Predictions of Distal Radius Compressive Strength

Home , Radius (bone)

PREDICTIONS OF DISTAL RADIUS COMPRESSIVE STRENGTH

BY MEASUREMENTS OF BONE MINERAL AND STIFFNESS

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A Thesis Presented to

The College of Arts and Sciences,

Ohio University

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In Partial Fulfillment of the

Requirements for Graduation with Honors from the

College of Arts and Sciences with the degree of

Bachelor of Science in Biological Sciences

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Maureen A Dean

April 2016 2

Table of Contents Acknowledgements……………………………………….…….……...... 3 Abstract……………………………………………………….……….…4 1. Background…………………………………………………...... 5 1.1 Bone Health and Development…………………………….…….5 1.2 Osteoporosis Disease and Diagnosis……………………….…..8 1.3 Bone Stiffness and Strength………………………………….….12 1.4 Osteoporotic Fracture Sites………………………………….….18 1.5 Specific Aims……………………………………………………....21 1.6 Hypotheses…………………………………………………....……21 2. Methods………………………………………………………….…....22 2.1 Experimental Design……………………………………….……..22 2.2 Specimens…………………………………………………….…….25 2.3 Experimental Protocol……………………………………….…...30 2.4 Data Analysis……………………………………………….……..41 2.5 Statistical Analysis………………………………………….…….48 3. Results………………………………………………………….….….50 3.1 In Situ and Ex Situ Measurements………………………………50 3.2 Univariate Analysis…………………………………….…………51 3.3 Bivariate Analysis……………………………………….………...52 4. Discussion…………………………………………………….….….....61 4.1 Main Findings………………………………………….…………..61 4.2 Diagnostic Error Rate……………………………….……………61

4.3 Relation to Previous Research...…………………………………63

4.4 Strengths……………………………………………….…………...65

4.5 Weaknesses…………………………………………….…………..69

4.6 Future Research……………………………………….…………..72

References…………………………………………………..……….…...73

Acknowledgments

This thesis was made possible by funding from the Student Enhancement Award, the Ohio Space Grant Consortium, and Dr. Anne Loucks of the Department of Biological Sciences. I am extremely thankful for those outside of Dr. Loucks’ Laboratory who aided me during this project. I want to personally thank Dr. Leatha Clark of the Ohio Musculoskeletal and Neurological Institute for being this project’s DXA technician and for teaching me how to analyze DXA images, as well as Dr. Betty Sindelar of the Ohio University Division of Physical Therapy, who allowed me to use her QMT system. A special thank you goes to my thesis advisor, Dr. Griffin, who guided me through the process of writing a senior thesis. Additionally, I am thankful to the human tissue banks, AdvancedMed and Science Care, for providing specimens for this project and to the donors themselves who gave their bodies to science. I would not have been able to complete this project without the extraordinary work accomplished by previous students in Dr. Loucks’ laboratory. I would especially like to acknowledge Emily Ellerbrock and Jennifer Neumeyer for their work on MRTA analysis, Tyler Beck for his analysis of ulna QMT data, and Gabrielle Hausfeld for laying the ground work on predictors of ulna bending strength and for making me laugh and enjoy my time in the laboratory. I want to express my gratitude for my family and cross country teammates who created an unbelievable support network for me during this project and inspired me to do better each day. Lastly, I would like to thank Dr. Loucks and Lyn Bowman who have encouraged, challenged, and guided me to accomplish more than I ever thought possible. I want to personally thank Dr. Loucks for accepting a previously inexperienced person such as myself into her laboratory and opening my mind to a different realm of science. I cannot express my gratitude enough to Lyn who has spent hours sitting patiently with me to teach me what I needed to know. This has been the most informative experience of my college career and I am fortunate to have been able to work under Dr. Loucks and Lyn for the past two years.

Abstract

Osteoporosis is a systemic disease that is characterized by a decrease in bone strength leading to an increased risk of fracture. Currently osteoporosis is diagnosed by measuring bone mineral density (BMD) by dual-energy X-ray absorptiometry (DXA). Previous literature has shown that DXA measurements do not accurately predict which individuals will fracture, leaving physicians with a limited ability to target those who need preventative care. Ohio University is developing a new technology, mechanical response tissue analysis (MRTA), to measure the stiffness (EI) and estimate the strength of human ulna bones in vivo. EI is strongly associated with bone strength, but this technology’s diagnostic ability is limited unless it can predict the strengths of other long bones where osteoporotic fractures occur. Nineteen percent of osteoporotic fractures occur in the distal radius of the forearm, and those fractures are an indicator for future osteoporotic spine and hip fractures. This project compared the accuracies with which ultra-distal (UD) radius compressive strength was predicted by donor demographics, measurements of ulna bending and radius compressive stiffness (EI, EA), ulna bending strength, and DXA measurements from the UD and 1/3 regions of the radius. This study used 32 fresh frozen cadaveric arms from men and women ranging in age from 23-99 years and in BMI from 13-40 kg/m2. Ulna EI and bending strength, and UD radius EA and compressive strength were all measured using the gold standard method, Quasistatic Mechanical Testing (QMT). Unlike DXA and MRTA, QMT cannot be used in vivo. Simple linear regression analyses revealed that the most accurate predictor of UD compressive strength was UD radius EA (standard error of the estimate, SEE = 874 N), which cannot be measured in vivo. The accuracies of all other predictors were indistinguishable from one another. Confidence in these results is reduced, however, by certain outliers in the data, which inflated the SEE values of all predictors.

1. Background 1.1 Bone Health and Development

Bone health will be increasingly important for Americans in the upcoming years as osteoporosis becomes a more prevalent disease. Osteoporosis is a systemic disease characterized by a decrease in bone strength causing an increased risk of fracture (25). In the United States alone, the World Health Organization estimates around ten million people are afflicted with this disease (8, 25). In the year 2005 two million osteoporotic fractures were recorded, but by the year 2025 the number of fractures has been predicted to rise by fifty percent. Additionally, this disease has a

great economic impact on the United States. In 2005 the cost of care related to osteoporotic fractures was almost 17 billion dollars. That cost is predicted to rise over

25 billion dollars by 2025 (5).

Bone tissue is composed of collagen, mineral and non-collagenous proteins. It

functions by providing support, mobility, and protection for the body while acting as a

storage site for essential minerals (7). Bone is comprised of two different types of

tissue. Compact or cortical bone (Figure 1) has porosity (fluid-filled voids) in the

range of 5-10%. It can be found within the shafts of long bones and as a shell or cortex

around vertebrae and other spongy bones. This type of tissue makes up 80% of the

mass of bones in young adults (14). Cortical bone contains Haversian canals with

capillaries and nerves, Volkmann’s canals that connect Haversian canals with blood

vessels and nerves, and resorption cavities or volumes created by osteoclast cells.

Figure 1. The dense microstructure of cortical bone (21).

The second type of bone tissue, trabecular bone, otherwise known as cancellous or spongy bone (Figure 2), has porosity in the range of 75-95%. It can be found in flat bones, cuboidal bones, and the ends of long bones. Trabecular bone is comprised of an interconnecting network of thin plates or trabeculae that create a largely open microstructure within the bone. It comprises 80% of the bone surface area in young adults. As a largely open structure, it provides support without increasing the weight of the bone. Widening the surface area at the ends of long bones

reduces stress (force per unit area) on joints and concentrates that load onto the more compact and stronger cortical bone in the bone shaft (21, 29).

Figure 2. Porous Trabecular bone (27).

Bone turnover is a normal process that ensures the skeletal system adapts to

changing conditions. Turnover occurs in two different ways: modeling and

remodeling. Modeling refers to the growth of bone during childhood. As we achieve

adulthood, the rate of modeling significantly decreases both radially and

longitudinally (7).

Remodeling is characterized by bone resorption and formation at the same site.

It takes place in three stages 1) activation 2) resorption 3) formation (7, 21). The goals

of remodeling include maintaining the balance of essential minerals in the blood,

adapting bone to the mechanical environment, and repair of bone damage (6). Bone is

removed and added through two types of cells: osteoclast cells act to resorb bone

while osteoblast cells form new bone. The remodeling sequence functions through a

basic multicellular unit (BMU) that is composed of approximately 10 osteoclasts and

hundreds of osteoblasts. Activation begins when a chemical or mechanical signal

causes osteoclasts to form and move to a spot on the bone. Over a course of three

weeks, osteoclasts resorb bone tissue to create a groove on a bone surface or a tunnel

within cortical bone. Next, osteoblast cells begin to replace the tissue that was

resorbed. This occurs over a period of up to three months. (Figure 3) Remodeling in

cortical bone creates a Haversian canal within the bone because the tunnel created by

osteoclasts is not fully filled by osteoblasts. In trabecular bone, trabecular trenches are

created and fully filled under normal circumstances (7, 21).

Figure 3. BMU with osteoclasts (red arrow) absorbing cortical bone and osteoblasts

(blue arrow forming new bone (purple arrow) (21).

1.2 Osteoporosis Disease and Diagnosis

The decrease in bone strength in osteoporosis is primarily due to excess

resorption of bone during bone turnover. The excess removal of bone can occur at

trabecular and cortical sites (7).

When excess removal occurs in trabecular bone, the plates within the

trabecular structure thin, become rod-like, and eventually break. As a result, connectivity is lost between the trabeculae. (Figure 4) This causes a significant decrease in trabecular bone surface area, as well as stiffness and strength. In cortical bone, the internal surface area increases as millions of Haversian canals accumulate with age. Excess removal of bone on these surfaces opens large resorption spaces

within the cortical bone. After the age of 60, the loss of cortical bone is much greater

than the loss of trabecular bone. Thus, cortical bone loss accelerates with age causing a decrease in overall bone strength (7, 27).

Figure 4. Normal trabecular bone plates (blue arrow) and trabecular bone rods affected by osteoporosis (green arrow) (27).

Currently, osteoporosis is diagnosed using dual energy x-ray absorptiometry

(DXA). DXA uses a fan beam with two X-rays at different energy levels. The

different energy sources distinguish between soft tissue and bone as one type is

absorbed by soft tissue and the other by bone. The X-ray exposure from DXA is 3

microsieverts (μSv) per scan compared to a single plane X-ray exposure of 600 μSv.

DXA radiation exposure is also small dose compared to normal day-to-day exposure,

which is typically 7 μSv per day (7).

DXA creates a 2-dimensional image of a bone without distinction between

cortical and trabecular bone. Software in the DXA scanner determines bone mineral

content (BMC), bone area, and bone mineral density (BMD = BMC/area) in particular

regions of interest (ROI). In the forearm, these ROI are the ultra-distal (UD), middle

(MID), and 1/3 regions of the radius, ulna or both. BMC is a measure of how much

mineral is in the ROI and is measured in grams (g), whereas ROI area is measured in

centimeters squared (cm2) and ROI BMD is measured in units of g/cm2 (7).

Without cross-calibration of different manufacturers of DXA systems, it is not possible to quantitatively compare BMD measurements made by different systems.

Therefore, T-scores must be used (25, 28). The DXA software calculates the BMD T-

scores and Z-scores of a patient in all three ROI. A T-score shows how many standard deviations a BMD measurement is from the young adult peak mean BMD (7). This

standard young adult mean BMD is calculated from the BMD of Caucasian women

ages 20-29. Z-scores measure how many standard deviations a BMD measurement is

from the mean BMD of a similar population. DXA Z-scores are for populations that

are age-matched, not gender, race, or ethnicity-matched.

Diagnostic DXA scans are usually taken in regions of the lumbar spine, hip

and femur. A typical scan of the spine includes L1-L4 unless there is a structural

artifact. At least two of the vertebrate must be interpreted for an appropriate diagnosis.

Vertebrae should be excluded if they are clearly abnormal, non-assessable, and if they differ by more than 1.0 T-score. An average T-score across the vertebrae will be presented and should be used for diagnosis (7, 28). The hip region of interest (ROI) is the average of the total hip and femoral neck. If the vertebral and hip ROIs are unavailable for use because they cannot be measured, interpreted, the patient has hyperparathyroidism, or if the patient is obese, a scan of the forearm can be substituted for diagnosis. The T-score from the 33% site (i.e. the one-third site) of the radius is used to diagnose a patient. Other ROIs from the forearm are not recommended for diagnostic purposes (28).

Unfortunately, this diagnostic approach is not a good predictor of fractures. In a prospective study of 163,935 post-menopausal women, 96% of those diagnosed with osteoporosis did not fracture while 81% of fractures occurred in women who were diagnosed as not having osteoporosis (30). There are many limitations to DXA technology that should be known. DXA software automatically determines the ROIs and the area of the bones, but it is necessary for a practitioner to review and redraw the bone edges in many cases. This can cause many variations in which BMD could be over or underestimated depending on the redrawn area. A skilled technician also must be precise when positioning of the patient before scanning. If positioned incorrectly, it will be challenging to compare BMD measurements to standardized databases (7).

Moreover, there is uncertainty on how to diagnose men, children, or those with different ethnicity than Caucasian because the reference population for T-scores is strictly young adult Caucasian women. Furthermore, there is no standardization of forearm ROI between manufacturers. Hence, many believe the standards of diagnosis of osteoporosis are controversial (25).

Additionally, there is no distinction between cortical and trabecular bone. Thus a DXA scan does not assess the architecture of geometry within the bone. Because

BMD only accounts for 60-70% of the difference in strength, many other factors such as bone microstructure and architecture influence bone strength. For instance, BMD does not distinguish between patients who have low BMD with a solid bone microstructure and those who have high BMD with a broken microstructure.

Furthermore, BMD is normalized to area and not volume, which does not assess true

volumetric BMD. Thus smaller patients are often over diagnosed while larger patients are under diagnosed (7, 20).

Furthermore, BMD T-scores are only accurate to ± 1 T-score, which can cause misdiagnosis of osteoporosis (2, 3, 32). For example, a BMD T-score of -1.6 could be anywhere in the range of -2.6 (i.e. osteoporotic) to - 0.6 (i.e. normal). Lastly, diagnostic decisions are made from measurements at the spine and hip where the composition of the bone is mostly trabecular. However, after the age of 60 most bone loss occurs in cortical bone, and 80% of fractures occur at cortical bone sites and not in the spine (37). Thus, fracture predictions based on BMD measurements at trabecular sites may not reflect the actual clinical risk of fracture.

1.3 Bone Stiffness and Strength

Because BMD is not an accurate diagnostic tool, other predictors of bone strength should be explored. Bone strength is defined as the maximum load a bone can carry before it breaks. Bones can experience load in many ways including tension, compression, shear, torsion, and bending (Figure 5) (7). Mechanical testing is used to measure bone strength as the force at fracture. Therefore, bone strength cannot be measured in vivo. Therefore, excised bones are used to measure strength. Mechanical testing can be split into two types of testing. Mechanical tests normalize for the size of a specimen and measure the inherent Material property of the material. Structural mechanical tests do not normalize for the size of a specimen, thereby taking into account how large or small the structure of a specimen is. Material tests are commonly

performed to assess effects on bone material, but bones break as structures. Therefore,

structural tests are needed to measure the strength of a whole bone

Figure 5. Different types of forces applied to bone (7).

Bone stiffness is defined as the load needed to deform the structure of bone a

specific amount. It can be measured as the slope of the elastic region of the force

displacement curve. (Figure 6) The elastic region is defined as the “linear” portion of

the force-displacement curve. For non-linear materials and structures, like many bones, stiffness is defined as the peak slope of the force/displacement curve. This peak slope occurs at the inflection point between positive and negative curvature on the force/displacement curve. Stiffness has been shown to be an accurate predictor of bone strength. Bending stiffness (Kb) and compressive stiffness (Kc) are both

important to this project.

Figure 6. Force-displacement curve where k is the slope and peak force is bone strength (10).

Kb is used to calculate flexural rigidity or EI, in a structural test. EI can be

3 calculated using the following equation: EI = Kb*L /48, where L is the length of the bone being tested. The E in EI stands for the elastic modulus, which is the ratio of stress to strain. It is the inherent stiffness for the material being tested (i.e. bone) while

EI is the stiffness of the bone structure. The I in EI is the cross-sectional moment of inertia, which measures the distribution of the bone material around its long axis. The product EI is useful for normalizing the confounding effects of variations in bone length on Kb. Therefore, EI enables bones of different lengths to be compared to one another (7, 10). Kc is the stiffness of a bone specimen in a compression test. The compressive rigidity (EA) is calculated as EA= Kc × H, where H is equal to the height of the specimen. The A in EA stands for the area of the specimen and the product EA allows specimens of different heights to be compared.

The gold standard method for measuring bone stiffness and strength is quasi-

static mechanical testing (QMT). QMT can be used for different tests including

bending tests to measure bending strength and compression tests to measure

compressive strength. Three-point bending tests are conducted by placing a long bone

on supports at either end. A force or load is applied at a central point. This allows for

forces and bending displacements of the bone to be measured. Previously, ulna EI was

shown to accurately predict ulna bending strength. In the regression of bending strength on EI in a study of 45 excised human ulnae, the correlation coefficient was

0.92 (15). Another study focusing on 56 excised canine radius, ulna, and tibia bones

found the correlation between bending strength and EI to be 0.93 (4).

QMT compression tests are most commonly used for measuring the mechanical properties of trabecular bone. During testing, a force is applied on the specimen, pressing it between two platens. (Figure 7) The force and deformation of the specimen (displacement) is recorded. The force/displacement curve has three different elastic, plastic, and fracture regions, as seen in Figure 6 (26).

Figure 7. (a) Compression test between static platens. (b) Compression test between a spherically seated ball-joint and static platen (26).

Compression tests are dependent on several factors. The specimen surfaces must be parallel and flat in order to reduce the risk of force being applied non- uniformly. If the force is applied in a non-uniform manner it can result in a lower predicted value of both the elastic modulus and the strength of the bone. To avoid this issue, a spherically seated or ball-joint platen is used to adjust for nonparallel surfaces.

Additionally, pre-conditioning cycles must be repeated until measurements stabilize.

Pre-conditioning cycles are small loads applied to the specimen multiple times before a fracture cycle is initiated. Friction between the specimens and platens can bias measurements high. Friction can be avoided by applying lubrication to the platen surfaces. Because measuring EA is a structural test, literature is rare or nonexistent in highlighting the relationship between EA and compressive strength of the radius (26).

The risk of fracture depends strongly on bone strength. Therefore, a new technology, mechanical response tissue analysis (MRTA), was invented to measure the stiffness of long bones in vivo. MRTA was invented at Stanford University in the

1980s to study how space flight affects bone stiffness (31). Dr. Anne B. Loucks and her staff and students have been further developing this technology (10) (13). Because of its superficiality under a thin layer of skin and its near ideal biomechanics in bending, the ulna bone in the forearm is best suited for MRTA testing. A specific aim of this project was to determine how well MRTA measurements of ulna EI predict the compressive strength of the UD region of the radius bone in the forearm.

MRTA is a radiation free, non-invasive vibration analysis technique for measuring ulna EI to predict ulna-bending strength. MRTA testing requires a patient

to lie supine with his or her forearm horizontal and elevated. The elbow is supported by the vertical upper arm and the wrist by an adjustable platform. A probe applies a

load to the midpoint of the ulna with an oscillating frequency spanning a range of 40-

1200 Hertz (Hz). Analysis of the collected force and acceleration data yields the complex compliance (i.e. displacement/force) and stiffness (force/displacement) frequency response functions (FRFs). These functions are fitted to a seven-parameter mathematical model of the mechanical skin-bone system to quantify the stiffness of the bone. (Figure 8) This measurement of stiffness is used to calculate EI to account for length differences between ulnas (10).

Figure 8. The 7-parameter model of the mechanical skin-bone system (10).

Previous students in Dr. Loucks’ laboratory have investigated the accuracy of

MRTA measurements of ulna EI. Figure 9a shows that MRTA measurements of ulna

EI predicted QMT measurements of ulna bending strength with a standard error of the

estimate (SEE) of 91 N. By comparison, Figure 9b shows that BMD in the 1/3 region

of the ulna predicted ulna bending strength with a larger SEE of 175 N. The clinical

usefulness of such MRTA measurements of ulna EI may depend on the ability of ulna

EI to predict the strength of other long bones in the body, such as the radius.

Figure 9. (a) Ulna bending strength vs. EI by MRTA (13) (b) Ulna bending strength vs. ulna BMD in the 1/3 region (preliminary data).

1.4 Osteoporotic Fracture Sites

Typical osteoporotic fractures occur in sites such as the thoracic and lumbar

spine, proximal femur, proximal humerus, pelvis, and in the distal radius (8). Fractures

in the distal radius occur soon after menopause in women, but these types of fractures

are less likely to occur in men. These distal radius fractures are called Colles’

Fractures and occur under compressive loads. Unfortunately, the patients that

experience Colles’ fractures typically have normal BMD values and are difficult to

identify in advance. Risk factors for these types of fractures are obscure even though

Colles fractures account for 19% of all osteoporotic fractures (11). These fractures

indicate higher risk for future hip and spine fractures. Therefore, it would be useful to

find ways to better diagnose individuals who are at an increased risk of distal radius fractures (1).

Colles’ fractures occur in the ultra-distal (UD) region in the radius. The UD region is composed of trabecular bone in a shell of cortical bone. (Figure 10)

Figure 10. UD radius slice.

The various DXA manufacturers define the UD region differently. For Hologic

DXA scans (the technology used in this project), the UD region is considered to be 15

mm proximal to the proximal end of the distal radio-ulnar joint (Region 1B and the proximal half of Region 2 in Figure 11). However, many previous researchers have defined the UD region in the radius as 10 mm proximal to the articular surface of the radius (Region 1 in Figure 11). (1, 9, 17-19, 23)

Figure 11. The distal radius with UD region and clinical UD region (23).

Previous researchers have studied compression tests of excised UD specimens

of the human radius. Compression tests are chosen because in a previous model of distal radius fractures, 99.99% of strain was compressive (34). Figure 12 illustrates a

previous experimental protocol where 10 mm specimens were removed from radius

bones and loaded in compression tests. Other studies have investigated the ability of

both BMC and BMD from DXA to predict the strength of the UD region in the radius

in hopes of finding methods that more accurately predict radius strength. In a study by

Wu et al. (36), BMD was found to predict compressive strength with R2 = 0.53. That

study used only 13 specimens from only older adults (48-93 years of age), but other

studies have reported similar findings. One goal of this project was to investigate how

accurately ulna-bending strength could predict UD radius compressive strength.

Figure 12. Procedure for a compression test of the UD region (18).

1.5 Specific Aims

The specific aims for this project were:

1. To acquire DXA scans of excised radius bones,

2. To analyze the DXA scans to determine BMC, area, BMD, and T-scores from

each scan in the UD, Mid, and 1/3 regions,

3. To cut 10 mm UD specimens for compression testing,

4. To perform QMT compression tests to quantify the compressive stiffness,

compressive rigidity, and compressive strength of the specimens, and

5. To perform statistical analyses to compare the accuracies with which

predictors from donor demographics, mechanical testing, and DXA estimate

the compressive strength of the UD region of the radius.

1.6 Hypotheses

This thesis tested the following null hypotheses:

H01: The Standard Error of the Estimate (SEE) in the regression of ultra-distal (UD)

radius compressive strength on UD radius EA is not smaller than SEEs for other

predictors (i.e., age, BMI, UD area, UD BMC, UD BMD, UD T-scores, 1/3 area,

1/3 BMC, 1/3 BMD, 1/3 T-scores, ulna EI and bending strength by QMT, and

ulna EI by MRTA).

H02: The SEEs in the regressions of UD radius compressive strength on other

predictors are not different from each other.

2. Methods 2.1 Experimental Design

Previous Data Collection

Frozen cadaveric arms were obtained from human tissue banks. Upon receipt,

they were transferred to a freezer (–20 °C) to prevent deterioration of the mechanical

properties of bones within the arms (26). On an agreed day, the frozen arms were taken to Holzer Clinic in Athens, Ohio where the Radiology Department scanned the arms by computed tomography (CT). The arms were then returned to cold storage.

Previous researchers in Dr. Loucks laboratory have already collected data that will be used for statistical analysis in this project. (Figure 13) Ulna bending stiffness

(kB) was measured in MRTA (Step 2) and during QMT (Step 6). Ulna 3-point bending strength was also measured by QMT (Step 6).

Figure 13. Previous experimental protocol.

MRTA is a dynamic vibration analysis technique where kB is estimated by a 7-

parameter mathematical model of the mechanical skin-bone system that is fitted to

frequency response function data collected during the test. By contrast, QMT is a quasi-static test in which kB is obtained as the slope of a force-displacement curve

recorded as the bone is slowly bent. In the MRTA and QMT 3-point bending tests, a

force probe was applied at the mid-span of the ulna bones. Ulna bending strength was

taken as the peak force before fracture in the QMT bending tests. (Figure 15) (13). In

order to compare ulnas of different lengths to one another, ulna flexural rigidity (EI)

was calculated to correct for the confounding effects of variations in ulna length on kB:

3 EI = kb x L / 48

where L stands for the length of the ulna.

Figure 14. Set up for MRTA 3-point bending test (13).

Figure 15. Set up for QMT 3-point bending tests (13).

Current Project Design

This research project was designed to compare the ability of different

predictors from donor demographics, mechanical testing, and DXA measurements to

predict the compressive strength of the ultra-distal (UD) region of the radius bone.

Donor demographics were age and body mass index (BMI). Predictors from

mechanical testing were ulna EI (by QMT and MRTA), ulna bending strength, and

radius compressive rigidity (EA). Predictors derived from DXA were area, BMC,

BMD, and BMD T-scores from both the UD and 1/3 regions of the radius.

The overall experimental design included two measurement activities. DXA

measurements of the UD and 1/3 regions of the radius were collected using a Hologic

DXA imaging system. The UD region of the radius was then cut from each frozen

radius bone to create compression testing specimens. The UD specimens were then

subjected to QMT compression tests to determine the specimen’s compressive rigidity

(EA) and strength. (Figure 16)

Figure 16. Experimental design of this project.

2.2 Specimens

Arm Donor Demographics

Dr. Loucks laboratory has acquired 44 fresh-frozen, cadaveric, human arms from human tissue banks. Seven specimens were acquired from AdvancedMed (Las

Vegas, NV) and thirty-seven from Science Care, Inc. (Phoenix, Arizona). The arm

donors were both male and female ranging from 17-99 years of age with body mass indices ranging from 13-40 kg/m2. (Figure17, Table 1) For this project and previous

projects in our laboratory, the first seven specimens (C001-C007) were used to develop the experimental protocol. Additionally, C022, C027, C028, and C036 were

not tested previously or in this project. Lastly, data from C042, a 17 year-old male,

were not analyzed in this project, because of its immature skeletal development, unlike

all the other arms.

Donor Requirements and Exceptions

This project excluded prospective donors with a medical history of bone cancer

or cancers that are likely to have metastasized to bone, including bladder, breast,

kidney, lung, melanoma, prostate, thyroid, and uterine cancers (24). Also prospective

donors were excluded if they had previous injuries or fractures of the arm. Donors

were required to be fresh-frozen within 10 days after death, because the stiffness of

bone degrades after the 10th day post-mortem at room or refrigeration temperatures

(33). To ensure wide ranges of bone stiffness and strength, donors were required to

span specific ranges of BMI: men greater than 25 kg/m2 and women less than 25

kg/m2. (Figure 17) Additionally, cadaveric arms were not accepted if donors had had

infectious diseases such hepatitis B virus, hepatitis C virus, and human immunodeficiency virus. To ensure donors were not infectious, Science Care, Inc. uses nucleic acid testing (NAT) on all donors for serologic evaluation of infectious diseases. This restriction was imposed to protect those working with human tissue.

Nevertheless, the arms were treated as though they were infectious and the blood

borne pathogens protocol was followed in handling them (10).

Figure 17. BMI vs Age for all arm donors (13).

Some exceptions were made to the above arm specifications. Despite having

had lung cancer, one donor with a large BMI was accepted to help increase the range

of EI measurements. Many donors who had had prostate cancer were rejected, but two were accepted because of their young age and large BMI. Another donor who had had lymphatic cancer was accepted, because there is little evidence that lymphatic cancer metastasizes to the bone (10). Table 1 summarizes demographic and clinical information about the donors of all the arms our lab received.

Table 1. Demographics and clinical information from arm donors. (Part 1)

Table 1. Demographics and clinical information from arm donors. (Part 2)

Arm Storage

Arms were shipped overnight to Dr. Loucks’ laboratory in insulated boxes

containing dry ice to ensure the arms remained frozen. Upon receipt, the arms were placed in freezers at -20°C to prevent degradation of bone stiffness (26).

Distal Radius Specimen Acquisition

As described above, in previous ulna testing (Figure 13, Step 3), researchers in

Dr. Loucks’ laboratory removed the fat and muscle tissue from the radius bones

during the forearm dissection. Each radius bone was cut adjacent but distal to the

radial tuberosity and the distal portion was removed. (Figure 18) The distal portion

was then wrapped in gauze soaked in calcium-buffered physiological saline, put into a

plastic bag, and placed into a freezer at -20 °C (Step 7) (12, 26).

Figure 18. Boney landmarks on the radius and location of the cut (in red).

2.3 Experimental Protocol

Vacuum Sealing

To avoid biocontamination of the DXA laboratory, each distal radius specimen

was removed from the freezer, unwrapped, and vacuum-sealed within a Cabela

vacuum sealable plastic bag using a Cabela’s 15” Commercial-Grade Vacuum Sealer

(Sidney, NE). As suggested by the user manual, the bags were clamped into the sealer with an inch of unused bag inside the sealer. The sealer was then placed on the dry setting and bags were automatically sealed. (Figure 19) If a bone was damp, or had excessive liquid, a paper towel was placed in the bag next to the bone to ensure proper sealing. The vacuum-sealed bones were then placed back into the freezer until later testing. (Figure 20) Artificial radius bones are shown in the figures below, because photographs of real human radius bones were not taken during this step.

Figure 19. An artificial radius being automatically vacuum sealed. Automatic sealing button (blue arrow). Cabela vacuum sealable bags (green arrow).

Figure 20. An artificial radius bone after sealing has been completed.

DXA Scanning

On a day of scanning, several vacuum-sealed distal radius bone specimens

were taken out of the freezer and placed into an insulated chest filled with ice packs to

prevent the bones from thawing (35). Because DXA measurements employ X-rays, a

licensed DXA technician from the Ohio Musculoskeletal and Neurological Institute,

Dr. Leatha Clark, performed each scan using a Hologic DXA imaging system. Each scanning session was scheduled to last for two hours to allow time for setup, duplicate scanning of eight bones (a total of 16 scans), and proper clean up.

Each specimen was mechanically secured in a plastic jig created by our laboratory to control positioning for DXA scanning (16). Polycarbonate was chosen for the jig structure and nylon for jig fasteners, because these materials do not absorb

X-rays. The jig included a plastic screw that pressed the proximal end of the radius bone onto the base of the jig to ensure the bone was securely fastened and level during scanning. (Figure 21) Pieces of plastic foam were placed under the proximal end of the specimen as necessary to help level the bone. (Figure 22)

Figure 21. Plastic jig with adjustable screw (blue arrow).

Figure 22. An artificial radius fastened in the plastic jig, leveled by foam pieces.

Additionally, the distal portion of the same side of the radius shaft as the styloid process was aligned parallel to that edge of the jig. Making the specimens level, parallel, and secure improved the repeatability of DXA scanning of the same bone and ensured that each bone was scanned in a similar fashion.

Once secured in the jig, each radius specimen was placed in 5 liters of chilled calcium-buffered saline solution bath (0-1°C) in an insulated plastic cooler to simulate the in vivo soft tissue surrounding bones, as suggested by previous investigators (16,

35). The temperature of the saline bath was monitored with a thermometer and kept at a constant by adding chunks of frozen saline between each scan. As specified by

Hologic, the cooler was placed so that the left edge of the scan contained at least an inch of air. This inch of air is necessary for Hologic software to calibrate BMC measurements during data collection. To ensure the jig and cooler did not confound measurements, a test scan was completed without a bone. As desired and expected,

because the plastic jig and saline cooler were transparent to X-rays, they were not

visible on the scan. The distal end of each specimen was positioned using the laser

beam crosshair of the DXA scanner so that the axial line of the crosshair ran parallel

to the distal portion of the styloid side of the specimen to ensure similar scans of each

bone were achieved.

The age, height, and weight of the arm donor, and the arm side (i.e. left or right arm) were entered into the Hologic software before each scan so T-scores could be determined. The template for the right or left forearm was selected and the scan took place after all investigators were clear of the scanner, to prevent radiation exposure.

After all specimens had been scanned one at a time in this manner, they were rescanned in the same way. Between scans, specimens were kept in an insulated chest with ice packs, and after all were scanned twice, they were returned to the freezer.

Within a week, specimens were removed from their vacuum-sealed bags, rewrapped in saline soaked gauze, and placed in plastic bags for longer term storage at -20 °C.

Cutting of Compression Test Specimens

After BMD measurements were collected, a precision wafer saw (PICO 155,

PACE Technologies, Tucson, AZ) was used to cut 10 mm ultra-distal (UD) regions of the distal radius specimens as compression test specimens. The edge of a nickel bonded diamond wafering blade (6” in diameter and 0.01” thick with a 0.5” bore and a circumference coated with fine, highly concentrated diamonds) was used for cutting

(Smart Cut UKAM industrial Superhard Tools, Valencia, CA). As suggested by the

manufacturer, this type of blade is commonly used to make smooth cuts on softer materials. A calcium-buffered chilled saline solution was used as a coolant to prevent overheating of the blade and thermal damage to bone protein during cutting.

Two modifications were made to the wafering saw to ensure the bone specimens could be properly cut. First, an adapter plate was made to enable a vice attached to the armature to hold radius bones orthogonally to the plane of the blade.

Second, a hole was cut into the side of the lid of the saw so that the lid could close over the shaft of the bone. (Figure 23)

Figure 23. The adaptor (blue arrow) for attachment of a fixture holding the bone and the hole in the lid for the bone shaft.

Before a distal radius specimen was mounted in the saw, a single dot was marked on the specimen where the most distal cut should occur. This location was taken from the specimen’s DXA scan, which showed the distance from the distal end of the radius to the distal edge of the UD region in millimeters. The UD region was defined as the 10 millimeters proximal to the internal margin of cortical bone on articular surface of the

wrist joint (1, 17-19, 23). A mm

graticule was then used to ensure the

dots were placed in the correct position.

(Figure 24)

Figure 24. Radius being marked on a graticule.

The bones were secured in a fixture scored with parallel axial lines to ensure the medial side of the bone (the side with the styloid process) was parallel to the fixture’s axis. (Figure 25) The fixture was then screwed into the armature adapter with an Allen wrench, taking care to mount the fixture orthogonally to the adapter plate.

Figure 25. Fixture with parallel axial lines scored into it.

The first cut was made 2-3 mm distal to the dot. The micrometer on the precision saw was then used to position the specimen so the blade would cut through the center of the dot. After this cut was made, the micrometer was again used to move the specimen 10.29 mm forward for the second cut to create the 10 mm specimen.

(Figure 26) The distance between cuts was 0.29 mm greater than the nominal thickness of the specimen to account for the 0.29 mm width of the kerf of the blade.

The 0.29 mm ensured that the standard deviation of the nominal length was less than the 0.25 mm thickness of the blade.

After specimens were cut, each piece of the radius was rewrapped in saline- soaked gauze and placed back into the freezer until testing.

Figure 26. Micrometer on the precision saw.

QMT Compression Tests

For each testing session, four specimens were removed from the freezer and

thawed in a calcium-buffered saline solution. (Figure 27) Mechanical tests of bone

require thawed bones to represent living tissue in vivo (26). A 10 kN load frame (Q-

Test Elite, MTS Systems, Eden Prairie, MN) in the laboratory of Dr. Betty Sindelar in

the School of Physical Therapy was used for QMT testing.

Figure 27. UD specimens thawing in saline.

To prepare for testing, the platens must be attached to the QMT test frame. A

10 kN load cell was attached the crosshead of the test frame and a hollow cylinder adaptor was screwed and secured into the load cell using a wrench. A cylinder was

then inserted into the adaptor and secured with a pin. A clamp ring was turned onto

the cylinder to ensure stability of the structure. A screw attached the bottom of the

cylinder to the spherically seated platen. On the bottom of the test frame, a similar set

up is used, except that a static platen was screwed into the cylinder. (Figure 28)

Figure 28. Arrangement of the spherically seated and static platens.

Before testing began, both surfaces of the platens were lubricated with

petroleum jelly to eliminate the effects of friction on the test (26). A thawed specimen

was removed from its saline filled container and the height of the specimen was

recorded as the average of 10 measurements with a micrometer. The specimen was

then placed in the center of the bottom static platen with the proximal (narrower) side

up. (Figure 29) The test frame was manually lowered until the top, spherically seated

platen was almost touching the specimen.

Figure 29. UD specimen on static platen.

Connected to the test frame is a computer equipped with Testworks (MTS

Systems) software. A pre-programed compression test program was opened to control

vertical displacement of the crosshead and to record force and displacement during

testing. The load cell was then calibrated and the force and displacement channels

were zeroed. To begin testing, quasi-static preconditioning cycles with a load limit of

100 N were repeated until EA measurements stabilized (26). Data points were

collected at 10 Hz at a crosshead speed of 0.1608 mm/min using a stepper motor that

incremented 0.000268 mm / Step. Thereby, this speed achieved = 0.1608 mm / 1 min

× 1 Step / 0.000268 mm × 1 sec / 10 datum × 1 min / 60 sec = 1 Step / datum. At this

speed, the strain rate of the 10 mm thick specimen was <0.000268/sec, since some of

the displacement of the crosshead was consumed in the compliance of the test frame,

primarily that of the load cell. Strain rates < 0.001/s prevent inertial and damping

components forces from confounding elastic force measurements, thereby achieving

the objective of a quasi-static test (21, 22). Preconditioning cycles were repeated until the coefficient of variation (standard deviation/mean) of EA measurements in the last

5 cycles declined to less than 1% (Figure 30).

Figure 30. Typical sequence of EA measurements in pre-conditioning cycles.

Once EA had stabilized, a fracture cycle was initiated by changing the load limit to 9.9 kN. For convenience, the crosshead speed was increased to 4 Steps/datum

(strain rate still <0.001/s). The Testworks program displays a graph of force vs

displacement during the test and

each test was terminated when it

was clear that the load was

monotonically declining with

further increases in crosshead

displacement (19). Figure 31 shows a typical fracture cycle in a compression test of the UD region.

Figure 31. Testworks force/displacement curve

The crosshead was then raised, and the specimen was removed. The force and

displacement data were then saved for later analysis in Dr. Loucks’ laboratory. After all four specimens had been tested, they were wrapped in calcium-buffered saline- soaked gauze and returned to cold storage.

2.4 Data Analysis

DXA Analysis

After DXA scans were completed, Hologic software was used to calculate the

area, BMC and BMD in the regions of interest. Following the Hologic instructions, the

following steps were taken when analyzing a scan: 1) Enter the ulna bone length; 2)

Position global region of interest (ROI); 3) Create bone map; 4) Define mid and UD

regions; and 5) Finalize the results.

The length of the ulna is entered to enable the Hologic software to find the so- called 1/3 region of the radius (actually the region that extends both proximally and distally 10 millimeters from the point that is 1/3 the length of the ulna bone from the distal end). The lengths of the ulna bones were previously found using the CT images.

After entering the ulna length, the global ROI must be positioned correctly. For this step, the distal end of the global ROI was aligned with the tip of the radius. The left line was then positioned to include least one inch of air (i.e., the black area in the scan). This allows for proper calibration of BMC and BMD measurements.

To create the bone map in the next step, the “bone map” button was pressed and the bone map tool box was used for editing. For each radius bone, the outline of the bone was redrawn using the delete and add bone functions to correct for errors by

Hologic’s bone detection algorithm (7). Some bones required filling using the add bone function because the threshold of the DXA software did not detect bone in areas of very low mineral content. (Figure 32)

Figure 32. DXA interface before and after re-outlining and adding bone.

To define the mid and UD regions, the “MID/UD” button was clicked. The UD region was changed from the default 15 mm to 10 mm by moving the proximal line of the default region distally 5 mm. The entire UD region was then shifted until the distal edge was adjacent to the articular surface (1, 17-19,

23). The length from the tip of the radius to the start of the

UD region was then recorded in a separate Excel spreadsheet for use in the cutting procedure mentioned above. (Figure 33)

Figure 33. DXA interface after the ROI was positioned.

Lastly, the “Results” button was clicked and the software performed the final

analysis. Results files were then transferred to a flash drive and thereby to a computer in Dr. Loucks’ laboratory. Figure 34 below shows a typical results file visualized with

ImageJ, an image analysis program. Area, BMD, BMD and BMD T-Score data were transcribed into an Excel spreadsheet for data analysis.

Figure 34. Final DXA analysis report viewed with ImageJ.

QMT Analysis

The force and displacement data were transferred by a flashdrive from the

QMT laboratory onto Dr. Loucks’ computers. The data were input into an Excel file

where the force (F) and displacement (X) data were first smoothed by symmetric

windowing to form Fs and Xs data sets. The Fs data were differentiated with respect to

the Xs data to obtain raw stiffness measurements for each data point (kmss):

kmss = (Fs(i+1) – Fs(i)) / (Xs(i+1) – Xs(i)) Eqn 1 where i=1 started at a load of 260 N. kmss data were then smoothed by symmetric

windowing to yield the measured stiffness kM.

It is well known that such stiffness measurements (kM) under-estimate the specimen stiffness (kS), because the stiffness of the test frame (kTF) is not infinite. As a

result, at any load (F), displacement of the stepper motor (x) partitions between

displacement of the specimen (xS) and displacement of the test frame (xTF), primarily

displacement of the sensing member inside the load cell. Thus,

1/kM = x/F = (xS + xTF)/F = xS/F + xTF/F = 1/kS + 1/kTF Eqn 2

Thus, the stiffness of the specimen and test frame add harmonically:

1/kM = 1/kS + 1/kTF Eqn 3

This relation rearranges algebraically to

kM = kTF × kS /(kTF + kS) Eqn 4 and

kS = kTF × kM / (kTF – kM) Eqn 5

There are two well-known ways to correct the underestimation of kS by kM.

One way is to measure xS directly, which can be done with several types of sensors,

and to ignore x. The other way is to measure kTF and to calculate kS as indicated

above. Lacking a sensor for measuring xS, and being able to measure kTF at no cost,

the latter method was chosen. kTF was measured by a running QMT compression test

up to 9900 N with no specimen between the compression platens, and calculating kTF

= kM as described above. kTF was found not to be constant value as is widely assumed.

Because displacements at a given load vary from specimen to specimen, the

th functional relationship between kTF and the applied load F was found. A 6 order

polynomial was fitted to the relationship between kTF and the applied load F to obtain

the following relationship:

6 5 4 3 2 kTF = a6F + a5F +a4F + a3F + a2F + a1F + a0

where a6 = -8.61×10-19, a5 = 2.9×10-14, a4 = -3.9×10-10, a3 = 2.669×10-6, a2 = -

-3 9.85×10 , a1 = 19.791, and a0 = 5925.5. This relationship was then used to calculate

the value of machine stiffness at every value of applied load (F) for each test. Eqn 5

was then used to find the stiffness of the specimen at each value of load (F).

Figure 35 shows results of such calculations for a typical specimen. Note in

Figure 35 that the stiffness of the specimen exceeded the stiffness of the test frame at

displacements from 0.7 to 1.4 mm. For such specimens, the peak load (where kS = 0

N/mm) was recorded as the compressive strength. As per ASTM standard 970, for such nonlinear materials in which kS is not constant, peak stiffness was taken as the

value of kS for calculation of EA.

Figure 36 shows the force displacement curve of an atypical specimen with

two major declines in kS, indicating the occurrence of two fractures. For such specimens, the load where kS declined to a local minimum was recorded as the load at

first fracture and the preceding peak value of kS was used to calculate EA.

Figure 35. Typical specimen with one fracture.

Figure 36: Atypical specimen with two fractures.

2.5 Statistical Analysis

Simple linear regressions were used to fit the simple linear model to dependent

(Y) and independent variables (X):

Yi = b1×Xi + b0 + εi

For these regressions, the following usual assumptions were made: 1) εi is a normally

distributed random error; 2) εi has a mean of 0 and a variance of σ2 or N(0, σ2); and 3)

the data are distributed with equal variance across the range of X. The simple linear regression analyses were used to estimate the slope b1, y-intercept b0, the coefficient of

determination R2, and σ. σ was estimated as the standard deviation of the residuals

around the regression line, otherwise known as the standard error of the estimate

(SEE):

-k)]

n 2 where SSESEE is= √[SSE/(nthe sum of squares for error, i.e. SSE = Σ i=1(Yi - b1×Xi - b0) , n is the number of observations, and k is the number of predictors in the model (in this case 2, the slope and y-intercept).

SEEs were used as the measures of the accuracies of predictions of compressive strength. The accuracies of pairs of predictors (SEE1 and SEE2) were then

compared by an F-statistic:

2 F = (SEE1/SEE2)

SEE1 was regarded to be significantly greater than SEE2 whenever F > F1-α(m,n),

where α = the tolerated Type 1 error rate 0.05, and m and n were the numbers of

degrees of freedom for SEE1 and SEE2, respectively.

Two additional regression results were also of interest for reasons that will be discussed below. These were the predicted values for the minimum and maximum values of the predictor:

Y(Xmax) = b1×Xmax + b0

Y(Xmin) = b1×Xmin + b0

3. Results 3.1 In Situ and Ex Situ DXA Measurements

Before previous testing had been done on the arms, DXA scans of eleven of

the whole frozen arms were taken. The UD regions were analyzed based on the

Hologic definition (i.e. 15 mm from the proximal end of the distal radio-ulnar joint) and results were recorded in an Excel spreadsheet. In addition to the analysis completed in the Methods section, DXA scans of the excised radius bones from the same arms were also analyzed in the same fashion as Hologic protocol mentioned above. Figure 37 compares BMC and BMD from the in situ and ex situ conditions with linear regression lines (in black) and the identity lines (in red). The relationships between in situ and ex situ measurements were indistinguishable from the identity line for both BMC (p{slope=1} = 0.08 and BMD (p{slope=1} = 0.97). Therefore, in this study, ex situ measurements of BMC and BMD were regarded as unbiased.

Figure 37. Comparisons between full arm and excised radius DXA measurements.

3.2 Univariate Analyses

Univariate analyses summarized the distributions of the predictors and

predicted variables in this study. Donor demographics or variables that could be collected in a clinical setting were 1) age and 2) body mass index (BMI). Variables

measured by mechanical testing included the compressive strength of the UD radius

specimens measured by QMT and its predictors 1) the compression rigidity (EA) of the UD radius specimens measured in the same tests; 2) the bending strength (i.e., peak load) of the associated ulna bones measured previously ex vivo in 3-point QMT

bending tests; 3) the bending stiffness (EI) of the associated ulna bones measured in

those bending tests; and 4) ulna EI measured in situ by MRTA. Predictors measured

by analyzing DXA images of the whole excised radius bones included 1) the area, 2)

BMC, 3) BMD, and 4) BMD T-scores of the UD and 1/3 regions.

Table 2 displays the results of the univariate analyses. In this table, comparison

of the max/min ratios of the maximum and minimum values of each predictor

indicates the relative amounts of leverage (i.e., experimental power) of the predictors

in the regression analyses. High leverage increases the likelihood of detecting a

relationship between (in this study) UD compressive strength and a predictor, if such a

relationship exists. Thus, UD radius EA had the largest max/min ratio, making it the

predictor with the greatest likelihood of being detected. UD area had the lowest ratio

and the least likelihood of being detected.

Table 2. Univariate analyses of the data collected in this project.

3.3 Bivariate Analyses

Heteroscedasticity of Variance

Linear regression analysis assumes homoscedasticity of variance (i.e., equal variance across the range of X values) and some of the relationships in this study displayed heteroscedastic data. For example, in the graphs of compressive strength vs.

BMD, variance increased with BMD. To correct for this, compressive strength data were transformed by taking the logarithm of compressive strength. As seen in Figure

38b below, the transformed data were homoscedastic across the range of BMD.

Retransformation of the regression line in Figure 38b back into the

untransformed domain yielded the nonlinear regression line in Figure 38a. In no case,

did such transformations alter the findings of this study. In comparing the accuracies

with which UD radius BMD and ulna EI measured by QMT predicted UD radius

2 compressive strength, for example, F = (SEEEI/SEEBMD) = 1.34 in the linear domain

and 1.29 in the transformed domain. Neither was close to being statistically significant

with F(32,32)α=0.05 = 1.84. Because transformation did not affect statistical results,

linear regression results are presented for simplicity and clarity.

Figure 38. (a) Linear regression results (grey) with contrasting logarithmic regression (blue). (b) Transformed regression on log scale.

Coefficient of Determination (R2)

In regression analysis, R2 values for predictors that do not have a significant

Y-intercept (i.e., BMI, UD area, UD BMC, and UD BMD) cannot be compared to R2

values of predictors that did have a significant Y-intercept (i.e., Age, BMD T-score,

Ulna EI, and UD Radius EA). This is because R2 is calculated differently in the two cases. With a significant Y-intercept, R2 is calculated in terms of the residuals from

the regression line, whereas without a significant Y-intercept, R2 is calculated in terms of residuals around the X-axis.

For example, Figure 39 shows the relationships between UD radius compressive strength and the donor demographic predictors age (R2=0.12, Figure 39a) and BMI (R2=0.79, Figure 39b). The higher R2 value for the regression on BMI should not be interpreted as indicating that BMI predicts UD compression strength more accurately than age.

Figure 39. Regressions of UD compressive strength on (a) age and (b) BMI.

Standard Error of the Estimate (SEE)

The accuracies of two predictors of the same variable can be compared by comparing their SEEs (SEE1 and SEE2) by means of F-statistics:

2 F = (SEE1/SEE2)

To test hypothesis H01, SEE for UD radius EA was used as SEE2 to compare the SEEs of other predictors of UD radius compression strength. Table 3 lists the F-statistics for

those comparisons with 32 observations of both predictors. All other predictors were

2 less accurate than UD radius EA (F = (SEE1/SEE2) > 1.83, p<0.05).

Table 3. Results of H01 hypothesis tests (all F > 1.83; all p < 0.05).

To test hypothesis H02, the maximum and minimum SEEs of the other predictors were compared. None of the other predictors was more accurate than any

2 2 other (F ≤ SEEmax/SEEmin) = (1491/1209) = 1.52 < 1.83, p = 0.12).

Clinical Error Rate (CER).

In the CER , SEE is normalized to the difference between the predicted values of the minimum(13) and maximum values of the predictor. This ratio is of clinical interest, because it corresponds to the proportion of a population that is incorrectly diagnosed (i.e., the sum of the false positive and false negative errors) when a threshold value of a predictor (e.g., low BMD) is used as a proxy for a threshold value

of correlated but unmeasurable variable (e.g., UD radius compressive strength). The clinical error rate is calculated by the following equation:

CER = SEE/[Y(Xmax)- Y(Xmin)] ×100

Values of CER are listed in Table 4 along with the results of the bivariate linear regression analyses used to compare the accuracies with which the measured variables predicted UD radius compressive strength in this study.

Table 4. Bivariate analyses of the data collected in this project.

UD Radius Compressive Stiffness and Strength

Figure 40 shows the relationship between UD radius compressive strength and

EA. This relationship had the smallest CER (15%) and explains the most variance of predictors with Y-intercepts (R2 = 0.70). Additionally, UD radius EA was significantly more accurate (SEE = 874 N) than the rest of the predictors (SEEmin = 1209 N) at estimating UD radius compressive strength (F > (1209/874)2 = 1.91 < 1.83, p=0.04) .

In this graph, the red box shows that UD radius EA discriminated well between radius bones with weak and strong UD regions (i.e., compressive strengths less and more than 3000 N). The disadvantage of UD radius EA as a predictor, of course, is that like

UD radius compressive strength, it is not measurable in vivo.

Figure 40. Regression of UD compressive strength on compressive rigidity (EA).

Ulna Bending Mechanics Predictors

Figure 41 illustrates the relationships between UD radius compressive strength and (a) ulna EI measured by QMT, (b) ulna EI measured by MRTA, and (c) ulna bending strength. Among these predictors, ulna EI measured by MRTA explained the most variance in UD radius compressive strength (R2=0.29), but there was no

difference in the accuracies with which these variables predicted UD radius

2 2 compressive strength (F = (SEEmax/SEEmin) = (1415/1346) = 1.11 < 1.83, p=0.38).

Furthermore, the red boxes in Figure 41 show how these predictors failed to

discriminate well between weak and strong UD radius specimens (i.e., compressive

strengths below and above 3000 N). However, the CER for ulna EI measured by

MRTA was much smaller than that measured by QMT (Table 4, 38% vs 60%).

8000 8000 y = 50x + 1400 7000 y = 40x + 1500 7000 R² = 0.23 R² = 0.29 6000 6000 SEE = 1401 SEE = 1346 N 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000 Compression Strength (N) Compression Strength (N) 0 0 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 (a) Ulna EI_QMT (Nm2) (b) Ulna EI_MRTA (Nm2)

8000 7000 y = 2.4x + 1400 R² = 0.21 6000 SEE = 1415 N 5000 4000 3000 2000 1000 Compression Strength (N) 0 0 200 400 600 800 1000 1200 1400 (c) Ulna Bending Strength (N)

Figure 41. Regressions of UD compressive strength on mechanical testing predictors.

DXA Predictors.

Figure 42 illustrates the relationships between UD compressive strength and

UD radius (a) area, (b) BMC (c) BMD, and (d) BMD T-scores. UD area explained less

variance (R2 = 0.80) than UD BMC and UD BMD (R2 = 0.85). For the reason

explained above, the amount of variance explained by T-scores (R2 = 0.27) cannot be

compared to the other DXA variables, but it can be compared to the amount explained

by age (R2= 0.12). There was no difference in the accuracies with which these four

DXA variables in the UD region predicted UD radius compressive strength (F =

2 2 (SEEmax/SEEmin) = (1405/1209) = 1.35 < 1.83, p=0.20).

Figure 42. Regressions of UD compressive strength and UD DXA predictors.

Figure 43 illustrates the relationships between UD compressive strength and

1/3 radius (a) area, (b) BMC (c) BMD, and (d) BMD T-scores. 1/3 area and BMD

explained less variance (R2 = 0.80) than 1/3 BMC and UD BMD (R2 = 0.82). For the

reason explained above, the amount of variance explained by T-scores (R2 = 0.13)

cannot be compared to the other DXA variables, but it can be compared to the amount

explained by age (R2= 0.12) and UD T-scores (R2= 0.27). There was no difference in

the accuracies of the four DXA variables in the 1/3 region predicted UD radius

2 2 compressive strength (F = (SEEmax/SEEmin) = (1488/1343) = 1.23 < 1.83, p=0.28).

Figure 43. Regressions of UD compressive strength and 1/3 DXA predictors

4. Discussion 4.1 Main Findings

The main findings in this study were:

(1) UD radius compressive strength, which is unmeasurable in vivo, was more

accurately predicted by UD radius compressive stiffness (EA), which is also

2 unmeasurable in vivo, than by any other predictor (Fmin = (SEEOthers/SEEEA) >

1.83) and

(2) None of the other predictors was more accurate than any other (Fmax =

2 (SEEmax/SEEmin) < 1.83.

Thus the null hypothesis H01 was rejected and the null hypothesis H02 was not

rejected.

4.2. Diagnostic Error Rate

The Clinical Error Rate (CER) considers the predictors from a different

perspective. Rather than quantifying prediction accuracy, it quantifies the proportion

of patients who will be mis-diagnosed by a physician using a predictor (e.g., UD

radius BMD) to estimate an unmeasurable variable (e.g., UD radius compression

strength) (13). Table 5 lists the CER results for the predictors studied in this project in

order from the fewest to most errors.

Table 5. CERs of predictors in increasing order.

As might be expected, these results indicate that UD radius compressive

stiffness (EA) would cause the fewest diagnostic errors (15%), but as mentioned previously, UD radius EA is unmeasurable in vivo. By comparison, the current criterion for diagnosing osteoporosis by measuring BMD in the 1/3 region of the radius (BMD T-score <-2.5), as specified by the International Society for Clinical

Densitometry (ISCD) (28), would cause about three times as many diagnostic errors

(44%). A physician would have the same error rate (46%) without DXA by simply

using the patient’s BMI to predict UD radius compressive strength. Three predictors

(UD radius BMD, radius BMC in the 1/3 region, and ulna EI measured by MRTA)

were somewhat better than the other predictors (35%-38%). UD radius BMC was

substantially better (22%), but UD radius BMC is not currently recognized by the

ISCD as diagnostic for osteoporosis. These results suggest that there may be better ways to identify patients with weak radius bones than by using BMD T-scores from the 1/3 site on the radius.

4.3 Relation to Previous Research Previous studies have used alternative methods for measuring the compressive strength of the radius to understand the mechanics of Colles’ fractures (Figure 44).

Some have used platens to compress the radius bone with the hand and soft tissue still attached (Figure 44 Left), or have potted one end of the excised radius to facilitate uniform loading of the entire bone (Figure 44 Right). Both of these procedures attempt to replicate the position of the forearm during a fall. Leaving the hand and soft tissue on the forearm may better emulate real falls, but it may not accurately assess radius strength, because force is transmitted through the carpal joints. Full excised radius procedures are better able to assess bending forces on the radius shaft as a compression force is imposed. A study by Wagner et al. (34) compared the alternative compression testing methods and concluded that best way to determine the compressive strength of the radius is yet to be determined. Because 99.99% of the load in the alternative configurations has been shown to be compressive (34), yet other studies, like this study, have performed axial compression tests on 10 mm slices cut from different positions along the distal radius. Axial compression tests like this need to be further investigated to determine if they adequately represent Colles’ fractures.

Figure 44. Alternative radius compression test methods (34).

Other studies, like this one, have also investigated the relationship between the compressive strength and BMD of the UD radius (10 mm proximal to the radio-carpal articular surface). The findings reported in this thesis are similar to those of other authors. Similar ranges of peak force or maximum load (1, 17-19, 23, 36) and similar ranges of BMD (1, 17-19, 23) were found. Ranges reported for males varied from 0.37

± 0.09 g/cm2 to 0.58 ± 0.14 g/cm2. For females, ranges of 0.24 ± .08 g/cm2 and 0.44 ±

0.10 g/cm2 were reported. One study listed an overall mean of 0.43 ± 0.09 g/cm2, while this thesis reports a mean BMD of 0.34 ± 0.11 g/cm2. Peculiarly, Eckstein et al.

reported values of BMC with an upper limit of 12 g, while our maximum BMC value(9) was only 2.20 g, even though BMD measurements were similar in both experiments and similar methods were used. Additionally, in the relationship between compressive strength and BMC, Eckstein et al. reported a similar flare in data points as BMC values increased. (Figure 45)

Figure 45. Regression from Wu, showing flared data (36).

Although similar ranges of BMD have been reported, R2 values have differed

from study to study. Others have reported values in the relationship between

compressive strength and BMD to range from R2 = 0.53 - 0.67, while this experiment

found R2 = 0.85. This difference could be due to other studies reporting a significant

Y-intercept. Therefore, it is not possible to compare R2 values. In the relationship

between distal radius compressive strength and BMC, R2 values were found ranging

from R2 = 0.53 - 0.62, while this study found R2 = 0.85. Again, this difference could

be due to the absence of a significant Y-intercept in the present study. Other literature

did not report SEE values that would have permitted comparisons between those studies and this (1, 17-19, 23, 36).

4.4 Strengths

Clinical Demographics

The large ranges of arm donor BMI and age are strengths of this project. The

age range spanned from 23 to 99 years while the BMI measurements spanned from 13

to 40 kg/m2 (i.e., from anorexic to obese). The large ranges in these two variables ensured that specimens would vary widely in strength, stiffness, BMD, and radius size. A wide range in predictor variables increases the likelihood that regression analysis will find a relationship between the X and Y variables, if such a relationship exists. Other variables with wide ranges included UD BMC, ulna EI by QMT and

MRTA, ulna bending strength, and UD radius EA.

Another strength of the study was our care to keep specimens frozen throughout each step of specimen preparation (vacuum sealing, DXA scanning, and cutting) prior to mechanical testing (35). This preserved the mechanical properties of bones throughout the experiment. Specimens were only thawed before mechanical testing to simulate in situ conditions (26, 33).

DXA scanning

Consistent DXA scanning conditions including saline temperature (0°C), depth

of saline, frozen radius bones, parallel and level positioning of the radius bones.

Additionally, repeated DXA scans and analyses were done to verify measurements.

The average values between the scans were used for all statistical analyses. Regression analysis of DXA BMD results for a subset of radius bones scanned both ex situ underwater and in situ within their arms found the data to fall along a regression line that was indistinguishable from the identity line (p=0.97). This increases confidence in the correctness of the underwater DXA measurements of the rest of the radius bones.

Specimen Cutting

Anatomically, this study ensured that the most distal portion of the UD region

was immediately adjacent to but did not include cortical bone of the radio-carpal joint

surface. This prevented that cortical bone from confounding mechanical

measurements. Use of a wafering saw to cut UD specimens ensured that the cut surfaces were parallel, and use of a diamond blade ensured that cuts were made

quickly. A typical cutting time was 8 seconds. Radius bones were kept frozen and the

blade was bathed in chilled saline to prevent friction from overheating and denaturing

bone protein while cutting.

QMT Compression Tests

Mechanical tests can be performed as material tests or as structural tests. Most

studies of bone mechanics assess the condition of bone material in terms of stress,

strain and modulus of elasticity. However, when bones break, they do not break as a

material, they break as structures. Therefore, this study assessed the condition of bone

specimens as structures in terms of load, displacement and stiffness.

This study used the gold standard method for measuring bone stiffness and

strength. Using QMT gives credibility to the force and displacement data that were

collected in the compression tests. During compression testing of the UD specimens,

additional precautions were taken to ensure proper measurement of force and

displacement. A spherically seated platen was used to ensure that no stress

concentration points arose on the surfaces of the specimen if surfaces were not

parallel. Additionally, a lubricant was used between the specimen and the platens to

ensure friction force did not arise to confound force measurements. Lastly, pre-

conditioning cycles were repeated until the coefficient of variation of repeated

measures of EA declined to less than 1%. Strain rates < 0.001/sec ensured stiffness

measurements were not confounded by inertial or damping reaction forces (26).

It is well known that QMT measurements of specimen stiffness are

confounded by the non-infinite stiffness of the test frame itself. There are two ways to

prevent this. One is to avoid the problem by measuring the specific displacement of

the specimen by means of a deflectometer, or other sensor. The second method is to

correct the QMT system’s measurement using prior knowledge of the test frame’s

stiffness. In the absence of a separate sensor, the latter method was used. Prior to

measuring specimens, the stiffness of the test frame itself was measured by pressing

the compression platens against each other. Contrary to what is widely assumed, we

found the stiffness of the test frame was neither constant nor linear with respect to the

applied load. Therefore, we fitted a 6th order polynomial to the test frame’s force-

displacement curve and used that to correct stiffness measurements for the non-infinite test frame stiffness. Indeed, several specimens were stiffer than the test frame!

Additionally, to prevent measurements of specimen stiffness (k) from being confounded by differences in specimen height (H), we corrected for any such unintended variations by calculating compressive rigidity EA = kH as our compressive stiffness predictor.

4.5 Weaknesses

Outliers

The results of this study were greatly affected by the presence of five outliers

in the data. In the relationship of UD radius compressive strength vs UD radius EA,

for example, three UD radius specimens displayed atypically high values of

compressive strength, and two displayed atypically low values (Figure 40). Because

compressive strength was the abscissa in all regression analyses, these outliers

increased the SEE of all predictors.

To put the data collected in this study into context, the study in the literature

most similar to this project was reported by MacNeil et al. (19). MacNeil et al. performed a materials test on 10 specimens from the same UD region of the radius in which they measured apparent strength as the peak stress (i.e., force per unit cross- sectional area in units of MPa) before fracture and apparent stiffness as the elastic modulus (i.e., stress per unit strain, in units of GPa) in the linear region before fracture.

Because MacNeil et al. did not report the cross-sectional areas of their specimens, which would have allowed us to convert their results to the structural units of measure in this experiment, we measured the cross-sectional areas of our specimens in CT images and converted our structural units of measure to material units of measure. The resulting comparison of test results is shown in Figure 46, which has been adapted from MacNeil et al. Compared in this way, the data of MacNeil et al. and

2 2 this study are similarly dispersed (F(10,32) = (SEEMacNeil/SEEDean) = (2.0/1.9) = 1.11,

p = 0.38). The stronger and stiffer arms in this study may have derived from the way

arm donors were specified for this experiment. Women with BMI as low as 13 and

men with BMI as high as 40 were

selected. Thus, the arm donors in

this experiment may represent a

wider range of the population than

the arm donors in the study of

MacNeil et al.

Figure 46. Regressions from MacNeil et el.(19) and this project.

The slope of the relationship between apparent strength and apparent stiffness

was substantially steeper in MacNeil’s study than in this one (18 ± 1 vs 8 ± 1, p =

0.0001). This may have occurred because MacNeil et al. loaded their specimens 30×

faster than specimens were loaded in this experiment (0.03/s vs 0.001/s). This would

have caused the force measurements of MacNeil et al. to be biased high due to the

induction of viscous damping forces as well as elastic forces (22). Viscous damping

effects were carefully avoided in this study.

QMT Testing

Specimens should be fully thawed before mechanical testing. Because

mechanical testing was completed within a few hours, there is a possibility that some specimens were not fully thawed before testing. Future studies should take greater pains to ensure that this does not occur (26).

Lack of Robustness in CER

Robustness is a statistical property reflecting the effect of changing one or two

data points on a statistic. The Clinical Error Rate (CER) is the ratio of a numerator and

denominator. SEE in the numerator is determined by the entire data set, but Y(Xmax) and Y(Xmin) in the denominator are each determined by only a single data point.

Therefore, variations in these two data points have a stronger influence on the

denominator and thereby on CER than they do on the numerator. In a previous study

in this lab (13), the relationships between ulna bending strength and ulna EI measured by QMT and MRTA were not significantly different, but their SEE values differed by

19% (91 vs 74 N) (13). In this study, their SEE values differed by only 4% (1401 vs

1346 N). More importantly, in the previous study, the denominators differed by 6%

(1060 vs 992 N), whereas they differed by 28% (3200 vs 2500 N) in the present study.

Most importantly, in the previous study, these differences between predictors tended to cancel out, because the larger SEE was associated with the larger denominator. In this study, the differences were compounded, because the larger SEE was associated with the smaller denominator. The net effects were a difference in CER of only 2%

(7% vs 9%) in the previous study but a difference of 22% (60% vs 38%) in the present study. The origin of this discrepancy was a large difference between ulna EI measurements by QMT and MRTA for the ulna with the largest EI. This caused large differences in the corresponding predicted values of UD radius compression strength

(i.e., Y(Xmax)) and thereby on CER. This high sensitivity of CER to individual data

points (i.e., its low statistical robustness) means that its values should be expected to have wide confidence intervals.

4.6 Future research

Previously, others have investigated the relationship between radius BMD and radius mechanics in bending and compression, but this study is unique in having investigated the ability of ulna bending strength and bending stiffness to predict compressive strength of the radius. Future research should repeat the present study in the effort to avoid outliers and the widely dispersed distal radius data found in other predictors. An additional study should investigate the ability of ulnar bending strength and stiffness to predict the bending strength of the radius and other long bones.

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