Development, Validation and Clinical Application of Finite Element Human Pelvis Model

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FINAL APPROVAL OF THESIS Master of Science in Biomedical Sciences

Development, validation and clinical application of finite element human pelvis model

Submitted by: Alexander A. Ivanov

In partial fulfillment of the requirements for the degree of Master of Science in Biomedical Sciences

Examination Committee Signature/Date

Major Advisor: Nabil Ebraheim, M.D.

Academic Vijay Goel, Ph.D. Advisory Committee: Ashok Biyani, M.D.

Senior Associate Dean College of Graduate Studies Michael S. Bisesi, Ph.D.

Date of Defense: May 15, 2008

A Thesis Entitled

Development, Validation and Clinical Application of the Finite

Element Model of Human Pelvis.

Alexander A. Ivanov, M.D.

Submitted as partial fulfillment of the requirements for

the Master of Science in Orthopaedic Science

______Advisor: Dr. Nabil A. Ebraheim, M.D.

______Co-Advisor: Dr. Vijay K. Goel, Ph.D.

______Graduate School

The University of Toledo 2008

College of Health Science

I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY: Alexander A Ivanov, M.D.

ENTITLED: Development, validation and clinical application of finite element human pelvis model

BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF: Master of Science in Orthopaedic Science

______Thesis Advisor: Dr. Nabil A. Ebraheim, M.D.

______Thesis Co-Advisor: Dr. Vijay K. Goel, Ph.D.

Recommendation concurred by:

______Committee Dr.Ashok Biyani, M.D. Of Final Examination

______Dean, College of Health Science

3 Acknowledgment

I would like to extend my gratitude to my advisors Dr. Nabil Ebraheim and Dr. Vijay

Goel for their incredible support of this work. I will always consider them as a part of the foundation of my future success. I would also like to thank Dr. Ashok Biyani, my committee member for offering learning and research assistance throughout the process.

Special thanks go to Ali Kiapour who has been through it all. Ahmad Faizan and Jayant

Jagra who were always available when it was most needed. I thank all my colleagues at the Orthopaedic Surgery and Bioengineering Departments for creating a wonderful learning environment.

4 Abstract

Finite element analysis became a very effective and essential tool in the studies of spinal and pelvic biomechanics. Most previous pelvic models included such simplifications as non-complete pelvic structures presentation, non-physiologic properties of ligaments, model validation against just only one mode. Out study is the first attempt, to our knowledge, to generate model with physiologic non-linear characteristic of the ligamentous structures of sacroiliac joint and accurate presentation of entirely pelvic anatomy. The model validation against data in literature showed good prediction of motions in the sacroiliac joint and stress-distribution across pelvic bone. The clinical application showed increased motions and stresses across sacroiliac joint which were not previously confirmed by the clinical and experimental studies due to their low sensitivity and specificity. The developed finite element human pelvis model might be a useful instrument in further clinical and biomechanical studies.

5 Table of Contents Page

Acknowledgement...... 4 Abstract...... 5

Chapter I-Introduction

Significance of Low Back Pain Syndrome…………………………………………8 Sacroiliac Joint Syndrome………………………………………………………… 8 Pelvis and Sacroiliac Joint Anatomy…………………………………………….....8 Difficulties in Sacroiliac Joint Biomechanics Studies……………………………..15

Chapter II-Literature Review…………………………………………………...17

Morphometric Studies of Human Pelvis…………………………………………..17 Morphometric Studies of Human Sacroiliac Joint………………………………...21 Biomechanics of Sacroiliac Joint Motions……………………………………….. 23 Previous FE Studies Simulated Human Pelvis…………………………………….30 Previous FE Studies Simulated Human Sacroiliac Joint…………………………..33

Chapter III- Materials and Methods……………………………………………38

Human Pelvis Model………………………………………………………………38 Geometry ……………………………………………………………………..38 Bony Element Modeling ………………………………………………………40 Sacroiliac Joint Modeling …………………………………………………….41 Ligaments Modeling …………………………………………………………..42 Material Property Definitions ………………………………………………...43 Finite Element Model Validation ………………………………………………….45

Chapter IV- Results………………………………………………………………53

Finite Element Model Result……………………………………………………….53 Statistical Analysis of Data…………………………………………………………62

Chapter V-Discussion……………………………………………………………..72

Chapter VI- Clinical Application of Finite Element Human Pelvis Model……80

Introduction………………………………………………………………………….80 Significance of Low Back Pain in Patient after Lumbar Fusion Sacroiliac Joint as a Cause of LBP in Patient after Lumbar Fusion Material and Methods……………………………………………………………….82 Modifications in FE Pelvis Model

6 Boundary and Loading Conditions Results……………………………………………………………………………....86 Discussion…………………………………………………………………………..91

Conclusion…………………………………………………………………………94 Simplifications……………………………………………………………………..95

Future Work……………………………………………………………………...... 95

References…………………………………………………………………………..96

7 CHAPTER I

INTRODUCTION

Significance of Low Back Pain

Low back pain (LBP) is a very frequent complaint and it’s the second most common cause of people to seek medical attention [1]. It appears that LBP is the most common reason of disability for person after 45 years old [2]. Life time prevalence of this condition ranges from 60 to 90% with annual incidence of 5% [3]. Therefore, it’s easy to understand the importance of studies with objective to elucidate the etiology and pathomechanism of this problem.

Sacroiliac Joint Syndrome

Among the different sources of LBP, the prevalence of sacroiliac joint syndrome ranges from 13 to 30% of all patients with LBP [4, 5]. The involvement of areas closed to SIJ can simulate SIJ dysfunction; therefore, the diagnosing of syndrome can be very challengeable for a physician [4]. One of the reasons of difficulties in establishing the correct diagnose in SIJ syndrome is a unique anatomy of pelvis, its innervation and specific biomechanics of sacroiliac joint.

Anatomy of Pelvis and Sacroiliac Joint

From biomechanical perspectives, the pelvis represents the integral complex structure which serves like a link between trunk and lower extremities. The main function of it is to transmit and decrease the force of gravity from lumbar spine to lower extremities and vise versa. The anatomy of pelvis is completely accommodated to its main

8 function. The pelvis consists of three bones (two hip bones and sacrum) and three joints (paired sacroiliac joints and pubic symphysis).

Figure 1. The anatomy of pelvis (adopted from Gray H. The anatomy of human body. 1918).

Sacrum

Sacroiliac Joint Hip Bone

Pubic Symphysis

Sacrum is a triangular bone situated between two hip bones as a wedge. It connects with lumbar spine by L5/S1 intervertebral disk, and with hip bones by the paired sacroiliac joints. Sacrum is curved upon itself and is titled anteriorly forming a prominent promontorium. The shape of lateral surface of sacrum which corresponds to articular surface of SIJ, “…resembles the shape of the propeller” [6] where

9 posterior aspect in wider than anterior one in the upper part of sacrum, and vise versa at the lower part of sacrum. Pelvis has prominent irregularities with increase contact area in SIJ. The triangular shape with the base in the top and specific lateral surface shape of sacrum makes it highly resistant to movement between hip bones.

Figure 2. The anatomy of sacrum (adopted from Gray H. The anatomy of human body. 1918).

Hip bone consists of three parts, ilium (Figure 3, 1), ischium (Figure 3, 2) and pubis

(Figure 3, 3) which are fused together in the adults. The fusion takes place around acetabulum, articular cavity which connects pelvis to femur. The medial surface of ilium forms the articulate surface of the sacroiliac joint (anterior part of medial surface) and iliac tuberosity (posterior part of medial surface) which serves as a place for attachment massive posterior ligamentous structures of sacroiliac joint. Iliac wing is the thinnest part of the pelvis. It forms iliac crest superiorly which extends from anterior superior iliac spine (ASIS) to posterior superior iliac spine (PSIS). Ilium

10 body is much thicker and extends to acetabulum anteriorly and to the sacroiliac joint posteriorly. Ischium lies below the ilium and serves as place for attachment of massive muscles of lower extremity and ligaments of sacroiliac joint. Pubis is anterior part of pelvis and consists of body, superior and inferior ramus. One third of the pubic bone body contributes to the acetabulum. Superior ramus extends medially from body and connects to the opposite superior ramus by pubic symphysis. The pubis, the ischium and acetabulum enclose the foramen obturator.

Figure 3. The anatomy of hip bone (adopted from Gray H. The anatomy of human body. 1918).

Iliac Tuberosity PSIS ASIS 1

Articulate Acetabulum Surface 2 of SIJ

Ischium 3

ASIS- anterior superior iliac spine

PSIS- posterior superior iliac spine

SIJ- sacroiliac joint

11 Sacroiliac joint is the joint between articular surfaces of the ilium and sacrum bones.

The anterior part of it represents the synovial joint and the posterior part represents the syndesmosis. Usually, the articulate surface corresponds to the three sacrum vertebrae (S1, S2 and S3). Large variations in surface configuration exist from person to person and even side to side. The irregularities develop on SIJ surfaces from childhood, but they are always reciprocal. The elevations and depressions on the SIJ surface vary in height and depth from 2 to 11 mm. Such anatomical peculiarities significantly decrease the range of motion in SIJ.

Additionally, the massive ligaments surround a joint and make it the stiffest joint in human. Anterior sacroiliac ligament (ASL) is located on the anterior and inferior part of SIJ and resist external rotation and anteroposterior shear forces. Iliolumbar ligament (ILL) extends from the fifth lumbar transverse process to the posterior end of the iliac crest. It resists the shear forces. Interosseous sacroiliac ligaments (IOL)

(Figure 6) are short and strong, and connects iliac tuberosity and the posterior part of sacral surface area forming syndesmosis.

12 Figure 4. The anatomy of anterior surface of the pelvis (adopted from Gray H.

The anatomy of human body. 1918).

ILL

ASL

SSL STL

ILL- Iliolumbar ligament

ASL- Anterior sacroiliac ligament

SSL- Sacrospinous ligament

STL- Sacrotuberous ligament

The posterior group of ligaments consists of posterior sacroiliac ligaments (PSL) which pass from the sacral spine to the posterior superior iliac crest in the superior part and from the lateral sacral margin to the PSIS obliquely down and supplements the sacrotuberous ligament. The sacrotuberous ligament (STL) attaches to PIIS and the inferior iliac spine, the lateral part of the sacrum and coccyx and the medial margin of the ischial tuberosity. It resists the vertical shear forces and the flexion of

13 sacrum. The sacrospinous ligament (SSL) extends from ischial spine to the lateral margin of sacrum and prevents the sacrum from flexing and moving posteriorly.

Figure 5. The anatomy of the posterior surface of the pelvis (adopted from Gray

H. The anatomy of human body. 1918).

PSL

SSL

STL

PSL - Posterior Sacroiliac Ligament SSL - Sacrospinous Ligamnent STL - Sacrotuberous Ligament

The SIJ has extensive innervation from the L2 to the L4 lumbar spinal nerves with involvement of both anterior and posterior primary rami [7,8].

Figure 6. The anatomy of the sacroiliac joint and the interosseous ligament. The section across the first sacrum vertebra (adopted from Gray H. The anatomy of human body. 1918).

IOL

SIJ

IOL - Interosseous Ligament SIJ - Sacroiliac Joint

Difficulties in Study of Biomechanics of Sacroiliac Joint

The anatomy of the sacroiliac joint creates many difficulties in the proper study of the biomechanical behavior of SIJ. There are many cases of variability in the morphology from one side to another side and from one person to another person which raises a problem in running the comparative studies. The ligaments are short with a wide area of attachment to the pelvis which makes it difficult to study the biomechanics of ligaments. Aging and pregnancy have direct influence on the SIJ ligament properties, which may alter the sacroiliac joint mobility. Moreover, the sacroiliac joint may be fused. There are many muscles which attach to the pelvis and influence on the SIJ

15 stability in an indirect way. Therefore, theoretically, the exact FE subject-specific model may not predict the exact value of measured parameter in a specimen which has different morphology. To overcome such difficulties in FE modeling, a researcher can simplify some of the anatomical signs of pelvis to make the

“idealized” model, which can be used for comparative studies. We assumed absence of any degenerative process in the SIJ, homogenous distribution of bony properties across the pelvis, and we did not consider the influence of muscle groups on the SIJ biomechanics.

16 CHAPTER II

LITERATURE REVIEW

Morphometric Studies of the Human Pelvis

Numerous studies have been conducted to measure the pelvic morphology. Clinical evaluation and radiographic analysis are utilized in clinics [9,10]. The direct measurements are mostly applied in forensic medicine and studies which objectives are to determine sex, race, or age of the specimen [11,12]. The most frequently used measurements are the following:

- Pelvic height: from the most superior point on the iliac crest to the most inferior point on the ischial tuberosity, measured parallel to central axis.

- Pelvic breadth: the maximum distance between lateral margins of the iliac crest.

- Anterior upper spinal breadth: between the lateral edges of the anterior superior iliac spines.

- Breadth at symphysis: between the most medial points on the anterior margin of the foramen obturator.

- Transverse diameter of pelvic brim: the maximum distance between the arcuate lines.

- Height of ilium: from the intersection of the sacroiliac joint and the pelvic brim to highest point of iliac crest, measured parallel to central axis.

- Sacroiliac breadth: between the points where the sacroiliac joints meet the pelvic ring.

17 The data obtained by mentioned above methods have allowed clinicians and researchers to find significant difference in pelvic size by gender, age, weight, height, ethnicity etc.

Figure 7. Pelvic measurements. Adopted from Schroeder et al (1997) [18].

a) Pelvic height b) Pelvic breadth c) Anterior upper spinal breadth d) Breadth at symphysis e) Transverse diameter of pelvic brim f) Height of ilium g) Sacroiliac breadth

18 In cadaveric studies it was shown that nutrition has significant impact on the pelvis development and pelvic shape. Nicholson et al (1946) [13] Bernard (1952)[14], Angel

(1978) [15] revealed flattening of the pelvic inlet associated with poor nutrition and light growth retardation.

The study of sexual pelvic dimorphism showed a potent role of male hormones in determining pelvic shape. Animal experiments with rats, mice and rabbits demonstrated influence of testosterone on adult pelvic pattern [16,17]. The result is similar on the mechanism of reproductive system development. In the presence of male hormones, male reproductive system is developing with apoptosis of feminized reproductive organs. In the absence of male hormones, feminized structures remain after birth.

Schroeder et al (1997) [18] reviewed previous data regarding pelvic measurement in different socioeconomic time and geographical areas. The comparison of pelvic breadth and transverse diameter of the pelvic brim revealed interesting peculiarities regarding the specimen’s groups which were used in studies.

19 Table 1. Comparison of two measurements of pelvis from literature data

(adapted from Schroeder et al, 1997[18])

Pelvis Female Male Source of measurement (mean ± SD (mean ±SD date and authors (n)) (n)) Pelvic Breadth Schroeder et Texas cadavers 276±21.4 (20) 294±18.6 (30) al [18] Iscan and Terry collection 277±16.39 (100) 275.07±15.2 (100) Cotton [116] Hammann-Todd Tague [118] 269±18 (50) 277±15 (49) collection “Small females” and Reynolds et al “medium males” from 244±11 (28) 266±8 (33) [117] Hammann-Todd collection Transverse Brim Schroeder et Texas cadavers 131.4±9.6 (20) 127.2±9 (30) al [18] Iscan and Terry collection 132.96±7.91 (100) 124.08±7.86 (100) Cotton [116] Hammann-Todd Tague [118] 134±8 (50) 130±8 (50) collection “Small females” and Reynolds et al “medium males” from 124±6 (28) 122±5 (33) [117] Hammann-Todd collection

Authors concluded that for current antropometric studies the new set of data might be

required due to different contemplative population, nutrition factors and

socioeconomic grouping.

Morphometric Studies of Human Sacroiliac Joint

Despite the high degree of variations in the size and shape of the sacroiliac joint,

many studies have revealed common patterns in SIJ structures. The articular surface

has “auricular” or “L” shape with cephalad segment oriented posteromedially and

cranially, and caudal segment oriented posterolaterally and caudally [19]. At birth the

20 joint is narrow and straight [20,21]. Further, the mechanical factors (such as bipedal gait, weight, etc) influence on the shape and contour of the SIJ during further growth period. Bakland and Hanson (1984) [22] showed the intra- and interindividual differences in the articular surface shapes (Figure 8).

Figure 8. The shape differences of the human pelvis specimens. The symbol “+” indicates the highest and deepest points of the iliac and sacral part of the “axial sacroiliac joint” (adopted from Bakland et al, 1984 [22]).

“+”- the highest and deepest

points of SIJ

♀- male

♂-female

sin - left side

dext - right side

Number in the left up corner-

the specimens’ numbers

According to data from the Weisl study (1954) [23] which are based on morphometric study of SIJ surface characteristics, the articular surfaces did not differ significantly in male and female specimens. The sacral surfaces were longer and

21 narrower than the corresponding iliac articular surfaces. The author applied his own method to investigate the relations of SIJ surfaces width and length to each other. The contour of each articular surface were put inside a rectangle (Figure 9), “where one side was tangential to the dorsal parts of the cranial (N) and caudal rami (O) , and the others touching the corresponding extremities of the articular surfaces (PEQ)”.

Figure 9. The measurement of SIJ articular surfaces using method offered by

Weisl (1954). AD and BC are the lengths, AB and DC are the widths of rectangle. Adopted from Weisl (1954)[23].

The length and width of the rectangle and articular surface were taken and the sacrum and ilium angle were calculated. Ohba (1985) [24] used the same technique to measure the articular surfaces of the SIJ in 24 Japanese individuals. The obtained

22 results are quite similar with the Weisl study results of aged SIJ [23] and are shown in

Table 2.

Table 2. Comparison of SIJ articular surfaces from literature data. Adopted from Zheng (1995) [25].

Measured Fetal (Weisl, Adult (Weisl, Elderly Adult Distance 1954) 1954) (Ohba, 1985) Sacral Width 8.6±0.2 35±0.62 34±3.1 Sacral Length 15.4±0.3 61±0.86 59±5.9 Sacral (56±1.90)% (58±0.93)% (58±7)% Width/Length Iliac Width 9.1±0.3 36±0.59 34±3.2 Iliac Length 14.6±0.2 60±0.91 59±5.9 Iliac (63±2.14)% (61±0.93)% (59±7)% Width/Length

The biomechanics of Sacroiliac Joint

At the beginning of the XX century multiple clinical studies were directed to clarify if the sacroiliac joint mobile or non-mobile. The results of Sashin (1930) [26], Thorp and Fray (1938) [27], Pitkin (1936) [28] studies have confirmed mobility of the sacroiliac joint. More sophisticated further studies suggested several theories of the pattern of the SIJ motion. The classical Farabeuf theory [29] considers the motion of joint about the axis which represents the interosseous ligament. During the movement of nutation the sacrum rotates about this axis, and promontory moves inferiorly and anteriorly, while the apex of the sacrum and the tip of the coccyx move posteriorly.

Those motions are restricted by sacrotuberous and sacrospinous ligaments. During the movement of counter-nutation the sacrum rotates in such way that the promontory

23 moves superiorly and posteriorly, and the apex of the sacrum and the tip of the coccyx move inferiorly and anteriorly. The motion is restricted by the sacroiliac ligaments [29].

Weisl (1955) [30] suggested two other possible theories. According to the theory of pure linear displacement, the sacrum moves across the axis which is a caudal part of the articular surface of the sacroiliac joint. According to theory of the rotational movement, the sacrum moves around the axis which lies anteriorly to the articular facet and inferiorly and anteriorly to the sacrum.

Bonnaire theory considered motion of the sacrum around axis which was a Bonnaire tubercle located between the cranial and caudal segments of the articular facet [29].

The existence of numerous theories represents the complex pattern of SIJ motion and individual variety of the motion from one person to another person.

In more recent studies, the researchers measured the motion in the sacroiliac joint.

The cadaveric studies have remained the “gold standard” in determining the actual value of sacrum displacement and angulation. Miller et al (1987) [31] studied the displacement of the SIJ under the different loads, which were applied to the superior endplate of the S1 vertebra. Using various directions of the loads, displacement of the centrum of the sacrum, angular motions (Table 3) and three-dimensional locations of the SIJ were measured.

24 Table 3. Mean displacements (mm) and rotations (degs) of the center of the sacrum in each test direction. Adopted from Miller (1987) [31].

Test Both Ilia One Ilium Fixed Load direction Fixed Mean Range Superior 294 N 0.28 (0.25) 1.87 (1.76) 0.20-5.75 Inferior 294 N 0.26 (0.25) 0.99 (0.43) 0.47-1.63 Anterior 294 N 0.48 (0.38) 2.74 (1.07) 0.02-2.90 Posterior 294 N 0.53 (0.75) 1.58 (1.69) 0.31-4.98 Medial 294 N 0.01 (0.08) 0.76 (1.41) 0.64-3.65 Flexion 42 N-m 1.31 (0.6) 2.68 (1.59) 0.91-4.53 Extension 42 N-m 1.94 (1.29) 3.52 (1.46) 1.92-4.66 Lateral 42 N-m 0.37 (0.27) 1.4 (0.71) 0.41-2.16 Bending Torsion 42 N-m 0.8 (0.51) 6.21 (3.29) 1.15-8.25

Rothkotter and Berner at 1988 [32] studied the sacroiliac joint under the loading conditions and measured the threshold of disruption and displacement of the intact

SIJ. The pelvis was exposed to three different directions of the load: transverse distraction, ventrocranial loading and dorsocranial loading (Figure10).

Figure 10. The loading directions of the SIJ. Adopted from Rothkotter et al,

1988 [32].

A. Transverse distractions, B. Ventrocranial loading, C. Dorsocranial loading.

The load-induced displacements were recorded with the transducers on the ventral part of the joint surface. Under transverse loading the length of displacement was equal to 0.9 mm under 2000 N, under ventrocranial loading the value of the displacement was 3.6 mm and under dorsocranial loading the displacement was 1.5 mm. (Figure 11).

Figure 11. Joint displacement and clamp distance at the different load. Adopted from Rothkotter et al (1988) [32].

A. Transverse distractions, B. Ventrocranial loading, C. Dorsocranial loading.

Failure of the SIJ was observed under transverse, ventrocranial, and dorsocranial loading at 3368 ±923N, 4933 ±1038 N and at 5150±947 N, respectively. Authors concluded that only a small degree of displacement occurs under physiological joint loading.

Simonian et al (1994) [33] tested an intact pelvis and a pelvis after gradual disruptions of the ligamentous structures. Each specimen was loaded with a vertical compression load, lateral bending and rotation. The obtained results from the intact

27 pelvis were compared with the modified pelvis ligaments. The following injuries were undertaken: symphysis pubis ligament disruption, one side anterior and interosseous ligaments disruption and ipsilateral sacrospinous and sacrotuberous ligaments disruption. Authors measured symphysis injured SIJ displacement and injured SIJ angulation. The loading of the intact pelvis under different condition showed the following data (Table 4).

Table 4. Motion of the intact pelvis under differing loading conditions. Adopted from Simonian et al (1994) [33].

Sacroiliac Joint Sacroiliac Joint Loading Condition Displacement (mm) Flexion Angle (deg)

Compression (400 N at neutral point of lumbar vertebra L4) 0.043 ± 0.053 0.431 ±0.378

Lateral Bend (400 N compression, 47 mm lateral to neutral 0.059 ± 0.056 0.434 ± 0.356 point)

Torsion (150 N compression at neutral point, 15 Nm 0.090± 0.092 0.124 ± 0.107 torsion)

They concluded that sectioning of the pubic symphysis did not increase motion in the

SIJ, sectioning of the anterior and interosseous ligaments increased the SIJ motion,

28 sectioning the sacrospinous and sacrotuberous ligaments had little effect on the SIJ motion (Figure 12).

Figure 12. Response of the pelvis with varying degrees of injury to compressive loading. Adopted from Simonian et al (1994) [33].

A. Injured sacroiliac joint

displacement.

B. Sacral flexion with respect

to the ilium at the injured

sacroiliac joint.

29 Previous Finite Element studies simulating pelvis

The first validated three-dimensional pelvis model was developed by Dalstra et al

(1995) [34]. CT scans of the human pelvis were used to simulate the cortical and trabecular layers of the bone. The model validation was conducted by the comparison of loading test results in vitro using the cadaveric specimen and using the FE model of the pelvis. The experimental data was obtained by the insertion of the strain gages into the lateral (Figure 13) and medial cortical shell of the human pelvis and followed forces apply which simulated an one-leg stance (Figures 14).

Figures 13. The locations of strain gauges in pelvic specimens (adopted from

Dalstra et al, 1995)

30 Figure 14. Simulation of one leg stance in FE pelvis model simulation (after

Dalstra et al, 1995)

The analysis of stresses showed increase magnitude of stress in the medial cortical shell underneath the acetabulum dome and at the superior acetabulum rim. The area with the minimal stress was in the cortical layer which surrounded the incisura ischiadica. The results were compared with the simulation the same loading condition using realistic FE human pelvis model with individual cortical shell thickness distribution and trabecular bone density. Authors used the FE model with the homogenous material properties and uniform thickness of trabecular layer to determine the influence of those parameters on predicted result. The analysis of stresses showed reasonable agreement of experimental outcomes and numerical outcomes where magnitude of both realistic and simplified model stresses were close to the cadaveric specimen stresses.

31 The next model with the outcomes being compliant with cadaveric study outcomes

was a model presented by Anderson et al (2005) [35]. Authors simulated location-

dependent cortical thickness, fine geometry and elastic modulus of the cortical and

trabecular pelvic bone. A developed model was assessed to changes in cortical bone

thickness and bone and mechanical properties of cartilage. Distinctively from Dalstra

et al study, researchers applied advanced computer technology to generate fine mesh

of the cortical and trabecular bone structure, and to calculate material properties.

Sensitivity study was conducted with experimental and assumed biomechanical

parameters which were taken from the literature (Table 5).

Table 5. Material properties and cortical thickness used in model performed by Anderson et al. Data are taken from experimentally measured values as well as data reported in literature (adopted from Anderson et al, 2005 [35]).

Type Models Analyzed Reference Thickness=±0, 0.5, 1SD (0.49 CST Experiment mm) CTEM E=45, 164, 456 MPa Experiment Thickness=1.41 mm, E=164 CST/CTEM Experiment MPa SSCV ν = 0.2, ν = 0.39 Lappi et al (1979) [36] SSTV f ν = 0.29 Oonishi et al (1983) [37] SSCM E= ± 1 SD (1.62 GPa) Snyder et al (1991) [38] Thickness 0.0, 4.0 mm ACT Experiment (min/max) ACEM E=1.36, 7.79 MPa (min/max) Armstrong et al (1979) [39]

CST - constant cortical shell thickness CTEM - constant trabecular elastic modulus SSCV - subject-specific cortical Poisson’s ratio SSTV - subject-specific trabecular Poisson’s ratio SSCM - subject-specific cortical Poisson’s ratio ACT - alteration in cortical thickness ACEM - alteration in cortical elastic modulus

Authors concluded that the model accurately predicted the cortical bone stresses

during acetabular loading. Anderson and co-authors showed moderate deviations of

32 stresses (and low sensitivity) in models with changed trabecular bone elastic modulus, and very high sensitivity of cortical strain after modulation of different cortical bone thickness and elastic modulus.

The most recent study of a developed FE pelvis model was undertaken by Leung et al

(2008) [40]. Using CT data of pelvic specimen, authors created 3-dimentional computer model and validated it against cadaveric pelvis specimen by comparing stress pattern in cortical bony shell. The next object of that study was to analyze pelvic strain as a function of cortical and trabecular layer bone density. They compared stress distribution after changes in elastic modulus of trabecular and cortical bony structures. Similar to Anderson et al findings, authors revealed high impact of cortical bone density on pelvis strain. Additionally, the impact of each cortical and trabecular elastic modulus impact was calculated. It was shown that influence of cortical bone density is 60% greater that trabecular bone density.

The other models of the pelvic bone and pelvis found in literature were either two- dimensional [41, 42] or were not validated with accuracy of FE model to predict stress values [43-45].

Previous FE studies simulating sacroiliac joint ligaments

There are a few studies which explored the sacroiliac joint ligaments using the finite element analysis. The greatest difficulties researchers faced were the complex three- dimensional geometry of bones and unknown properties of the SIJ ligaments due to small ligaments length and broad area of connection to the bone structure. Zheng et al

33 (2002) [46] overcame these difficulties by simulation of non-linear physiologic behavior of the SIJ ligaments by applying the mathematical length-tension equation of knee ligaments from the Wismans et al study (1980) [47]. Wismans et al. used force-elongation function to describe the mechanical behavior of ligaments in their mathematical model of the knee ligament. Further studies has been used the same equation in mathematical model of the knee [48, 49]. The primary pelvic model used in Zheng study (1995) [25] was based on the female cadaveric specimen. Authors generated ligaments as nonlinear elastic line elements. The individual SIJ ligament’s stiffness set and number of bundles in each ligament are listed in following Table 6.

Table 6. Ligament stiffness value used in the SIJ model performed by Zheng.

Adopted from Zheng [25].

Number of Elements Stiffness Ligament (N/m) Left Right Anterior Sacroiliac 700 20 22 Ligament+ Capsule Posterior Sacroiliac 400 11 11 Ligament (Inner Layer) Posterior Sacroiliac 1000 18 18 Ligament (Outer Layer) Intraosseous 2800 8 8 Ligament Sacrospinous 1400 15 15 Ligament Sacrospinous 1500 15 15 Ligament

34 The primary model was loaded under different load and different load directions. The

outcomes, such as main motion and coupled motion in the SIJ were estimated. After

that, the motion in SIJ were measured after changing the individual ligament’s

stiffness and impact of each ligamentous group on SIJ mobility was described. The

author found that obtained motion in the primary model had a very small magnitude

(Table 7) which was in line with outcomes of previous cadaveric studies, although the

authors did not undertake the direct comparison of numerical data with experimental

or literature data.

Table 7. Translations of the pelvic joints in the FE model after applying 1000 N

load in test performed by Zheng. Adopted from Zheng et al, 1997 [46].

Load and Posterior/Anterior Superior/Inferior Lateral (mm) Motion (mm) (mm) Direction Left Right Posterior Anterior Superior Inferior Left SIJ 0.380 0.5 1.839 1.778 1.638 1.483 Right SIJ 0.026 0.036 0.952 0.614 -0.102 -0.217

The exploration of ligament stiffness change on the SIJ mobility revealed significant

effect of sacrotuberous, sacrospinous and intraosseous ligaments properties on sacrum

inferior translation, and little effect of aforementioned ligaments on anteroposterior

translation and axial rotation of the SIJ. Author concluded, that motion in SIJ

appeared to be a complex process in multiple plans, such as transverse, frontal planes.

Additionally, rotation motions combines with translation motions. Regarding

35 ligaments stiffness properties, author concluded that increase the magnitude of that parameter in sacrospinous ligament led the SIJ motion to inferior position, increase stiffness in sacrotuberous ligament led SIJ to inferior position and also the same changes in intraosseous ligaments led to more superior SIJ motion.

The correlation approach was used by Garsia et al (2000) [43] to validate the motion in sacroiliac joint after generating SIJ ligament properties. They used noncompressive one-dimensional rods with null bending and compressive stiffness. By the adjustment of ligament stiffness, authors compared the motion in the SIJ by computer simulation of cadaveric experiment performed by Simonian et al (1994) [33]. Cadaveric test included the measurement of sacrum and pubic gap displacement in response on progressive disruption of different ligament of the SIJ with following vertical compression load applied on L4 vertebrae. The FE model was considered validated after achieving the same experimental mean of displacement in the SIJ and the pubis symphysis. Finally, Garsia et al obtained accurate prediction of motion which allowed them further to simulate the instrumentation of the pelvis and represent the response of the SIJ motion after surgical procedures.

36 Table 8. Estimated ligament stiffness and number of ligament bundles used in

FE pelvis model (adopted form Garsia et al, 2000 [43])

Number of Ligament Stiffness (N/m) elements on each side Anterior Sacroiliac 1 10 Ligament Posterior Sacroiliac 1 10 Ligament Intraosseous 292.2 132 Ligament Sacrospinous 0.028 10 Ligament Sacrospinous 0.042 12 Ligament

37 CHAPTER III

MATERIAL AND METHODS

Geometry

Computer tomography (CT) of young man’s pelvis without any abnormalities, deformities or severe degeneration of the pelvis, was used to reconstruct the pelvic bone model (IRB approval protocol # 105598).

Figure 15. CT of the pelvis and surround structures served as a matrix for FEM.

The distance between CT axial slices was 2 mm in the transverse plane. The geometry and mesh were generated with the ImageJ program

(http://rsb.info.nih.gov//ij ). The axial CT slices were transferred to ImageJ viewport and nodes coordinates were taken to reconstruct accurate geometrical copies of bony structures of each CT image scan.

38 Figure 16. Axial CT scan of the pelvis and the cross-section of the FE pelvis model on the same level after meshing and reconstruction in Abaqus 6.7.

A) CT B) Mesh (FEM)

The homogenous distribution of cortical bone thickness was chosen to represent the pelvic model.

Figure 17. CT scan of the pelvis with distinction of cortical and trabecular layers and the cross-section of FE pelvis model on the same level after meshing and reconstructing in Abaqus 6.7.

A) CT B) Mesh (FEM)

39 Bony element modeling

The CT images with defined nodes of bony margins were transferred into the commercial ABAQUS 6.7 software (Simulia, Providence, RI, USA) to create the finite element mesh. The pelvic model consisted of 32,586 hexahedral elements and

44,595 nodes and it was symmetrical across the mid-sagittal plan. Eight-node solid elements were used for modeling cancellous bone and cortical shell. The thickness of cortical shell ranged between 1 and 8 mm. The sacrum consisted of 3684 elements in cortical shell and 1384 elements in trabecular layer. The hip bone consisted of 10590 elements in cortical shell and 3169 elements in trabecular layer.

Figure 18. Initial FE pelvis model without ligamentous structures.

Sacroiliac joint modeling

To represent the SIJ in the finite element human pelvis model, a number of nodes were chosen from CT scans to determine the articular surfaces. The nodes were picked up in the way which would reproduce the shape of SIJ with its area of elevation and depression as accurate as possible. The average distance between adjacent nodes was 2 between 8 mm.

Figure 19. Axial view of the FE pelvis model through area of the sacroiliac joint.

Connected nodes represent the surface area of the joint.

10 mm

The surface area was meshed after transferring data from ImageJ program to Abaqus

6.7. Finally, the articular surface of sacrum was represented by 77 brick elements, the articulate surface of ilium bone were represented by 92 brick elements, 112 and 152 nodes, respectively.

Figure 20. The FE pelvis model with highlighted SIJ articular surfaces on the ilium and sacrum.

Modeling of Sacroiliac Joint Ligaments

The ligamentous bundles of sacroiliac joint were simulated using truss elements. The

SIJ ligaments were represented by the following ligamentous groups:

- Anterior sacroiliac joints ligament (ASL)

- Posterior sacroiliac ligament with subdivision on inner and outer layers (PSL).

- Interosseous ligament (IOL).

- Sacrotuberous ligament (STL).

- Sacrospinous ligament (SSL).

ASL was represented by 38 bundles which were attached to the points around 10-15 mm away from anterior margins of the sacroiliac joint. PSL inner layer consisted of

23 bundles with attachment points on the posterior surface of the sacrum and the ilium and around 0-3 mm away from posterior margin of the sacroiliac joint. Outer layer had 28 bundles which connected the median crest of sacrum and the points from the posterior superior iliac crest to posterior inferior iliac crest. The sacrospinous ligament had attachment points on the ishial spine and the lateral margin of sacrum and included 15 bundles. The points on the lateral margin of the sacrum and the ischial tuberosity were picked up to create the sacrospinous ligament (15 bundles also). The interosseous ligament had 110 bundles, and the attachment points of the interosseous ligament were situated posteriorly to the sacroiliac joint surfaces and they were located between the cranial and caudal limb of the auricular surfaces of both sacrum and ilium bones.

Material properties

Material properties of the pelvic bones were selected from the literature [13]. The bone tissue in all parts were defined as cancellous bone cores surrounded by cortical shells (Tables 9). The range of cortical bone thickness was 1 to 8 mm.

43 Tables 9. Material properties of bony components of FE pelvis model. Adopted from Dalstra et al, 1995 [34].

Young’s Modulus PART Poisson’s Ratio (MPa)

Cortical Bone 17000 0.3

Cancellous Bone 70 0.2

The properties of the SIJ ligaments were generated using data from a previous experimental study of the biomechanics of the knee anterior cruciate ligament [50].

The individual Young modulus for each ligamentous group of the SIJ was calculated with consideration of stiffness differences using data from Zheng’s et al (1995) [25].

The obtained properties are listed in Table 10.

Table 10. Material properties of ligamentous structures of FE pelvis model

Poisson’s PART Young’s Modulus (MPa) Ratio

Anterior Sacroiliac 125(<2.5%),175(>5%),325(>10%),316(>15%) 0.3 Ligament

Inner Posterior Sacroiliac 43(<2.5%),61(>5%),113(>10%),110(>15%) 0.3 Ligament

Outer Posterior Sacroiliac 150(<2.5%),211(>5%),391(>10%),381(>15%) 0.3 Ligament

Intraosseous Ligament 40(<2.5%),57(>5%),105(>10%),102(>15%) 0.3

Sacrospinous Ligament 304(<2.5%),428(>5%),792(>10%),771(>15%) 0.3

Sacrotuberous Ligament 326(<2.5%),458(>5%),848(>10%),826(>15%) 0.3

44 The cartilaginous layer between the contact surfaces of the SIJ was simulated using

ABAQUS’s “softened contact” parameter, which adjusted the force transfer across the joint depending on the size of the gap exponentially. At full closure, the joint assumed the same stiffness as the surrounding bone [51].

Finite Element Model Validation

The validation study was based on simulation of different loadings and their directions from previous cadaveric studies which investigated the biomechanical behavior of the intact and injured sacroiliac joint, and stress distribution across cortical bone of the pelvis. Numerical data was compared with the results which were reported in literature.

According to Miller et al study (1987) [31], the center of the sacrum was defined as a point located in the midsagittal plane, midway between the inferior S1 and superior

S2 vertebral endplates and the anterior and posterior margins of the articular SI joint surfaces viewed laterally. The average values of the center point to corresponding superior S1 endplates were used in simulation. The center was located 29 mm inferiorly and 11.5 mm posteriorly to the center of the superior point of S1 endplate.

Figure 21. Midsagital section of the FE sacrum model with marked center point.

11.5 mm

29 mm

The boundary condition were simulated as 1)both iliac bones were fixed, and 2)one iliac bone was fixed. The load was equal to 294 N and the moment was equal 42 N- m. The load directions were oriented along the superior S1 endplate in anterior, posterior and lateral shear forces, normal to S1 endplate in case of inferior and superior shear forces.

Figure 22. Midsagittal FE sacrum model section with force directions.

The displacements (mm) and rotations (degs) value of the sacrum center were compared with mean value of the displacement and rotation from cadaveric study.

Second study of the intact FE pelvis model was based on previous cadaveric study conducted by Rothkotter et al (1988) [32]. Authors evaluated failure load and displacement of the SIJ under several loading conditions. According to a researcher’s test description, a simulation of transverse distraction, ventrocranial and dorsocranial loading were conducted after defining the boundary conditions (Figure 23).

47 Figure 23. Simulated force directions according to Rothkotter et al experimental study (1988)

A B C

The displacement of the sacroiliac joint margin was measured as a difference of distance between two points on the ventral surface of the SIJ before and after load simulation. The test included the measurement of displacement in 500 N, 1000 N,

1500 N and 2000 N in transverse loading direction, and the measurement of displacement in 500 N, 1000 N, 1500 N, 2500 N and 3000 N in ventro-and dorsocranial loading directions. Numerical data were compared with in-vitro outcomes.

The investigation of biomechanics of destabilized SIJ was conducted by simulation of in-vitro SIJ motions performed by Simonian et al (1994) [33]. Authors undertook investigation of biomechanical behavior of the SIJ after progressive injury of the SIJ ligamentous structures and after following fixation of destabilizing SIJ. They used

48 L4-S1-pelvis-proximal femur cadaveric complex. To reproduce the same loading condition, additional details were added to the current pelvis model. Authors applied chain with attachment to the pelvis and the ground to provide stability in both hip joints. To maintain stability in FE model, the model was constrained in both acetabulum surfaces, therefore the motions in the hip joint were constrained in all directions. Next modification was done in direction of applied force. The load direction on superior S1 endplate were chosen according to the average value of lumbar-sacral angle (30 degree).

Figure 24. Pelvic FEM with constrained area (A) and load direction (B) according to Simonian et al study (1994) [33].

30º

A B

The intact model was modified to simulate the progressive injury of the ligamentous complex. The following ligaments were disrupted in sequence: 1) pubic symphysis

(injured SP), 2) left side anterior and intraosseous sacroiliac (injured SP-SI). The

49 acetabelum surfaces were fixed in all 6 degrees of freedom to simulate the initial boundary condition. A 400 N compressive force was applied to S1 with an angle of 60º with respect to endplate (representing lumbosacral angle). The sacrum angular motions data and sacroiliac joint displacement were measured and obtained results were compared with in-vitro data.

To investigate stress distribution across the pelvic bone, the loads and constrained areas were simulated from experimental and numerical study performed by Dalstra et al (1995) [34]. The proximal part of femur was added to form a hip joint, but the motions in it were restricted in all 6 degree of freedom. The one leg stance was achieved by alignment of the anterior superior iliac spines and the pubic symphysis in a coronal plane, the ischial tuberosities in a horizontal plane, and the shaft of the femur in a coronal plane [52] (Figure 25)

50 Figure 25. Loading and boundary condition simulated in the FE analysis of the pelvis according to Dalstra et al study (1995) [34].

After Dalstra et al, Tested FE model of pelvis 1995

The Von Mises stress was calculated as average value of stress in area which corresponded to locations on rosette stain gages from experimental study.

Figure 26. Locations of the strain gages in experimental study and area on the

FE pelvic surface where calculation was performed.

After Dalstra et al, 1995

Tested FE model of pelvis

51 The axis of rotation (AR) was defined in each case of pelvis loading when angular motions of sacroiliac joint were achieved as a result of application of moment force in sagittal plane (flexion and extention). To calculated the AR, two nodes were selected at the mid-sagittal plane passing through center of the segment, then the motion of the nodes were captured and based on their displacement, two lines each connecting between initial and displaced coordinated of each node were drawn. Then for each of these lines, a perpendicular line passing through the center of the line was defined and finally the intersection of these two perpendicular lines defined the AR.

52 CHAPTER IV

RESULTS

Simulation of Miller et al cadaveric study (1987)

After simulation of loading and boundary condition and applying 294 N compressive load, the displacement of the sacrum center was measured. The smallest motion in both ilia fixed were found in medial force direction (0.22 mm). The motions were larger in anterior and posterior shear forces (0.66 and 0.64 mm, respectively) and were the largest in anterior load application. In condition when one left iliac bone was fixed, the smallest motion was observed in medial force direction also (0.89 mm), and the maximum value corresponded to anterior and posterior shear forces (2.67 and

2.86 mm, respectively). The release of one ilium led to considerable increase of displacement magnitude. The displacement in anterior and posterior direction increased four time. (2.67 vs 0.66 mm and 2.86 vs 0.64 mm, respectively). Five times increase of displacement was observed in superior load direction (2.21 vs 0.39 mm) and four time increase of sacrum center displacement was received after applying a load in medial direction (0.89 vs 0.22 mm) (Table 11).

53 Table 11. Displacement of the center of the sacrum (mm) in the FE pelvis model after simulation Miller et al (1987) cadaveric study [31].

Test Both Ilium Left Ilium Load Direction Fixed Fixed

Anterior 294 N 0.66 2.67

Posterior 294 N 0.64 2.86

Superior 294 N 0.39 2.21

Inferior 294 N 0.53 1.23 Medial 294 N 0.22 0.89

In testing of angular motions with a moment of 42 N-m and both ilium fixed, the smallest motions were observed in lateral bending and torsion (0.21 and 0.19 deg, respectively) and the largest one was corresponded to flexion and extension (0.9 and

0.88 deg, respectively). After one iliac bone was released, the range of motion increased substantially in torsion and lateral bending. A sixteen times increase was observed in applying 42 N-m in torsion (3.272 in one ilium fixed vs 0.21 deg in two iliac bone fixed) and seven times increase of displacement value was observed in lateral bending (1.49 deg vs 0.19 deg, respectively) The extension and flexion was not such sensitive to release of one ilium. Twofold increase in sacrum center angular motion was received in extension (1.87 vs 0.88 deg in one ilium fixed and two ilium fixed, respectively) and these values increased 1.4 times after flexion test (1.26 and

0.9 deg in one ilium fixed and two ilium fixed, respectively). The SIJ was the stiffest

54 in lateral bending and both iliac bone fixed (0.21 deg) and the smallest value was observed in flexion in just only one iliac bone fixed (1.26 deg) (Table 12).

Table 12. Displacement of the center of the sacrum (mm) in the FE pelvis model after simulation Miller et al (1987) cadaveric study.

Test Both Ilia Left Ilium Load Direction Fixed Fixed

Flexion 42 N-m 0.9 1.26

Extension 42 N-m 0.88 1.87 Lateral 42 N-m 0.21 1.49 bending Torsion 42 N-m 0.19 3.272

The axis of rotation was defined in mid-sagittal plane of the pelvis model. The AR located at lower posterior border of the S3 vertebra in extension and it located at lower anterior border of the S3 vertebra (Figure 27). Those areas corresponded to inferior margin of caudal part of articular surface of the sacroiliac joint.

55 Figure 27. Section of pelvis model through mid-sagittal plane with marked axial of rotation in extension and flexion.

1. – AR in flexion 2. – AR in extension

Simulation of Rothkotter and Berner experimental study (1988)

After modeling a boundary condition, the loads were applied with increased magnitude after each loading accordingly to original study. SIJ motions seemed to be the stiffest in transverse loading direction with maximum SIJ displacement of 0.58 mm after 2000 N load value. The values of SIJ displacement were 0.2, 0.31, 0.4 and

56 0.58 mm in 500, 1000, 1500 and 2000 N load, respectively. Adding of the next 500 N to the previous load caused increase displacement value on 0.09-0.18 mm (Table 13)

Table 13. Sacrum displacement in the FE pelvis model after simulation cadaveric study (Rothkotter et al, 1988 [32]) and applying transverse loading direction.

Load SIJ Displacement (mm)

500 N 0.2

1000 N 0.31

1500 N 0.4

2000 N 0.58

After simulation of ventrocranial load direction by increasing load value from 500 N to 3000 N, the SIJ displacement increased from 0.89 mm in 500 N load to 1.05, 1.99,

2.25, 2.34 and 2.38 mm in 1000, 1500, 2000, 2500 and 3000 N, respectively. The difference in displacement value lied in the range 0.04- 0.26 mm after adding each time the equal amount of 500 N to the previous loading set. The measured parameter was less than 2 mm in loading value up to 1500 N (Table 14)

57 Table 14. Sacrum displacement in the FE pelvis model after simulation cadaveric study (Rothkotter et al, 1988 [32]) and applying ventrocranial loading direction.

Load SIJ Displacement (mm)

500 N 0.89

1000 N 1.05

1500 N 1.99

2000 N 2.25

2500 N 2.34

3000 N 2.38

The SIJ displacement in dorsocranial load direction increased from 1.25 mm in 500 N to 2.38 mm in 3000 N. The values of displacement in 1000- 2500 N load were almost the same as in ventrocranial load direction. The range of difference in measured parameter after increase loads were not steady like in previous loading set and it lied in 0.05- 0.36 mm interval (Table 15).

58 Table 15. Sacrum displacement in the FE pelvis model after simulation cadaveric study (Rothkotter et al, 1988 [32]) and applying the load in dorsocranial direction.

Load SIJ Displacement (mm)

500 N 1.25

1000 N 1.61

1500 N 1.80

2000 N 1.95

2500 N 2.15

3000 N 2.34

Simulation of Simonian et al. (1994) cadaveric study.

After reconstructing the loading and boundary condition of the original study (see above), comprehensive loading was applied with progressive ligaments injury.

Several parameters were measured, such as SI joint displacement and sacrum angular motion. The obtained results are showed in tables 16 and 17.

The sacrum angular motions did not change after cutting of symphysis pubis ligaments and remained equal to the sacrum angulation of the intact pelvis (0.35 deg before and after SP cut simulation). The disruption of the anterior sacroiliac and intraosseous ligaments led to increased motion from 0.35º to 0.6º deg. After

59 sactotuberous and sacrospinous ligament, the sacrum angular motion increased negligibly from 0.6 to 0.63 mm. (Table 16)

Table 16. Sacrum angular motion in the FE pelvis model after simulation

Smonian et al (1994) experimental study [33].

Sacrum Angular Type of Injury Load Motion

Intact 400 N 0.35

SP Cut 400 N 0.35

SP-SI Cut 400 N 0.6

SP-SI-SS-ST Cut 400 N 0.63

The measurement of the SIJ gap displacement after progressive SIJ ligaments disruption showed a small value of angular sacrum motion after cutting of SP (0.8 mm). The magnitude was not changed comparing with the SIJ gap displacement in intact model (0.8 mm). The removal of anterior and intraosseous ligaments led to the gap increased by 0.58 mm. The value was remained the same after SS and ST ligaments removal (0.58 mm) (Table 17).

60 Table 17. Sacroiliac joint gap displacement in the FE pelvis model after simulation of Simonian et al (1994) experimental study [33].

Type of SIJ Gap Displacement (mm) Load Injury Intact 400 N 0.08

SP Cut 400 N 0.08

SP-SI Cut 400 N 0.58 SP-SI-SS-ST 400 N 0.58 Cut

Simulation of Dalstra et al. experimental study (1995).

After imitation of one leg stance, the ilium was constrained and a 600 N load was applied on the top of distal femur part. The highest magnitude of average stress was observed in the interior side of acetabular region and superior acetabular rim (4.86,

6.13, 3.51 and 4.92 MPa in area corresponded to location #1, #2, #3 and #8 strain gages in experimental study). The areas with the highest stress values matched with the areas where the force was applied through the femur to pelvic bone. The smallest value was found in the area adjusted to incisura ischiatica and ilium ala (3.31 and

1.48 MPa in the area corresponded to location #7, #6 strain gages in experimental study) (Table 18)

61 Table 18. The average von Mises stresses found in a numerical study after simulation Dalstra et al (1995) experiment and applying 600 N load [34].

Location of strain Von Mises Stress Load gages (MPa) #1 600 N 4.86

#2 600 N 6.13

#3 600 N 3.51

#4 600 N 2.57

#5 600 N 4.06

#6 600 N 1.48

#7 600 N 3.31

#8 600 N 4.92

Statistical Analysis

For model validation, the statistical analysis of obtained results was undertaken using the method previously used for validation of the FE lumbosacral spine model [53].

The mean of values and their standard deviation from experimental studies published in literature was compared with numerical results of the FE tests. In case if predicted response fell in the range of standard deviation, the model was considered validated for those specific mode loads.

After simulation of Rothkotter et al study (1988) [32], the values of the SIJ displacements in ventrocranial loading direction were close, but did not get into 1 SD

62 interval in 500 - 1000 N load (0.36 (±0.16) and 0.89, 0.78 (±0.21) and 1.05 in 500 and

1000 N load, respectively), and it was inside 1 SD interval in 2500 and 3000 N load

(1.68 (±0.67) and 2.34, 1.82 (±0.83) and 2.38 in 500 and 1000 N load, respectively).

The overestimation of SIJ displacement was observed comparing the values from experimental study (Figure 28).

Figure 28. Comparison of sacrum displacement in simulated FE pelvis model and in cadaveric study (Rothkotter et al, 1988) after applying ventrocranial loading direction.

SIJ Displacement (mm) Displacement SIJ 0 500 N 1000 N 1500 N 2000 N 2500 N 3000 N

Rothkotter et al (1988) FE Pelvis Model

SIJ Displacement Load Rothkotter et al Our Model (1988) 500 N 0.36 (0.16) 0.89 1000 N 0.78 (0.21) 1.05 1500 N 1.1 (0.36) 1.99 2000 N 1.5 (0.6) 2.25 2500 N 1.68 (0.67) 2.34 3000 N 1.82 (0.83) 2.38

63 Comparison of numerical results of the SIJ displacement in dorsocranial load direction with cadaveric data showed that in the FE study the values were in line with mean and 1 SD in 1000, 1500 and 2000 N load (1.23(±0.82) and 1.61, 1.95 (±0.97) and 1.8, 2.66 (±1.1) and 1,80 in 1000, 1500 and 2000 N load, respectively).

Displacement after applying 500 N led to larger displacement in the FE pelvis model study than in the experimental study (0.5 (±0.29) and 1.25). The value of measured parameter in 3000 N in the FE test was lower than mean and 1 SD in cadaveric test

(4.27 (±1.12) and 2.34).

64 Figure 29. Comparison of sacrum displacement in simulated FE pelvis model and in cadaveric study (Rothkotter et al, 1988) after applying dorsocranial loading direction.

SIJ Displacement (mm) Displacement SIJ 0 500 N 1000 N 1500 N 2000 N 2500 N 3000 N

Rothkotter et al (1988) FE Pelvis Model

SIJ Displacement Load Rothkotter et al Our Model (1988) 500 N 0.5 (0.29) 1.25 1000 N 1.23 (0.82) 1.61 1500 N 1.95 (0.97) 1.80 2000 N 2.66 (1.1) 1.95 2500 N 3.38 (1.11) 2.15 3000 N 4.27 (1.12) 2.34

Analysis of transverse loading in Rothkotter et al study (1988) [32] showed that values of the SIJ displacement in FE study were beyond of 1 SD of experimental study, and the actual magnitudes were lower than values in cadaveric test (0.62

(±0.21) and 0.2, 1.16 (±0.21) and 0.31, 1.89 (±0.34) and 0.4, 2.58 (±0.3) and 0.58 in

500, 1000, 1500 and 2000 N load, respectively). However, the progressive increase of measured parameter was observed after each test (Figure 30).

65 Figure 30. Comparison of sacrum displacement in simulated FE pelvis model and in cadaveric study (Rothkotter et al, 1988) after applying a transverse loading direction.

SIJ Displacement (mm) Displacement SIJ 0 500 N 1000 N 1500 N 2000 N

Rothkotter et al (1988) FE Pelvis Model

SIJ Displacement Load Rothkotter et al Our Model (1988) 500 N 0.62 (0.21) 0.2 1000 N 1.16 (0.21) 0.31 1500 N 1.89 (0.34) 0.4 2000 N 2.58 (0.3) 0.58

The FE study outcomes were compared with experimental data of Simonian et al study (1994). The values of sacrum angular motions were in line with the cadaveric study and lied inside 1 SD interval in intact model, SP Cut model, SP-SI Cut model

(0.41 (±0.38) and 0.35, 0.41 (±0.34) and 0.35, 0.83 (±0.25) and 0.6, 0.98 (±0.25) and

0.63 in intact, SP Cut and SP-SI Cut model). The result after SP-SI-SS-ST Cut model

66 simulation was close to experimental mean and SD interval, but was lower than SD

(0.98 (±0.25) and 0.63) (Figure 31).

Figure 31. Comparison of the sacrum angular motion in experiment and FEM simulation after different injuries.

0 Sacrum Angular Motion (deg) Intact SP Cut SP-SI Cut SP-SI-SS-ST Cut

Rothkotter et al (1988) FE Pelvis Model

Sacrum Angular Motion Type of Load Injury Simonian et Our Model al (1994) Intact 400 N 0.41 (0.38) 0.35 SP Cut 400 N 0.41 (0.34) 0.35 SP-SI Cut 400 N 0.83 (0.25) 0.6 SP-SI-SS- 400 N 0.98 (0.25) 0.63 ST Cut

Analysis of the SIJ gap displacement showed good agreement of simulated FE model data with experimental data. Numerical results after running the test with loading and boundary condition taken from previous experiment got into 1 SD in each tested

67 model (0.1 (±0.08) and 0.08, 0.1 (0.078) and 0.08, 0.46 (±0.25) and 0.58, 0.4 (±0.25) and 0.58 in in intact, SP Cut and SP-SI Cut, SP-SI-SS-ST Cut model, respectively).

Figure 32. Comparison of intact and injured sacroiliac joint gap displacement in the FE pelvis model with cadaveric study (Simonian et al. 1994).

0.5

0 Sacrum Angular Motion (deg) Intact SP Cut SP-SI Cut SP-SI-SS-ST Cut

Rothkotter et al (1988) FE Pelvis Model

SIJ Gap Displacement (deg) Type of Load Injury Simonian et Our Model al (1994) Intact 400 N 0.1 (0.38) 0.08 SP Cut 400 N 0.1 (0.34) 0.08 SP-SI Cut 400 N 0.46 (0.25) 0.58 SP-SI-SS- 400 N 0.4 (0.25) 0.58 ST Cut

Comparison of experimental study result performed by Dalstra et al (1995) [34] with the FE study showed that, although, the value of numerical test were nearby the value in cadaveric test (4.21 (±0.28) and 4.86 in #1, 5.23 (±0.2) and 6.13 in #2, 2.72

(±0.22) and 3.51 in #3, 5.15 (±0.43) and 4.06 in #5, 2.03 (±0.76) and 1.48 in #6, 1.04

68 (±0.28) and 3.31 in #7, 6.73 (1.05) and 4.92 in #8), only in #4 strain gage location the value was inside SD interval (1.92 (±0.65) and 2.57 in #4) (Figure 33).

Figure 33. The average von Mises stresses found in the experiment (Dalstra et al,

1995) and numerical study at a load 600 N.

Sacrum Angular Motion (deg) 0 #1 #2 #3 #4 #5 #6 #7 #8

Rothkotter et al (1988) FE Pelvis Model

Location Von Mises Stress (MPa) of strain Load Dalstra et al Our Model gages (1995) #1 600 N 4.21(0.285) 4.86 #2 600 N 5.23(0.2) 6.13 #3 600 N 2.72(0.22) 3.51 #4 600 N 1.92(0.65) 2.57 #5 600 N 5.15(0.43) 4.06 #6 600 N 2.03(0.76) 1.48 #7 600 N 1.04(0.28) 3.31 #8 600 N 6.73(1.05) 4.92

The statistical comparison of data from cadaveric study performed by Miller et al

(1987) [31] and results from the FE study was not conducted due to no significant experimental value in the original study. The mean of measured parameters and their

69 SD are introduced in tables 19 and 20. The descriptive comparison is undertaken in discussion chapter.

Table 19. Comparison of the mean displacement (mm) of the center of the sacrum in cadaveric [31] and numerical studies.

Test Both Ilium Fixed Left Ilium Fixed Directi Load on Miller Our Miller Our et al Model et al Model Anterior 0.48 2.74 294 N 0.66 2.67 (0.38) (1.07) Posterior 0.53 1.58 294 N 0.64 2.86 (0.75) (1.69) Superior 0.28 1.87 294 N 0.39 2.21 (0.25) (1.76) Inferior 0.26 0.99 294 N 0.53 1.23 (0.25) (0.43) Medial 0.01 0.76 294 N 0.22 0.89 (0.08) (1.41)

70 Table 20. Comparison of the rotation mean (deg) of the center of the sacrum in cadaveric [31] and numerical studies.

Both Ilium Fixed Left Ilium Fixed

Test Rotation (deg) Rotation (deg) Directi Moment Miller Miller on Our Our et al et al Model Model (1987) (1987) Flexion 1.31 42 N-m 1.26 (0.6) Extension 1.94 3.52 42 N-m 0.88 1.87 (1.29) (1.46) Lateral 0.37 1.4 42 N-m 0.21 1.49 bending (0.27) (0.71) Torsion 0.8 6.21 42 N-m 0.19 3.272 (0.51) (3.29)

71 CHAPTER IV

DISCUSSION

Finite Element Analysis is an effective accurate numerical method of computer simulation of objects to calculate their response (deformation, strain, stress) after applied structural loads such as force, pressure and gravity. It is broadly used in engineering to analyze many types of problems, for example in heat transfer, fluid dynamics, and electromagnetism. Growing computer technologies and advance computer processing power allows a simulation of such subjects as bony structures, ligaments and muscles of human body. More advanced technology and software allowes simulating even more complex configurations (biological systems or models) consisted on several structures. There are many finite element models, for example models of brain and cranium [54,55], liver [56], lumbar and cervical spine with included bony structures, ligaments, intervertabral disks [57-61].

The prevalense of back pain syndrome in population, advance in imaging studies and growing of capability in minimally invasive surgery increased a popularity of Finite

Element Methods substantially for the last decade. Determination of stresses and displacement became a very valuable tool in predicting a biological response after simulation such conditions as congenital structural anomaly of the spine, fractures, applied instrumentation [62-65]. FE method became very popular in designing spinal instrumentation where the virtual prototype of implant may be refined and optimized

72 in shape, geometry and material properties based on analysis of stresses and displacements in biological objects and implants.

The first step in FEA of any structure is a developing its virtual prototype with the same surface geometry, shape and material properties. This can be done by utilizing 2 dimensional or 3 dimensional computer technologies. Regarding a history of developing finite element model of the pelvis, the first 3D validated FE model of pelvic bone was performed by Dalstra et al (1995) [34], one of the first subject- specific validated model was developed by Anderson et al (2005) [35]. Both authors created advanced model with simulated cortical bone thickness distribution, accurate bone geometry [Anderson], and close to in vivo cortical, trabecular bone and cartilage material properties. One of the disadvantages of both studies was a simulation just only one of the pelvic component- hip bones. Pelvis is a complex polycomponent structure; therefore the developing of whole anatomic model would give opportunity to predict the biomechanical behavior of pelvis more accurately under any modulated conditions. The attempt to process the entire pelvis with simulated sacroiliac joint ligaments was conducted by Garsia et al (2000) [43]. Authors validated the biomechanical behavior of the SIJ ligaments against data from experimental study performed by Simonian et al (1994) [33]. Our model simulated whole pelvis components which was similar to Garsia et al FE model of the pelvis, however the properties of the sacroiliac joint ligaments had non-linear physiological properties

(linear properties in Garsia et al study), the FE mesh was fine and more accurate. The

73 distance between CT scans used to pre-process pelvis geometry was 2 mm (8 mm in

Garsia et al study). As a result of more laborious meshing, the FE pelvis model in our study had 44,595 nodes (4968 nodes in Garsia et al study) and 32,586 elements (6425 total amount of elements in Garsia et al model). It is known fact in finite element modeling that the accuracy of the model prediction depends on number of nodes and elements used in the model. Therefore, we may suggest that our FE pelvis model is more realistic in predicting pelvis biomechanical response on different loading condition than previous one.

The biomechanical behavior of any object is highly depended on its biomechanical properties and specific anatomical features, such as elasticity which is characterized by resistance material to strain forces (Young modulus), characteristic of material to become narrower when stretched force is applied (Poisson’s ratio), and cortical bone thickness. Previous studies utilizing tensile techniques revealed that average value of

Young modulus for cortical bone equal to 18.6 GPa [66,67], this value was equal to

70-250 MPa for pelvic trabecular bone [34]. In developing FE pelvis model, previous studies assumed Young modulus = 17 GPa for cortical bone [34,35], Young modulus

= 70 Gpa [34,43] for trabecular bone. Cortical bone thickness was determined by measuring distance between outer surface of cortical bone and boundary between cortical bone and cartilage bone in Anderson et al study (2005) [35]. The estimated value was 1-4 mm. As in any biological subject, it was shown that properties of pelvis are not equally disturbed along the pelvic bone. Anisotropy was revealed in all above mentioned studies evaluated structural properties of the pelvic bone [34,35,68]. In the

74 current study, the homogenous distribution of Yong modulus, Poisson’s ratio and cortical bone thickness was assumed. This assumption was based on results of comparison of the FE pelvis model with subject-specific versus homogenous properties distribution to predict the strain and stress distribution in their prototypes.

Both studies [34,35] showed that the difference was not substantial and both models predicted strain similar to subject-specific models results.

The evaluation of ligaments properties such as stiffness and stress-relaxation gave unique opportunity to researchers and clinicians to clarify some of the clinical aspect of joint pain syndromes, for example in knee joint problems [69,70], shoulder ligaments trauma and their repair [71,72]. The study of SIJ ligaments might also open some light on origin and pathogenesis of the sacroiliac joint syndrome, however, at this time, the extensive search of literature did not reveal any information regarding experimental studies of biomechanical properties of the SIJ ligaments. The reason of information scarcity is based on unique anatomy of SIJ ligaments. They are very short relatively to any ligaments in human body and they have very wide area of attachment to bony structures. It makes them very difficult to test. However, FE models of pelvis with reliable ligaments simulation were developed despite on above mentioned circumstances. Zheng [25] used Wismans equation which described the non-linear behavior of anterior cruciate ligament of knee joint [47] to generate properties of ligaments. We used the same approach and generated their non-linear property by calculating Young modulus based on Butler et al experimental study where stress-strain dependence of ACL of knee was presented as a result of tensile

75 test [50]. The individual stiffness of each ligament bundle was adopted from the FE study of Zheng [25].

Validation is a process of checking if a developed product satisfies a certain criteria.

In pelvis biomechanics and in spine biomechanics as well, the cadaveric study serves as a “gold standard” to obtain a value of those criteria which is the most accurate to in vivo condition. There were two ways applied in validation of the FE pelvis model.

The first one used subject-specific FE model and its real prototype [34,35]. Virtual and original prototypes were subjected to the same loading and boundary conditions and the final results were compared to each other. The second way utilized the data from previous experimental studies to compare the numerical data after simulating the same loading conditions [43]. Current FE study of pelvis applied the last method, however the model was compared against several modes, such as sacrum angular motion, sacroiliac joint displacement, sacroiliac joint gap displacement, stress distribution versus one mode in all previous studies (sacrum angular motion in Garsia et al study [43], stress distribution in Dalstra et al study [34], Anderson et al study

[35]). The numerical value of measured parameters and pattern of parameter changes were compared with the mean and standard deviation of the mean from literature data.

Analysis of Miller and Rothkotter experimental studies [31, 32] simulation showed that the SIJ was most stiff in axial rotation, medial direction of loading and lateral bending. This observation might be explained by the spatial ligament bundles

76 orientation, where applied forces were in almost the same plane as ligament bundles orientation but in opposite direction to ligament resistance forces. The obtained result was in line with the Miller et al study [31], however Rothkotter et al [32] result revealed, that load at the medial direction led to almost the most prominent SIJ displacement in their test series. This fact might be explained by the cadaveric study design specifics. The followed loads in the different directions of the same SIJ might lead to increase laxity in SIJ. The disproportion of the Miller result and Rothkotter results in comparable loading conditions were noticed previously [32]. Authors explained them by the different chosen technique to measure sacrum displacement.

Miller et al chose to measure a center of sacrum when Rothkotter chose to measure the displacement of node near anterior surface of joint space. The measurement of the nodes displacement on ventral surface of the SIJ in Miller et al study simulation showed values closed to Rothkotter data. Thus previous suggestion was confirmed.

Comparison of sacrum angular motion and the SIJ displacement results showed that simulation of applied moment force to the sacrum led to outcomes which had statistically insignificance difference comparing with Simonian et al experimental study outcomes. At the same time, modeling of applied forces along sacrum axis as

Rothkotter et al conducted in their study, caused displacement where values were above of the displacement means and above of 1 standard deviations of the means.

Those two observations might be a consequence of the SIJ modeling specifics. The major curves and nonlinearity of the SIJ were simulated in pre-processing stage of the

FE pelvis model development; therefore moment force application might lead to more

77 extent contact between sacroiliac joint surfaces which ultimately restricted motion in

SIJ in a more effective way. Another observation which may support our suggestion was found in comparing the SIJ gap displacement of FE study and cadaveric test. The disruption of anterior and intraosseous SIJ ligament caused increase SIJ gap after applied moment force in both simulated and original studies. Therefore, it also might be caused by more extensive contiguity of articular surfaces which led finally to increased distance between SIJ ventral boundaries. Interlocking mechanism is described as the phenomenon in SIJ biomechanics which restricts SIJ motion by interlocking SIJ articular surfaces. We believe that these two observations (decreased sacrum angular motion in intact SIJ and increase SIJ gap with increase sacrum angular motion after ASL and IOSL sectioning) reflect above-mentioned mechanism.

Simonian et al cadaveric study [33] simulation revealed a good agreement between numerical outcomes and experimental results. Sacrum angular motion remained the same after symphysis pubis cutting with increased value of motion after ASL and

IOSL cutting. There was not substantial motion increase after STL and SSL cutting.

The difference between numerical value of the sacrum angular motion, SIJ gap displacement and experimental data were not statistically significant in all settings.

Some previous experimental studies came to conclusion that STL and SSL do not have considerable influence on the SIJ mobility, also [73]. We suggest that influence is existed, but the SIJ is surrounded by the strongest ligaments of the human body,

78 therefore applied force value was not probably enough to evaluate the changes in SIJ mobility after STL and SSL disruption.

Statistical analysis of the Miller et al study simulation was not undertaken due to statistically insignificant difference in values of sacrum center displacement under different loadings in original study. The overall comparison of measured parameter pattern changes showed that the most prominent motion were found after simulation anterior and posterior load direction, and after flexion and extension after applied moment force which were in line with experimental study. The smallest values were also corresponded to the same loading settings as Miller at al study had (medial load direction, lateral bending and torsion). Previous studies of sacroiliac motion found most prominent motions in flexion and extension [74,75], therefore, our data were in line with them, also.

Simulation of Dalstra et al experimental study (1995) [34] with estimation of average stress values across iliac bone showed that the highest value corresponded to area where force was applied. As in original study, those areas were the superior rim of acetabulum and interior surface of acetabular cap. Although, the absolute values were beyond 1 standard deviation of the means of cadaveric study, the pattern of stresses changes across iliac bone surface was similar to original study.

79 As mentioned, to statistically evaluate the results of our study we adopted a method used previously for validation FE biological models [34,43]. The models in those studies were validated against their original prototype despite the fact that some of the numerical outcomes did not corresponded to experimental results. These observations need to clarify such terms as statistical significance and practical significance.

According to statistical analysis, if two values have “statistically significant difference” they are different. Applying to the FE modeling, it means that this model does not predict exact value of measured parameter in these specific loading settings.

However, from practical perspective of the FE pelvis model simulation, the values of the SIJ displacement, sacrum angular motion, sacrum center displacement are very small, the difference in obtained numerical result and results in experimental studies are close to each other and the pattern of parameter changes in the FE model tests are similar to experimental data changes. Therefore, we concluded that current FE pelvis model is capable to predict sacrum angular motions, SIJ displacement, SIJ gap displacement, stress-distribution close to realistic situation and can be used for comparative studies especially. For exact value of measured parameter, more elaborate subject-specific model is required.

CHAPTER VI

CLINICAL APPLICATION

Introduction

Despite careful patient selection and advanced spinal fusion techniques, the frequency of failed back surgery syndrome (FBSS) still exists in 20 to 30% [76,77]. This syndrome constitutes a heterogeneous group of patients who have a similar scope of debilitating pain after surgical procedures [78]. Prevalence of sacroiliac joint involvement in post-fusion LBP ranges from 29 to 40% [79-81]; however, the exact frequency of sacroiliac dysfunction in a population suffering from LBP after lumbar fusion is unknown. This can be attributed to the lack of high sensitivity and specificity of clinical tests [82], and perhaps the infrequent use of anesthetic blocks in clinical settings due to its potential risks and high degree of difficulty for the procedure [83, 84].

The description of differences in biomechanical patterns of sacroiliac joint behavior after lumbar fusion in the literature is sparse. Frymoyer et al (1978) conducted clinical study of sacrum motion in patients after lumbar fusion; however, due to low test sensitivity, they did not find significant differences in data compared to the control group [85]. Four studies have delineated the evidence of sacroiliac joint dysfunction in patients with LBP after lumbar spine surgical procedures. Two studies showed the effect of sacroiliac joint anesthetic block on pain relief [77,78]. The other

81 two studies found increased sacroiliac joint uptake by SPECT (Single Photon

Emission Computed Tomography) and bone scintiography in patients after lumbar

laminectomy and fusion [86,87]. To our knowledge, there is a lack of biomechanical

evidence to support an association of LBP with sacroiliac joint syndrome in this

group of patients. The biomechanical simulation of these procedures have not been

conducted yet. In general, these studies can be undertaken using cadaver experiments

or an analytical model. Cadaver studies would involve entire block of lumbar spine

connected to pelvis, and it would be very technically demanding (due to extremely

small motions at the SI joint) and expensive. Furthermore, it is impractical to quantify

stresses across the joint. In this light, the finite element analysis would be well suited.

We hypothesized that lumbar fusion leads to increased motion and stresses across the

sacroiliac joint after posterior lumbar fusion. We also hypothesize that the magnitude

of increase in these parameters is related to the number of segments fused (single vs

multiple). To test our assumption we simulated posterior fusion procedures across

different levels of the lumbar spine and sacrum in a three-dimensional nonlinear

experimentally validated ligamentous lumbar spine-pelvis finite element model and

computed sacrum angular motion and average stresses in sacroiliac joint articular

surfaces in response to external loads.

Material and Methods

To generate a Spine-Pelvis model, a n experimentally validated 3-dimensional, non- linear FE model of the intact L3-S1 segments was used. This model has been

82 previously used to investigate a number of clinical cases [88-91], including the biomechanics of the minimally invasive procedure [92]. The material properties of lumbar spine model were adapted from our previous studies and are presented in Table

21 [93-96].

Table 21. Material properties of L3-S1 lumbar spine finite element model components. Adapted from our previous studies [93-96].

Poisson’s PART Young’s Modulus (MPa) Ratio

Cortical Bone 12000 0.3

Cancellous Bone 100 0.2

Posterior Bone 3500 0.25

Annulus (ground) 4.2 0.45

Annulus (fiber) 175 X

Nucleus Pulposus 1 0.499

Anterior Ligament 7.8(<12%),20(>12%) 0.3

Posterior Ligament 10.0(<11%),20.0 (>11%) 0.3

Ligamentum Flavum 15(<6.2%),20.0(>6.2%) 0.3

Transverse Ligament 10(<18%),58.7(>18%) 0.3

Capsular Ligament 7.5(<25%),32.9(>25%) 0.3

Interspinous Ligament 10.0(<14%),11.6(>14%) 0.3

Supraspinous Ligament 8.0(<20%),15.0(>20%) 0.3

This L3-S1 model was then combined with validated FE pelvis model (Figure 34).

Figure 34. Different views of lumbar spine-pelvis FE model.

Additionally, proximal part of both femurs were developed and added to model. The

hip joint had 6 degree motion restriction.

84 The intact model was modified to simulate three posterior pedicle screw based fusion cases (L4-L5, L5-S1 and L4-S1 ) (Figure 35).

Figure 35. Simulated posterior lumbar fusion procedures.

The full fusion between bony structures and instrumentation was considered. The inferior-most surface of proximal femurs was fixed. A compressive load of 400N, plus a bending moments were applied to all superior-most L3 nodes of implanted and intact models to simulate the physiological flexion, extension, lateral bending and axial rotation through a hybrid loading protocol. The load control approach (hybrid protocol) involves varying the applied pure moment for the instrumented models until the angular motion of the L3-S1 equaled the values of intact load control case [97]. In each case, the bending moment was applied at L3 level and the pelvis was fixed in all degrees of freedom.

The sacrum angular motion across sacroiliac joints and the average value of Von Mises stresses of articular surfaces of SIJ were analyzed in each case. The results of implanted models were then compared with the corresponding intact lumbar spine-pelvis model.

85 .

Results

The results for compressive loading of 400 N with different moments (hybrid protocol) applied on the intact model, models with posterior fusion at L4-L5, L4-S1 and L5-S1 are shown in Figure 37 and Figure 38.

The motion increased steadily with the increase in number of levels fused and with involvement L5-S1 segment in fusion compared to the intact model, although the actual values were quite small as expected (Figure 37).

Figure 37. Sacrum angular motion (deg) after simulated procedures and followed compressive load of 400 N with moment forces (hybrid protocol).

3.00

2.50

2.00

1.50

1.00

0.50 Angular Motion (deg) AngularMotion 0.00 Flexion Extension Bending Rotation

intact L4-L5 L5-S1 fusion L4-S1 fusion

The motions in L4-5 fusion model increased by 0.06 deg in flexion (0.65 deg in L4-5 fusion model vs 0.59 deg in intact model), by 0.11 deg in extension (1.31 deg in L4-5 fusion model vs 1.20 deg in intact model, 0.15 deg in lateral bending (0.66 deg in L4-5 fusion model vs 0.51 deg in intact model, and by 0.31 deg in axial rotation (0.96 deg in

L4-5 fusion model vs 0.65 deg in intact model). The absolute values of motions changes corresponded to 9% increase in flexion, 9.5% increase in extension, 29% increase in lateral bending, and by 47% in axial rotation comparing the motions in intact model.

Results for L5-S1 fusion model showed more substantial motion increase. The differences in measured parameter between L5-S1 fusion model and the intact one were equal to 0.31 deg in flexion (0.91 deg in L5-S1 fusion model vs 0.59 deg in intact model), to 0.49 deg in extension (1.68 vs 1.20 deg), to 0.15 deg in bending (0.66 vs

0.51 deg), and to 0.34 deg in rotation (0.99 vs 0.65 deg). The absolute values changes corresponded to 52% motion increase in flexion, 40% motion increase in extension,

28% increase in bending, and 51% increase in rotation.

The most substantial increase in motion observed in L4-S1 fusion model. It increased by 1 deg in flexion (1.59 vs 0.59 deg in intact model), by 1.58 deg in extension (2.77 deg vs 1.20 deg in intact model), by 0.49 deg in bending (1 deg vs 0.51 deg in intact model), and by 0.45 deg in rotation (1.1 deg vs 0.65 deg in intact model). Those values

87 corresponded to the following percentile changes- 168% motion increase in flexion,

132% increase in extension, 95% increase in bending, and 69% increase in rotation.

Stresses gradually increased across SIJ surfaces with the maximum average value occurring in the model with L4-S1 posterior fusion (Figure 38, Figure 39).

Figure 38. The average stress values (MPa) across SIJ articular surfaces after procedures simulations and followed compressive load of 400 N with moment forces (hybrid protocol).

3.00

2.50

2.00

1.50

1.00

0.50

Von Mises Stress (MPa) Stress VonMises 0.00 Flexion Extension Bending Rotation

intact L4-L5 L5-S1 fusion L4-S1 fusion

The pattern of stress increase was similar to pattern of changes in sacrum angular motion, however the values of stress increase between simulated and intact model were much more considerable.

Figure 39. Contour plot of stress-distribution across sacroiliac joint surface area after simulation of L4-S1 fusion and followed compressive load 400 N and moment force 25 Nm (hybrid protocol).

In L4-5 fusion model, stress increased by 0.06 MPA (0.39 vs 0.33 MPa in intact

model), by 0.13 MPa in extension (0.53 vs 0.40 MPa), by 0.39 MPa in bending (1.22 vs

0.83 MPa), and by 0.23 MPa in rotation (1.22 vs 0.99 MPa). The absolute values of

89 stress changes corresponded to 19%, 31%, 46% and 23% increase in flexion, extension, bending and axial rotation, respectively.

The L5-S1 fusion model simulation showed that stress increased by 0.52 MPa in flexion (0.85 vs 0.33 MPa in intact model), by 0.55 MPa in extension (0.95 vs 0.4

MPa), by 0.51 MPa in bending (1.34 vs 0.83 MPa), and by 0.52 MPa in axial rotation

(1.51 vs 0.99 MPa) comparing the stresses at the intact model (156% increase, 136% increase, 61% increase, 53% increase in flexion, extension, bending and axial rotation, respectively).

The most substantial changes in stress values were observed in L4-S1 fusion model.

After simulation of loading conditions flexion, extension, lateral bending and axial rotation, the stress in SIJ articular surfaces increase by 1.69 MPa (2.02 vs 0.33 MPa in intact model which was six times of stress in intact model), by 2.16 MPa (2.57 vs 0.4

MPa in intact model which was six times of stress in intact model ), by 1.73 MPa (2.56 vs 0.83 MPa in intact model, which was three times of stress in intact model ), and by

1 MPa (1.99 vs 0.99 MPa, which was almost two times of stresses in intact model).

The maximum values of measured parameters (sacrum angular motion and average stress across sacroiliac joint articular surfaces) were observed in L4-S1 fusion model in flexion and extension loading settings.

90 The moments required to produce the same overall motion (hybrid protocol) are listed

in Table 20. The L4-S1 fusion model required maximum moment to achieve the same

motion.

Table 20. The hybrid moment in each case for the same L3-S1 motions

Moment applied to produce the same motions Model Flexion Extension Bending Rotation Intact 4.1 6.0 6.0 10.0

L4-5 Fusion 5.0 7.5 10.0 13.5

L5-S1 Fusion 6.0 11.25 11.0 16.25 L4-S1 Fusion 25.0 25 25.0 22.75

Discussion

The clinical problem of sacroiliac joint involvement in persistent low back pain in

patients after lumbar spine surgery was discussed in the literature. Frymoyer et al (1978)

were the first who suggested this clinical scenario [85], but were unable to confirm their

hypothesis based on patient radiographs (anteroposterior and functional films). Later, the

evidence of sacroiliac joint dysfunction in patients with spine surgery followed by LBP

was obtained after SPECT and bone scintigraphy [86,87]. Results have shown

significantly increased uptake in sacroiliac joint which might reflect mechanical

overloading and sacroiliitis. Our extensive literature search failed to find a biomechanical

study which would clarify the pattern of mechanical behavior of SIJ. The difficulties in

conducting of such studies are obvious. The specimen should include an entire block of

91 lumbar spine connected to the pelvis which may leads to technical errors. In addition, it may also be technically demanding and expensive. Hence we suggested that the finite element analysis would be ideal method in these circumstances.

Numerous studies were conducted to explore the biomechanics of the sacroiliac joint.

The radiographic method was popular in past decades, however, careful analysis of the data revealed spurious findings and artifacts [98,99]. This has led to doubts in using the two-dimensional method for valid sacroiliac joint motions assessment [100]. The flexion-extension lateral radiographs have been used by Frymoyer et al (1978) to assess sacroiliac joints movements in patients after lumbar fusion. Authors didn’t reveal significant differences in mobility in the SIJ after spine procedures. Considering the facts mentioned previously, one would argue that this statement may not be conclusive.

We observed that the lumbar fusion leads to increased angular motion at the SIJ. The value of differences between intact and instrumented model, however, was not large. The results might explain the lack of sufficient degenerative changes in patient’s SIJ after lumbar spine fusion [85]. We suggest that a small increase in angular motion would not generate excessive stress at the joint surface; however, the ligaments around SI articulation are richly innervated [101]. Therefore, even small motion increases (but with considerable percentile changes) may trigger a pain syndrome.

Numerous clinical and experimental studies of adjacent segment disease after lumbar fusion procedures showed increase mobility in the cephalad and/or caudad adjacent segments and increase stress on the facet and/or disk of adjacent mobile segments [102-

112]. The following changes might be due to transfer of motion from the fused segment

92 to the next mobile intact segment. The sacroiliac joint in case of lumbarsacral fusion is adjacent joint to fused segment; thus, one can predict similar biomechanical response on surgical procedure as any other adjacent segment behavior on lumbar or cervical spine level after fusion.

Although our model is sufficient to represent the accurate anatomy and biomechanical properties of its components (ligaments and bones), it has several simplifications which might have influenced the obtained results. The pelvis model was based on CT scans of healthy young man without any degenerative changes in SIJ. The bone properties were assumed to be homogenous across the pelvis. In addition, the interaction between screw surfaces and bone was simulated as complete fusion which cannot be a true. Pelvis and

SIJ are predisposed to broad variation in geometry, size and degeneration stage

[113,114]. The mathematical modeling of such increments is possible, but our model presented the “ideal” conditions where the influence of aforementioned factors were not considered. In addition, homogenously distributed material properties of the previous pelvis model showed similar results compared with the patient specific pelvis model in quantitative FE studies [34,115]. However, such fine tuning is not likely to alter the qualitative nature of our findings that there is an increase in motion and stress across the

SIJ following fusion.

93 Conclusion

Both cadaveric and finite element methods in study of spine biomechanics are complimentary. They supplement each other effectively with the most thorough analysis in studies where those two methods are utilized together. The application of finite element human pelvis model was restricted due to its complex geometry and shape, unknown properties of sacroiliac joint ligaments. The advance in computer technology and computer processing power allowed us to model and validate the realistic digital prototype of male pelvis with material properties close to original.

Validation is an important part of modeling which allows answering the question: “does the model predict the biomechanical response in the way as its original prototype?” The comparison of our study numerical results with experimental outcomes taken from literature showed close values correlation in such modes as sacroiliac joint displacement, sacroiliac gap displacement, sacrum center displacement, sacrum angular motion.

Therefore, the requirements for validated model were achieved in our study.

Clinical application of finite element model is valued especially where cadaveric studies are failed to clarify the nature of some clinical conditions. Sacroiliac joint syndrome has wide number of factors which contribute to its appearing. Existed clinical and diagnostic evidence supported a suggestion of SIJ involvement in LBP in patients after lumbar fusion. Testing of finite element pelvis model showed that influence, so clinician have to pay more close attention to probability of sacroiliac joint syndrome in such patient group.

94 Study Limitations

The average values of material properties and interior structure parameters (thickness of cortical and cancellous bone) were used in model. The exact simulation of those parameters would allow to obtain more close correlation of current model tests results with its prototype, and finally would lead to prediction of exact value of stresses and motions in SIJ. Thus, our model is suited well for comparative studies, but is not appropriate for studies where the exact, absolute value is required.

Future Work

The investigation of sensitivity of SIJ motions to stiffness of sacroiliac joint ligaments would lead to modeling more realistic model of sacroiliac joint. Using the pelvis mesh as a frame would allow to build the subject-specific pelvis model. Researcher has just to get subject-specific nodes for cortical and cancellous bone boundaries and implement them in already existed model. The simulations of model weight would allow to test such condition as osteoporosis and its complications (pelvis fractures). Dynamic loading conditions may predict the pattern of pelvic fractures and evaluate the effectiveness of implants in their capability to restore pelvic stability.

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