60- 0.61- 0.62- 0.63- 0.64 0.65- 0.66- 0.B7- 0.88- iuain Data Simulation Pom Wo in r I 1 159 4 3 1 TT-r'Y T-f—!■ 5 0.6J in 0 0 0 0 0 0 D 0 0 0 0

r 0 e = 0 0 Z 0-4 *0.4 0 . 4 0 . 4 0 . 4 0 0 0 0 0 0 0

0 ■p T r i r t r - i - r 'i ■■> i i i i i i i i | i i i -r t i i i i | i i i i i i i i i | i i i i i i i i i | 1 3 3 4 5 6

Post r in Wo I11

Figure 65: Width of Crater vs Incident Power for Constant Energy = 0.6J in Simulation Data

160 0.2 15 4 0 . 2 H 0.213 0.212 0.211 4 0.210 0.209 0.209 4 0.207 0.209 0.205 0.204 0.203 4 0.202 0.201 0 .200 0. 199 4 e 0. 199 , 0.197 - 0. 199 c 0.195 4 0.194 ; 0.193 - 0.192 ■* 0.191 4 0.190 0. 199 0.199 0.197 0. 199 0. 195 4 0.194 0. 193 0.192 0.191 4 0. 190 0.179 0.179 0.177 0.179 4 0. 175 I » I I I » » I I | I \ I I » I I I I I > I■}■ I I I I ...... I 1 t | 1 I T I I I I I I | 0 1 2 5 4 5 6

Po«« r in Vo t11

Figure 66: Ablated Area vs Incident Power for Constant Energy = 0.6J in Simulation Data

161 iue 7 Cae Sae s niet oe fr osat nry .J in 0.6J = Energy Constant for Power Incident vs Shape Crater 67: Figure

Shflpt, 4 in«n«ion I • t * 1.27- 1.26 1.29 1.31- 1.30- 1.32 1.33- 1.34 1.35 1.35- I . 57 H I i i ? i i i i i ■? i t » i » r | r » » i i i '» r t [ i ■ i - ^ ?■i i i i i i i i i i | i - n ? > i i i » I » iuain Data Simulation P o n tinNo r I 1 > 162 0 . 157 0 . 156 0 . 155 0 .154 0 .155 0 . 152 0 . 1 5 1 0 . 150 0 .149 0 .146 0 . 147 0 . 146 0 .145 0 . 144 0 .145 0 . 142 0 .14 1 0 . 140 0 .159 0 .1 56 0 .157 0 . 1 56 0 .155 0 .154 0 . 155 0 .152 0 . 151 0 .150 0 . 129 0 .126 0 .127 0 . 126 0 . 125 0 . 124 0 . 125 0 . 122 0 . 121 0 . 120 0 . 1 19 0 . 1 1 6 0 . 1 1 7 0 . 1 16

0 1 2 3 Pox r in Notts

Figure 68: Depth of Crater vs Incident Power for Constant Energy = 0.25J in Simulation Data

163 0

(

0 1 2 1

Figure 69: Width of Crater vs Incident Power for Constant Energy = 0.25J in Simulation Data

164 0.0)1

0 . 0)1

0.050 H

0.029

0.026

0.02 7 -

0.026 - e Z 0.0 2 5 - c m 0.024 - m * 0.023-

0.022

0.021 0.020 -

0.019 ■

0.016

0.017

Pour in Nolti

Figure 70: Ablated Area vs Incident Power for Constant Energy = 0.25J in Simulation Data

165 iue 1 Cae Sae s niet oe fr osat nry .5 in 0.25J = Energy Constant for Power Incident vs Shape Crater 71: Figure

Sh « p « , lintniinnltd 0.5 0.5 500 501 5 400 50 50 50 50 50 50 50 50 5 +++4 + iuain Data Simulation o i Walt* in Pon r 166 i r -i— 1 A P P E N D IX C

Simulation Data for Constant Power

167 4

* Power = 3Hf

3 *

x Power = UP

Power = 0.751P

0 ‘X —,— i — I— “T“ “1” — i------' r 100 2 DO 500 400 5 0 0 600 700 600 900 1000

Pulst 0 u f a t i o n in is

Figure 72: Crater Depth vs Pulse Duration for Three Values of Constant Power in Simulation Data

168 0.7- * Power = 31F

0 . 6

x Power = IIP 0 . 5

+ Power = 0.751P

.= 0.4

0. 3

0 . 2

0 . 1 -

0 . 0 -x ~T~ t ~T~ T — I------1------1— 100 200 300 400 $00 600 700 600 * 900 1000

Pulse Duration in rss

Figure 73: Crater Width vs Pulse Duration for Three Values of Constant Power in Simulation Data

169 Power = 311'

. 3

. 2 ■

. 1 -

. 0 - e e „ 0.9 •

• - 0 . 8 - < O?

“ 0.6 u 0.5-

0.4- x Power = nr

0 3-

0 . 2 - Power = 0.75H"

0 . 1 -

0.0 1— ~r ~r 1 00 200 300 400 500 600 700 600 900 1000

P u l s e O u r o l i o n in nt

Figure 74: Ablated Area vs Pulse Duration for Three Values of Constant Power in Simulation Data >

* Power = 3\V 5 ■

2 x Power = IIP

+ Power = 0.75H'

o ■ I ' I 1 1 ' I '----1----1----1----1----1----1----1---- '----1----' I 1 00 2 00 300 4 00 500 600 200 6 00 900 1 000

Pulit Duration in (is

Figure 75: Crater Shape vs Pulse Duration for Three Values of Constant Power in Simulation Data

171 A P P E N D IX D

Simulation Data for Constant Pulse Duration

172 Dt p t h in nn iue 6 Dph fCae v Icdn Pwr o Smlto Data Simulation for Power Incident vs Crater of Depth 76: Figure 0 0 0 0 0.4' 0.5 0 0.7 o. e ■ 0.9 j . . . . . J . 6 0 2 0 1-1 i + ' ' ------+ 2 4 5 4 J 2 1 i—■—i— ih osat us Drto = 1007ns = Duration Pulse Constant with + ' —i —1 — i —' — i — + ' —i—i—i—'—i—■—i—■—i—i—i—■—r i ■ i ■ i • 6 t 9 t 7 P dii 173 i W«1 inr I * 10

12 34 15 1314 1112 + 7

0 0 2 4 5 I 7 8 9 10 1 1 12 1J 1 4 t 5 Post r in Hoi It

Figure 77: Width of Crater vs Incident Power for Simulation Data with Constant Pulse Duration = 100ms

174 0 . 8

0 . 7

0 . 6

0 . 5

0 . 4

0 . 2

0 . 1

0 0 0 2 } 4 5 6 7 8 9 10 1 I 12 1 J 1 4 t 5

Po»«r in Wo I 11

Figure 78: Ablated Area vs Incident Power for Simulation Data with Constant Pulse Duration = 100ms

175 + +

•f +

-j— i— |— i— i— i— i— >—j— i— i— »— i— '— i i i' i i— i— i— i— i— i— j— ' i ' r 1 2 3 4 5 ft 7 6 9 10 1 1 1 2 13 14 15

Po*« r in W«I 11

Figure 79: Crater Shape vs Incident Power for Simulation Data with Data Constant Pulse Duration = 100ms

176 4 4

0 * 1 ------1------1------1----- 1------1------1---- 1------1----- 1------j------1------1-----1 r 1 2 i * 5 6 7 6 9 10

Po»«r in Its

Figure 80: Depth of Crater vs Incident Power for Simulation Data with Constant Pulse Duration = 200ms

177 0.7-

0 . 6

0.5

e 0 . 4 e

0.5

0.2

0 . I

0.0 i -----'------1----■------1----■ r ~r 5 4 5 t 10

Pour in Wo I I •

Figure 81: Width of Crater vs Incident Power for Simulation Data with Constant Pulse Duration = 200ms

178 I . 1

I . 0

0.9-

0 . 6 -

0.7-

0 . 6 -

0.5-

0.4-

0 . 5

0 . 2

0 . I

0 . 0 - l r' r 0 10

Po»•I in Wo I 11

Figure 82: Ablated Area vs Incident Power for Simulation Data with Constant Pulse Duration = 200ms

179 +

+ + +

o ■ “ 1------*------r 4 5 6 10

Povtr in Mfolts

Figure 83: Crater Shape vs Incident Power for Simulation Data with Constant Pulse Duration = 200ms

180 ]—I—I—r—I—I—I—I—i—i—|—i—i i i—i—r —1—<—I—|—i—i i i i i ' ' I i i i l i i i | 2 5 ♦ 5

Pont in No I 1 1

Figure 84: Depth of Crater vs Incident Power for Simulation Data with Constant Pulse Duration = 500m$

181 0.7-

0 . 6

0 . S

0.4-

0. J ■

0 . 1

0 . 1 -

0.0- ■ I ...... I ...... 'I i i i i i—|—i i i i i i i—i 1’ |' 1 2 S 4 S

Poair in Wa t 1 1

Figure 85: W idth of Crater vs Incident Power for Simulation D ata with Constant Pulse Duration = 500ms

182 2 J

Pov« r in Wo I1 1

Figure 86: Ablated Area vs Incident Power for Simulation Data with Constant Pulse Duration = 500ms

183 5

0 0 2 i 4 5

Figure 87: Crater Shape vs Incident Power for Simulation Data with Constant Pulse Duration = 100ms

184 +

■ i i i"

P o v i r in Wo I t s

Figure 88: Depth of Crater vs Incident Power for Simulation Data with Constant Pulse Duration = 1000ms

185 0.7-

0 . 6

0 . 5

0 . 4

0 . 3

0.2

0 1 2 3 Po»or in Walls

Figure 89: Width of Crater vs Incident Power for Simulation Data with Constant Pulse Duration = IOOOttos

186 0 0 . 9

0 . 9

0.7

0 . 6

0.5

0 . 4

0 . 3

0 . 2

0 . I

0.0 0 2 3 Po»« r in No II i

Figure 90: Ablated Area vs Incident Power for Simulation Data with Constant Pulse Duration = 1000ms

187 6 *

Wn -l*J* I I1 I » I 1 I » > I | | | | t | | | | | | i | ■ | I | I I " |

0 1 2 3

Po»o r in Wo I I s

Figure 91: Crater Shape vs Incident Power for Simulation Data with Constant Pulse Duration = lOOOms

188 CONSTANTPARAMETERS: ********************************************************* C C c c o o n o o o AAEE (nWID=400)PARAMETER AAEE (nDEP=1500)PARAMETER ota Prga o te i ain ih Absorption b A Light f o lation u Sim the for rogram P Fortran C0MM0N/BLK3/en(nDEP,nWID),min C0MM0N/BLK2/Fo,Dvert(nDEP,nWID),Dhorz(nDEP,nWID) real*4water COMMON/BLKl/eo(nDEP,nWID),ei(nDEP,nWID) real*4DTo,KTo,SK,SD,Ko,Do,K100,D100,Dhorz,Dvert,source alpha,beta,gamma,To.corr,power,z,cond,diff real*4 th,error,heat,spot,con,max,min,Fo,ur,Tavg real*4 charact ,parameters,twodim,type,damage,onset ,m er*14n d urf,lrf,acc,density,Cp,pi,emiss,onset,thresh real*4 udt,udx,in,la,d,dm,thalf,factor,ute,tp,lambda real*4 integer*4bbroad,thermal,count integer*4depth,finish.T,tissue,y,a,wmax,spatial,ZP,ZM int eger*4dmaxt emp,wmaxt emp,check,area,t dimensiononset(nDEP,nWID),thresh(nDEP,nWID)emporal dimensionKvert(nDEP.nWID),Khorz(nDEP,nWID) dimensionwmaxtemp(nDEP),depth(nWID),a(nDEP) integer*4 1,jm,jj,i,k,v,x,p,b,bb,jl,ss,w,q,r,RP,RM integer*41,jm,jj,i,k,v,x,p,b,bb,jl,ss,w,q,r,RP,RM dimensionacc(nDEP,nWID),max(nDEP,nWID) s(nDEP/2,nWID)dimension Method Difference Finite for a laser pulse of duration tp.durationof laser forpulse a BOPINAD SCATTERINGANDABSORPTION 3OFFOR TYPESTISSUE CONDUCTIVITY VARIABLETHERMAL SIMULTANEOUS ABSORPTION AND DIFFUSIONANDSIMULTANEOUS ABSORPTION drBYDIVIDED RADIUSBEAM dr=dz=dx, WITH W-IESOA, YIDIA COORDINATES, CYLINDRICAL TWO-DIMENSIONAL, n Het nd to i Areil su using issue T rterial A in ction du on C eat H and MULTIPLE ACCUMULATORS MULTIPLE nieDifrnc Methods M ce ifferen ite-D in F X E IX D N E P P A 189

dm=.25 Fo=dm Cp=4211.0

writeC’f.’C*’ multiply heat times: ’’/)’) read(*, *) water

heat=2257000.0*water

write(*,,(,> enter emissivity: ’’/)’) read(*,*)emiss

spot=0.000600

min=0.1 pi=3.14159265

To=25 th=100-To

C ********************************************************

C SIMULATION PARAMETERS:

writeC + .’C*’ no. iterations: ’’/)’) read(*,*)1 writeC*,^’’ print every pth point where p= ’ */)’) read(*,*)p write(*,*(’’.depth profile every bth point where b= ’* * /)») read(*,*)b

write(*,,(,> maximum temp, every yth point where y= ’’ * /)’) read(*,*)y C ********************************************************

C THERMAL PARAMETERS:

5 write(*,’ ’ 0=const ant thermal properties: ’V)’) writeC+.’C*’ l=variable thermal properties: *’/)’) writeC+.’C’’ Enter profile of thermal properties : ’ */)’) read(*,*)thermal IF (therm al.NE.l) THEN IF (thermal.NE.0) THEN GOTO 5 ENDIF ENDIF

190 10 write(*,’(//’ ’ l=normal, 2=fatty, 3=fibrous ’O ’) writeC+.’C’’ Enter type of tissue: ’’/)*) read(*,*)tissue IF (tissue.NE.l) THEN IF (tissue.NE.2) THEN IF (tissue.NE.3) THEN GOTO 10 ENDIF ENDIF ENDIF

IF (thermal.EQ.1) THEN

C THERMAL PROPERTIES OF Normal:

IF (tissue.eq.1) THEN SK=.00285714 Ko=.39285714 SD=0.0000000005277778 Do=.0000001080556 Fo=0.25 type=*NORMAL*

C THERMAL PROPERTIES OF Fatty:

ELSEIF (tissue.eq.2) THEN SK=.00356350 Ko=.15027778 SD=-0.00000000005555556 Do=.000000115 Fo=0.25*(Do+SD*100)/(Do+SD*To) dm=Fo type=*FATTY*

C THERMAL PROPERTIES OF Fibrous:

ELSEIF (tissue.eq.3) THEN SK=.00014462 Ko=.47138462 SD=-0.0000000001333333 Do=.000000134 Fo=0.25*(Do+SD*100)/(Do+SD*To) dm=Fo type=*FIBROUS* ELSE GOTO 10 ENDIF

KTo=Ko+SK*To DTo=Do+SD*To

191 K100=Ko+SK*100 D100=Do+SD*100 diff=D100

ELSEIF (thermal.Eq.O) THEN

writeC^t’C*’ constant diffusivity: ’’/)*) read(*,*)diff writeC*,^'' constant conductivity: **/)*) read(*,*)cond

ENDIF

C I*********************************************************

C OPTICAL PARAMETERS:

300 lambda=514.5 lambda=lambda/1000000000

IF (lambda.Eq.514.5E-09) THEN IF (tissue.EQ .1) THEN alpha=18 beta=12 ELSEIF (tissue.EQ .2) THEN alpha=27 beta=18 ENDIF ENDIF

alpha=alpha*100 beta=beta*100 gamma=alpha+beta

305 write(*,*(/*’ l=guassian TEMPORAL profile: ’'/)’) write^.'C’’ 0=chopped temporal profile: ’’/)’) write(*,,(,> Enter temporal profile of pulse: ’’/)’) read(*,*)temporal IF (temporal.NE.l) THEN IF (temporal.NE.O) THEN GOTO 305 ENDIF ENDIF

write^.’O* pulse width in milliseconds: ’’/)’) read(*,*)tp tp=tp/1000.00

310 write(*,>(/»» l=guassian SPATIAL profile: »»/)*)

192 writeC'S'C’’ O=uniform spatial profile: ’’/)’) writeC+.'C’’ Enter spatial profile of pulse: **/)’) read(*,*)spatial IF (spatial.NE.l) THEN IF (spatial.NE.O) THEN GOTO 310 ENDIF ENDIF

IF (spatial.EQ.l) THEN 320 write(*,’(/'’ l=beam broadening: ’’/)’) writeC+.’C’’ 0=no beam broadening: ’’/)*) writeC+.’C’’ Enter propagation profile of pulse: ’’/)’) read(*,*)bbroad IF (bbroad.NE.l) THEN IF (bbroad.NE.O) THEN GOTO 320 ENDIF ENDIF ENDIF

d=(diff*tp)**.5/lambda

write^.’O* unitless exp. duration: ’’/)’) read(*,*)ute

write(*,,(,> power in watts: ’’/)’) read(*,*)power

IF (spatial.EQ.O) THEN corr=power/(pi*(spot/2)**2)*(emiss)*(tp)*alpha ELSEIF (spatial.EQ.l) THEN corr=2*power/(pi*(spot/2)**2)*(emiss)*(tp)*alpha ENDIF

IF (thermal.EQ.O) THEN source=corr/(cond/diff) ENDIF

write(*,350)th 350 format(* threshold: ’,fl4.7)

Q ********************************************************

C OUTPUT FILES:

n=*ablate.dat’ open(2,file=n,statu s=’new *)

m=’depth.dat’

193 open(3,file=m,status=’new’)

parameters=,param.dat * open(4,FILE=paramet ers,status=’ new ’)

twodim=’twodim.dat ’ open(7,FILE=twodim,status=’new’)

damage=* damage.dat’ open(8,FILE=damage, status=’new’)

onsetd=’onset21.dat’ open(9,FILE=onsetd,status=’new’)

********************************************************

CALCULATE DIMENSIONLESS QUANTITIES, udt, udx, ur:

udt=ute/float(1)

udx=d*sqrt(ute)/sqrt(dm*l) ur=(udx*lambda)/(spot/2) write(*,405)l/ur format(’ radiusof beam= :: ’,fl4.7, * ’ units’/)

*********************************************************

find laser temporal profile params

IF (temporal.EQ.l) THEN factor=-4.*log(.5) thalf=sqrt(log(.005)/(4.*log(.5))) ENDIF

*********************************************************

FIND EXTINCTION PROFILE FOR LIGHT INTO THE SURFACE:

jm=int(-log(.005)/(gamma*lambda*udx))

write(*,600)jm format(’ penetration depth: ’,i3,’ boxes’/’ ’)

wmax=int(4.2*float(1)**.5)+int(1/ur)

DO 1000 i=l,jm IF (spatial.EQ.O) THEN s(i,l)=udt*exp(-gamma*lambda*udx*(float(i)-0.5)) ENDIF DO 900 w=l,wmax IF (spatial.EQ.0) THEN IF (float(w)*ur.GT.1.0) THEN r=0 ELSE r=l ENDIF s(i,w)=s(i,l)*r ELSEIF (spatial.eq.l) THEN IF (bbroad.EQ.O) THEN s(i,w)=udt*exp(-gamma*lambda*udx*(float(i)-0.5)) *exp(-2*((float(w)-0.5)*ur)**2) ELSEIF (bbroad.EQ.l) THEN s (i, w)=udt*exp(-gamma*lambda*udx* (f loat (i) -0.5) ) *exp(-2*((float(w)-0.5)*ur)**2/exp(beta*lambda *udx*(float(i)-0.5))) ENDIF ENDIF ■ 900 CONTINUE 1000 CONTINUE

C *********************************************************

C INITIALIZE THERMAL' CONDUCTIVITY AND DIFFUSIVITY:

DO 1200 j=l,nDEP DO 1100 w=l,nWID IF (thermal.Eq.l) THEN Dvert(j,w)=DTo/diff Dhorz(j,w)=DTo/diff Kvert(j,w)=KTo Khorz(j,w)=KTo ELSEIF (thermal.EQ.O) THEN Dvert(j,w)=l.0 Dhorz(j,w)=l.0 Kvert(j,w)=l.0 Khorz(j,w)=l.0 ENDIF 1100 CONTINUE 1200 CONTINUE

C ********************************************************

C START OF THE TIME LOOP:

v=0 x=0 f =0 ji=0

DO 9000 k=0,l

195 jj=jm+int(4.2*float(k)**.5) ss=jj-jm+int(1/ur)

C DETERMINE LIGHT SOURCE COMPONENT OF HEAT CONDUCTION EQUATION:

IF (temporal.EQ.O) THEN IF (k.eq.int(l/udt)+l) THEN DO 2500 j=(l),(jm+jl) DO 2400 w=(a(j)+l),ss ei(j,w)=0 2400 CONTINUE 2500 CONTINUE ENDIF IF (k.GE.int(l/udt)+l) THEN GOTO 3510 ENDIF ENDIF

IF (temporal.EQ.O) THEN IF (k.le.int(l/udt)) THEN z=l ENDIF ELSEIF (temporal.EQ.1) THEN z=exp(-factor*(float(k)*udt-thalf)**2) ENDIF 3000 DO 3500 j=(l),(jm+jl) DO 3400 w=(a(j)+l),ss IF (j-depth(w).eq.O) THEN write(*,*)j ,w,depth(w) ENDIF IF (thermal.EQ.l) THEN source=corr/((KTo+SK*eo(j,w))/(DTo+SD*eo(j,w))) ENDIF 3300 ei(j,w)=s(j-depth(w),w)*source*z 3400 CONTINUE 3500 CONTINUE c diffusion loop

C SURFACE LAYER WITHOUT ABLATION, J=l, jl=0:

3510 IF(jl.eq.O) THEN urf=2

en(l,l)=eo(l,l)+Fo*( * Dhorz(1,1)*(eo(2,l)-eo(1,1)) * +urf*Dvert(l,l)*(eo(l,2)-eo(l,l))) * +ei(l,l)

196 NON-BOUNDARY OFCHECK: VALUESBOXESFOR ALL C FRCEKGETRTA »1>GREATERTHANCHECK FOR C FRCEKGETRTA REUL O *1* TO OR EQUAL GREATERTHAN FORCHECK C C BOUNDARY BOXES FOR CHECK =0:CHECKFOR BOXES BOUNDARY C C LATERAL DIFFUSION ABOVE THE CRATER BASE:CRATER THE ABOVE DIFFUSION LATERAL C **'****************************************************** C i************************************** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * i C 90 CONTINUE 5900 o o DIFFUSION OF BOUNDARY LAYER AT SURFACE AFTER ONSET OF ABLATION:OFONSET AFTER SURFACE AT OFLAYER BOUNDARY DIFFUSION LEF (jl.GT.O) THEN ELSEIF ENDIF CALL CONDUCT(J,q+check,ss,1,1,1,1)CALL DO 5900 j=2,jl 5900 DO F (jl.GT.l) THENIF ENDIF ENDIF ENDIF F (check.GT.l)IF THEN F (check.GE.l)IF THEN q=a(j)+l F (check.EQ.O)IF THEN check=a(j-l)-a(j) CALL SURFACE(a(l)+2,ss,1,1,1)CALL SURFACE(a(l)+l,a(l)+1,1,1,0)CALL CALL SURFACE(2,ss,CALL 1,1,1) CALL CONDUCT(J,q+1,a(j-l),l,0,l,l)CALL CALL CONDUCT(J,q,q,1,0,1,0)CALL CALL CONDUCT(J,q,q,1,1,1,0)CALL check=l (J=1),(J1>0) 197 c * * * *-* *************************************************** c DIFFUSION AT BASE OF CRATER, (J=l+jl):

6000 enCjl+1,1)= AXIAL(jl+l,1,0,1)

EXCESS BOUNDARY BOXES AT BASE OF CRATER:

IF (a(jl).GT.l) THEN CALL CONDUCT(jl+l,2,a(jl),1,0,1,1) ENDIF

LATERAL DIFFUSION AT BASE OF CRATER

CALL CONDUCT(jl+l,a(jl)+l,ss,l,l,l,l)

ENDIF

C ********************************************************

C HEAT CONDUCTION: THERMAL DIFFUSION BELOW CRATER BASE:

DO 8500 j=(2+jl),(jj+jl) en(j,l)=AXIAL(j,1,1,1) CALL COHDUCT(j,2,ss,l,l,l,l) IF (en(j,1).LT.min) GOTO 8600 8500 CONTINUE

C ********************************************************

C UPDATE ENTIRE TEMPERATURE PROFILE:

8600 finish=jj+jl DO 8800 j=l,finish

CHECK FOR ABLATION IN AXIAL NODES:

v01 . eo(j,l)=en(j,1) IF (en(j.l).gt.th) THEN IF(j.gt.dmaxt emp) THEN dmaxtemp=j thresh(j, l)=k*udt*tp ENDIF eo(j,l)=th error=en(j,l)-th acc(j,l)= acc(j,l) + error*Cp IF(acc(j,1).ge.heat) THEN area=area+l onset(j,l)=k*udt*tp WRITE(9,8630)j,w,onset(j,w)

198 8630 format(14,lx,13,lx,f10.7) max(j,l)=-100 eo(j,1)=0 en(j,1)=0 acc(j,l) = acc(j,l) - heat a(j)=1 jl=jl+l depth(l)=jl write(*,8720)j,a(j) 8640 format(* ablation width: 1’, ’ depth: *,i4,* unit(s)*/* *) ENDIF ENDIF

C DETERMINE MAXIMUM TEMPERATURE OF EACH AXIAL BOX:

8700 IF (eo(j,1).gt.abs(max(j,1))) THEN max(j,l)=eo(j,1) ENDIF

C CHECK FOR ABLATION IN LATERAL NODES:

8705 DO 8790 w=(2),(ss) eo(j,w)=en(j,w) 8706 IF (en(j,w).gt.th) THEN IF(w.gt.wmaxtemp(j)) THEN wmaxtemp(j)=w thresh(j,w)=k*udt*tp ENDIF . eo(j,w)=th error=en(j,w)-th acc(j,w)= acc(j,w) + error*Cp IF(acc(j,w).ge.heat) THEN area=area+l onset(j,w)=k*udt*tp WRITE(9,8630)j,w,onset(j,w) a(j)=a(j)+l depth(w)=depth(w)+l max(j,w)=-100 eo(j ,w)=0 en(j,v)=0 acc(j,w) = acc(j,w) - heat 8720 format(’ at depth: *,i4, ’ ablation width: *,i5,’ box(es)’/’ ’) ENDIF ENDIF

C DETERMINE MAXIMUM TEMPERATURE OF EACH LATERAL BOX:

8750 IF (eo(j,w).gt.abs(max(j,w))) THEN max(j,w)=eo(j,w)

199 ENDIF

8790 CONTINUE 8800 CONTINUE

C ********************************************************

C WRITE TO RUNNING OUTPUT FILES:

IF (v.EQ.O) GOTO 8808 IF (v.lt.p) goto 8820 8808 write(*,8810)k*udt,jl v=l 8810 format(’+ut: ’ ,fl0.5,’ ablation: ’ ,i4) write(2,*)k*udt*tp,eo(l,l)

IF (x.Eq.O) GOTO 8822 8820 if (x.lt.b) goto 8840 8822 DO 8830 i=l,jj write(3,*)k*udt*tp, J i*d*sqrt(udt/dm)*lambda,eo(i,1) 8830 CONTINUE x=l

8840 v=v+l x=x+l

write(2,8850)k*udt*tp,depth(l),a(l)*2,area*2 8850 format(f8.6,lx,i5,lx,i5,lx,i6)

IF (onset(1,1).GT.0.0) THEN IF (STD.Eq.0.0) THEN STD=k*udt*tp ID=depth(l) ENDIF

IF (depth(l).GT.FND) THEN ED=k*udt*tp FND=depth(l) ENDIF

IF (STA.Eq.O.O) THEN STA=k*udt*tp IA=area*2 ENDIF IF (area*2.GT.FNA) THEN EA=k*iidt*tp FNA=area*2 ENDIF

200 ENDIF

C ********************************************************

C CALCULATE NEW VALUES FOR THERMAL CONDUCTIVITY AND DIFFUSIVITY

IF (thermal.EQ.l) THEN DO 8900 j=l,jj~l DO 8890 w=l,ss-1 Tavg=(eo(j,w+l)+eo(j,w))/2 Kvert(j,w)=(KTo+SK*Tavg) Dvert(j,w)=(DTo+SD*Tavg)/diff IF (Tavg.LT.min) GOTO 8900

Tavg=(eo(j+l,w)+eo(j,w))/2 Khorz(j,w)=(KTo+SK*Tavg) Dhorz(j,w)=(DTo+SD*Tavg)/diff IF (Tavg.LT.min) GOTO 9000

C ERROR CHECKING:

IF (DVERT(j,w)*Fo.gt.checkdv) THEN checkdv=DVERT(j,w)*Fo ELSEIF (DHORZ(j,w)*Fo.gt.checkdh) THEN checkdh=DHORZ(j,w)*Fo ENDIF

8890 CONTINUE 8900 CONTINUE ENDIF

C *********************************************************

9000 CONTINUE

C *********************************************************

C WRITE MAXIMUM TEMPERATURE FILE:

con=d*sqrt(udt/dm)* lambda

DO 9020 j=l,jj+jl,y DO 9010 w=l,ss write(7,9009)j,w,int(max(j,w)) 9009 format(14,lx,13,lx,15) 9010 CONTINUE 9020 CONTINUE

C **********************************************************

C WRITE ABLATION DATA TO THE SCREEN: DO 9040 j=l,jl IF(a(j).ne.O) THEN write(*,9030)j,a(j) ENDIF 9030 format(’ at depth = ’,i5,’ lateral ablation = ’, * i5) 9040 CONTINUE

C I********************************************************

CLOSE OUTPUT FILES:

close(2) close(3) close(5) close(7) close(8) close(9)

C ********************************************************

C WRITE PARAMETER FILE:

write(4,’(” 2-D, CYLINDRICAL COORDINATES ” )’) write (4, * (* ’ INDIVIDUAL ACCUMULATORS ” )’) write(4,’ (’ ’ SPOT DIVIDED BY dr” )’) write(4,’ (’ ’ ABSORPTION AND SCATTERING COEFFICIENTS” )’) write(4, * (’ ’ SIMULTANEOUS ABSORPTION AND DIFFUSION” /)’)

IF (thermal.EQ.1) THEN write(4,’( ” VARIABLE THERMAL CONDUCTIVITY FOR TYPE: ” /)’) write(4,*)type write(4,*) ELSEIF (thermal.Eq.O) THEN write(4,’(” CONSTANT THERMAL CONDUCTIVITY ” /)’) write(4,*) ENDIF

write(4,9110)1 9110 format(’ iterations= :: ’,114,’ ’) write(4,9120)in 9120 format(’ refractive index (imag)= :: ’,fl4.7,’ ’) write(4,9130)d 9130 format(’ TDP= :: ’,fl4.7,’ ’/) write(4,9131)alpha/100 9131 format(* absorption coefficient= :: ’ ,f14.7,’em-1 ’) write(4,9132)beta/100 9132 format(’ scattering coefficient= :: ’,fl4.7,’cm-1 ’) write(4,9133)emiss 9133 format(’ emissivity= :: ’,fl4.7,’ ’/)

202 write(4,9134)heat 9134 format(’ latent heat= :: ’,fl4.2,* ’/) write(4,9135)Fo 9135 format(’ Fo= :: ’,fl4.7, ’ ’/) write(4,9140)tp*1000 9140 format(* pulse width= :: ’,f14.2,’ms’)

IF (temporal.EQ.O) THEN write(4,’(’’ temporal pulse structure:: chopped’’)’) ELSEIF (temporal.Eq.l) THEN write(4,’(’’ temporal pulse structure:: gaussian’’)’) ENDIF

IF (spatial.Eq.O) THEN write(4,’(’’ spatial distribution:: UNIFORM” /) ’) ELSEIF (spatial.EQ.l) THEN IF (bbroad.EQ.O) THEN write(4,’(” spatial distribution:: GAUSSIAN’’/)’) ELSEIF (bbroad.EQ.l) THEN write(4,’(” spatial distribution:: GAUSSIAN WITH BEAM BROADENING” /)’) ENDIF ENDIF

write(4,9150)lambda*1000000000 9150 format(’ wavelength= :: ’ ,fl4.2,’nm*/) write(4,9160)power 9160 format(’ power= :: *,fl4.7,’W’) write(4,9170)spot*1000 9170 format(’ spot= :: ’,fl4.7,’mm’) write(4,405)1/ur write(4,9190)th 9190 format(’ dimensionless threshold= :: ’,fl4.7,’ */) write(4,9200)th 9200 format(’ temperature threshold= :: ’,fl4.2,’ degrees C ’/) write (4,9300) jm*d*sqrt (udt/dm)*lambda*1000 9300 format(’ light penetration depth :: ’ ,f14.7,’mm’) write(4,9330)jm 9330 format(’ incremental depth :: ’,i5,’ units’/) write(4,9335)0NSET(1,1)*1000 9335 format(’ onset of ablation = :: ’ ,fl4.7,’ms’/) IF (J1.GT.0) THEN write(4,9337) (FND-ID)*udx*lambda/(ED-STD) 9337 format(’ rate of ablated depth= :: ’,f14.7,’mm/ms’) ENDIF write(4,9340)jl*d*sqrt(udt/dm)*lambda*1000

203 9340 format(* ablation depth = :: *,f14.7,*mm*) write(4,9345)jl 9345 format(* ablation depth units = :: *,i5,’ */) write e4,9348)dmaxtemp*udx*lambda*1000 9348 formate/’ depth at threshold= :: ’ ,fl4.7,*mm’) write e4,9350)dmaxtemp 9350 formate* unit depth at threshold= :: *,i5,’ *//) writee4,9351)aei)*udx*lambda*1000*2 9351 formate* crater width = :: ’ ,f14.7,*mm*/) writee4,9353)aei)*2 9353 formate’units in crater width X2= :: ’,i5,’units’/) writee4,9354)eFNA-IA)*eudx*lambda)**2*1000/eEA-STA) 9354 formate* rate of ablated area = :: ’ ,f14.7,*mm2/ms*) write e4,9356)area* e udx*lambda*1000)**2 *2 9356 formate* crater area = :: ’ ,f14.7,*mm2 ’) writee4,9358)area*2 9358 formate* units in area X 2 = :: *,i5,’ ’/) write e4,9360)udt 9360 formate/’ udt= :: \fl4.7,’ ’) writee4,9365)udt*tp 9365 formate* dt= ’ ,f 14.7, ’ s ’/) write e4,9370)udx 9370 formate* udx= ’,f14.7,* ’) writee4,9375)udx*lambda*1000 9375 format(’ dr=dz=dx= ’,f14.7,*mm*) writee4,9380)ur 9380 format e * ur= ’,fl4.7,’ ’/)

DO 9500 j=l, dmaxt emp ifeaej).eq.0) goto 9450 writee8,9430)j,aej) 9430 formate* at depth= *,i4,*, lateral ablation= *, * i5 * ») do*9435 w=l,aej) writee8,*)j,w,threshej,w)*1000,onsetej,w)*1000 9432 formatei5,lx,i4,lx,fl0.4,lx,f10.4) 9435 continue

9450 ifewmaxtempej).eq.0) goto 9500 writeC8,9470)j,wmaxtempej) 9470 formate* at depth= *,i4,’ lateral threshold unites)= * ::’»i4)

9487 formatei5,lx,i4,lx,fl0.4,lx,f14.2,lx,f14.2) 9489 do 9490 w=aej)+l.wmaxtempej) writee8,9487)j,w,threshej,w)*1000,accej,w), * accej,w)/heat 9490 continue 9500 continue

writee4,*)

204 do 9600 w=l,a(l)+l write(4,*)depth(w) 9600 continue

write(4,*) do 9700 j=l,jl if(a(j).eq.0) goto 9700 write(4,9030)j,a(j) 9700 continue

end

C ******************* ******************* ***********************

FUNCTION AXIAL(J,ZP,ZM,RP)

PARAMETER (nDEP=1500) PARAMETER (nWID=400)

INTEGER*4 j,ZP,ZM,RP REAL*4 urf C0MM0N/BLK1/eo(nDEP,nWID),ei(nDEP,nWID) C0MM0N/BLK2/Fo,Dvert(nDEP,nWID),Dhorz(nDEP,nWID)

urf=2 AXIAL=eo(j,l)+Fo*( RP*urf*Dvert(j,l)*(eo(j,2)-eo(j,1)) + ZM*Dhorz(j-l,l)*(eo(j-l,l)-eo(j,1)) + ZP*Dhorz(j,l)*(eo(j+1,l)-eo(j,1))) +ei(j,l) RETURN END

*********************************************************

SUBROUTINE SURFACE(WI,WF,ZP,RP,RM)

PARAMETER (nDEP=1500) PARAMETER (nWID=400)

INTEGER*4 WI,WF,w,ZP,ZM,RP,RM REAL*4 lrf,urf,min C0MM0N/BLKl/eo(nDEP,nWID),ei(nDEP,nWID) COMMON/BLK2/Fo,Dvert(nDEP,nWID),Dhorz(nDEP,nWID) C0MM0N/BLK3/en(nDEP,nWID),min

DO 100 w=WI,WF urf=(float(w))/(float(w)-0.5) lrf = (float (w) -1.0 ) / (float (w) -0.5)

en(l,w)=eo(l,w)+Fo*(

205 * ZP*Dhorz(1,w)*(eo(2,w)-eo(1, w) ) * +RM*lrf*Dvert(1,w-l)*(eo(l,w-l)-eo(l,w)) * +RP*urf*Dvert(l,w)*(eo(l,w+1)-eo(l,w))) * +ei(l,w)

IF (en(l,w).LT.min) GOTO 200

CONTINUE

RETURN END

******************* lit******* I*******************

SUBROUTINE CONDUCT(J,WI,WF,ZP,ZM,RP,RM)

PARAMETER (nDEP=1500) PARAMETER (nWID=400)

INTEGERS j , WI, WF, w, ZP, ZM, RP, RM REAL*4 lrffurf,min COMMON/BLKl/eo(nDEP,nWID),ei(nDEP,nWID) C0MM0N/BLK2/Fo,Dvert(nDEP,nWID),Dhorz(nDEP,nWID) C0MM0N/BLK3/en(nDEP,nWID),min

DO 100 w=WI,WF urf=(float(w))/(float(w)-0.5) lrf=(float(w)-l.0)/(float(w)-0.5)

en(j,w)=eo(j,w)+Fo*( * RM*lrf*Dvert(j,w-l)*(eo(j,w-l)-eo(j ,w)) * +RP*urf*Dvert(j,w)*(eo(j,w+l)-eo(j,w)) * + ZM*Dhorz(j-l,w)*(eo(j-l,w)-eo(j,w)) * + ZP*Dhorz(j,w)*(eo(j+1,w)-eo(j,»))) * +ei(j,w)

IF (en(j,w).LT.min) GOTO 200

CONTINUE

RETURN END

******************************************************** R eferences

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INFORMATION to USERS the Most Advanced Technology Has Been Used to Photo­ Graph and Reproduce This Manuscript from the Microfilm Master

INFORMATION to USERS the Most Advanced Technology Has Been Used to Photo Graph and Reproduce This Manuscript from the Microfilm Master