Lumbar Skin Profile Prediction from Anterior and Lateral Torso Measurements

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Heath Barnhart Monat, B. S.

Graduate Program in Mechanical Engineering

The Ohio State University

2012

Master's Examination Committee:

Dr. William Marras, Advisor

Dr. Blaine Lilly

Abstract

Biomechanical modeling of the spine is an important aspect of reducing the incidence of low back pain in the population. These models often rely on instrumentation placed on the back, prohibiting or severely limiting the ability to analyze tasks where the back is hidden from view. It is therefore difficult to perform subject-specific prediction of spinal loads in these situations, such as during seated work. The goal of this study was to predict the shape of the lumbar skin profile using measurements taken from the anterior and lateral aspects of the torso, furthering the ability to analyze tasks that presently prove difficult.

Thirty-nine subjects were used to create a regression model that predicts the coefficients of a quadratic polynomial describing the shape of the lumbar skin profile in the sagittal plane. Reflective markers were placed on landmarks and an optical motion capture system was used to collect position data. Markers were placed over the sternum and iliac crest to create a sternopelvic angle measure that was used in conjunction with anthropometric regressors to create the predictive model. Subjects assumed postures of 0,

10, 20, and 30 degrees of flexion and a polynomial was fit to markers that were placed over the spine. Data from eight additional subjects were used as an independent validation set to compare measured skin profiles to those that were reconstructed from the predicted polynomial coefficients.

A quadratic polynomial was found to be adequate to describe the shape of the lumbar skin profile. The regression was strong (r2 = 0.87, 0.91 for coefficient prediction) and the skin profiles predicted for the validation subjects matched the measured profiles quite well (r2 = 0.88, AAE = 5.4 mm). Similar results were observed during additional tasks designed to test the robustness of the regression model. Lumbar and scapular supports were used as chair back analogues for the validation subjects to see if accurate results could still be obtained for tasks with a full seat.

It was shown that the shape of the lumbar skin profile can be accurately reconstructed with a polynomial using predicted coefficients. This can be achieved by measuring torso angle using landmarks that are visible when the back is hidden from view. This study improved upon previous work by also including subject-specific components in the prediction of the lumbar skin profile. This methodology will further the goal of modeling spinal loads during tasks for which it is currently difficult or impossible to do so.

iii

Dedication

To my parents, Charles and Constance, and my wife, Michelle

Acknowledgments

I am grateful to my advisor, Dr. William Marras, for his guidance during all phases of my graduate studies. He has changed my ways of examining the scientific process and has improved my ability to analyze and think critically.

I am also indebted to Dr. Blaine Lilly, both for his time and expertise regarding my thesis and for introducing me to the world of research.

I would also like to extend my thanks to the students and staff in the Biodynamics

Laboratory for their support during this project, especially to Zach Huber for his assistance during data collection.

Vita

June 2005 ...... GlenOak High School

2010...... B.S. Mechanical Engineering, The Ohio

State University

2010 to present ...... Graduate Research Associate, Biodynamics

Laboratory, Department of Integrated

Systems Engineering, The Ohio State

University

Publications

Le, Peter, Jonathan Dufour, Heath Monat, Joseph Rose, Zachary Huber, Emma Alder, Radin Zaid Radin Umar, Bryan Hennessey, Mohini Dutt, and William S. Marras. Association between spinal loads and the psychophysical determination of maximum acceptable force during pushing tasks. Ergonomics DOI:10.1080/00140139.2012.692819.

Boucher, Laura C., Amanda M. Agnew, Heath Monat, John H. Bolte IV. Case study: gross anatomic dissection and CT scan of a 94-year-old female achondroplastic dwarf [abstract]. In: 28th Annual Meeting: American Association of Clinical Anatomists; 2011 July 12-16, Columbus, Ohio.

Fields of Study

Major Field: Mechanical Engineering

Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments...... v

Vita ...... vi

List of Tables ...... ix

List of Figures ...... x

Chapter 1: Introduction ...... 1

Chapter 2: Methods ...... 6

2.1 Approach ...... 6

2.2 Subjects ...... 6

2.3 Experimental Design ...... 7

2.4 Procedure ...... 7

2.5 Data Analysis ...... 13

2.6 Validation ...... 14

Chapter 3: Results ...... 16

Chapter 4: Discussion ...... 24

vii

Chapter 5: Conclusions ...... 31

References ...... 32

viii

List of Tables

Table 2.1: Basic subject anthropometry...... 7

Table 2.2: Basic anthropometry for validation subjects ...... 14

Table 3.1: Fit of polynomial to lumbar spine markers (mean ± standard deviation) ...... 16

Table 3.2: Pearson correlation coefficients (r) for the linear relationship between sternopelvic angle and lumbar skin profile polynomial coefficients (mean ± standard deviation) ...... 17

Table 3.3: r2 values for the linear multiple regressions predicting polynomial coefficients

...... 17

Table 3.4: Regression data for x2 coefficient ...... 18

Table 3.5: Regression data for x coefficient ...... 18

Table 3.6: Comparison of MSPR and MSE values to test the appropriateness of the regression model for the validation dataset ...... 19

Table 3.7: Comparison of measured and predicted skin profiles for validation dataset ... 20

Table 3.8: Measured (M) and predicted (P) values of IV angle for all levels of the lumbar spine for validation subjects [degrees] ...... 22

Table 3.9: IV angle errors for the lumbar spine [degrees] ...... 23

List of Figures

Figure 2.1: Marker placement schematic with maker set 1 (black), marker set 2 (gray), and sternopelvic angle (θ) ...... 9

Figure 2.2: Marker set 1 over the spine from T10 to L5/S1 ...... 10

Figure 2.3: Sternum markers belonging to marker set 2; the clavicle marker was not used in calculation of the sternopelvic angle ...... 11

Figure 2.4: Sitting protocol used by the subjects ...... 12

Chapter 1: Introduction

Musculoskeletal disorders (MSDs) are very prevalent and are a major reason for seeking healthcare (National Research Council 2001). In regards to chronic pain, low back pain (LBP) is the most important health problem worldwide with an annual prevalence of chronic LBP of 15 to 45 % (Manchikanti, et al. 2009). In addition, the economic costs in the United States are enormous. Occupational MSDs cost $45 to $54 billion annually in work-related expenses alone (National Research Council 2001). Total healthcare costs for individuals with back pain were estimated at $90.7 billion in 1998, with $26.3 billion of that total directly attributable to back pain (Luo, et al. 2003).

Investigating tasks associated with this common and costly ailment is a very important research aim.

A multitude of risk factors have been identified for LBP including occupational tasks, tasks of daily living, and personal risk factors (National Research Council 2001).

Tasks related to seating are of increased interest as this position is common both inside and out of the workplace. Risk factors such as prolonged and slouched seating have been identified (Eklund and Liew 1991, Lengsfeld, et al. 2000, van Niekerk, et al. 2008).

Slouched seating leads to higher spinal forces and decreased support due to the stretching of posterior spinal elements (Callaghan and McGill 2001, Bendix 1994). Sitting in a slouched posture has also been shown to aggravate existing LBP (Williams, et al. 1991).

Biomechanical models are commonly used to analyze risky tasks and investigate a link between the task and LBP. A model is used to predict spinal loading patterns which are then compared to accepted tolerance limits for various tissues in the spine

(Marras and Sommerich 1991). It is necessary that such a model use forward dynamics if accurate spinal loading prediction is to be achieved (Granata and Marras 1995, Theado,

Knapik and Marras 2007). Using this approach, spinal kinematics are used as an input to the model. Intervertebral (IV) body angles represent the motion of one vertebra relative to adjacent vertebrae and are a requirement for determining spinal loads in this manner

(Chen and Lee 1997, Lee and Chen 2000, Zhang and Xiong 2003, Ma, et al. 2008, Mörl and Blickhan 2006). IV angles may be measured directly by several means. Radiography is the accepted gold standard, but radiation is a concern (Stokes, Bevins and Lunn 1987,

Kuo, Tully and Galea 2009, Y.-L. Chen 2000). Magnetic resonance imaging devices are very precise but are impractical in most laboratory investigations (Mörl and Blickhan

2006, Fujii, et al. 2007).

In light of the difficulties faced in measuring IV angles with invasive methods, several models have been developed to use measurements of the skin over the lumbar spine as a predictor of internal spinal geometry. The skin does not give a direct measurement of spinal motion, and it has been demonstrated that a prediction model is required in order to calculate spine motion from skin measurements (Gracovetsky, et al.

1995, Delisle, Gagnon and Sicard 1997, Rice, et al. 2002, Yang, et al. 2008). Previous studies have used stick marker angle (Chen and Lee 1997), absolute position of skin markers (Mörl and Blickhan 2006, Lee, et al. 1995), or angle of skin markers (Zhang and

Xiong 2003) to predict vertebral body orientation. Bryant and colleagues (1989) transformed the entire lumbar skin profile into a profile of vertebral body centroids.

Using a similar method, Sicard and Gagnon (1993) used the lumbar skin profile to predict vertebral body locations and orientations. These studies frequently use some type of noninvasive motion capture system to record the positions of skin markers for analysis.

A requirement for studies which use a model to predict internal spine geometry from external skin measurements is that the back be free and visible to the measuring device. It is therefore difficult to use a subject-specific forward dynamic biomechanical model for tasks where this is not the case, such as during seating (Reed, Manary and

Schneider 1999, Sprigle, et al. 2002). As a result, inferior generic models (Lengsfeld, et al. 2000) or physiological and subjective measures (Steumpfle, Drury and Wilson 2004,

Bakri, et al. 2012) have instead been used to study these tasks. Alternatively, some studies have used measurement devices between the back and the seat (Vergara and Page

2000) or have altered the chair in some way (Ferguson-Pell, et al. 1980, Parent, et al.

2000, Reed, Manary and Schneider 1999) to measure the skin over the lumbar spine and permit subject-specific modeling. Neither of these methods is desirable because they alter the interface between the chair and the subject.

Attempts have been made at predicting internal spine geometry directly from external measurements that can be made when the back is hidden from view. Lee and

Chen (2000) developed a method to predict vertebral body orientations using torso and knee angle in static lifting postures. Their previous skin surface model (Chen and Lee

1997) was used to determine vertebral body orientations which were then associated with

3 the knee and torso angles. The tasks performed in this study were normal lifting tasks which pose no difficulties for current subject-specific biomechanical modeling techniques. A similar approach was taken by Chen (2000) where vertebral inclination was predicted from gross trunk angle. However, with no initial starting point, these results would not further the goal of using a subject-specific biomechanical spine model in instances where the back cannot be observed.

A different path can be taken whereby the input to a skin profile model can be predicted by measurements taken from areas of the body other than the back. By predicting these inputs, it will be possible to use a subject-specific biomechanical model to analyze seated tasks. These tasks are presently difficult to analyze in this manner, and a proper analysis will allow for investigation of additional risk areas for LBP. Hirose

(2005) explored the possibility of the prediction of the skin surface of the back using measurements taken from the anterior of the torso. Because the goal was to compare profiles of seated subjects, no attempt was made to characterize the skin profile in a way that could be used as an input to a vertebral orientation model. Hirose found a strong correlation between frontal measurements and the shape of the lumbar skin profile, indicating a high level of predictability for this link.

Leitkam and colleagues (2011) attempted to predict a measure of the lumbar skin shape, citing the need to investigate seated posture non-invasively and without altering the seat. Measurements were taken from the anterior of the body and a measure of lumbar lordosis was predicted. It was discovered that variations in posture led to weakness in comparisons across the subject pool. In addition, the measure of lordosis

4 was not sufficient for use as an input to a skin surface model to obtain internal spinal geometry and thus provided no opportunity for subject-specific biomechanical modeling.

The goal of this research was to predict the shape of the lumbar skin profile such that it could be used as an input to a skin surface model. Internal spine geometry could then be calculated and a subject-specific forward-dynamic biomechanical spine model could be used to predict spinal loading for a given task. It was important that the predictors of the skin profile be measurements that could be taken while the back was hidden from view. This would enable the analysis of a wide array of tasks, such as seating, that currently pose a challenge for this type of modeling.

Chapter 2: Methods

2.1 Approach

The goal of this research was to predict the shape of the lumbar skin profile using inputs that can be measured from the anterior and lateral aspects of the torso. These anterior and lateral measurements were arranged such that they could be obtained with the subject seated in a chair with a full back. Posterior measurements were obtained with markers placed over the midline of the lumbar spine. A regression was developed to predict the coefficients of a polynomial that could be reconstructed to represent the shape of the lumbar skin profile.

2.2 Subjects

A set of 39 subjects (20 males, 19 females) served as participants in this study.

Basic subject anthropometry is found in Table 2.1. Healthy subjects aged 18 to 30 were recruited from a university population. All subjects had never experienced back pain that had limited daily activities for seven days in a row and had never been diagnosed with any spinal disorder. Pregnant females were excluded. Approval from the Institutional

Review Board was obtained and informed consent was given by each subject.

Standard Mean Minimum Maximum Deviation Age 22.3 1.9 19 26

Stature [cm] 172.8 8.2 160.2 188.4

Mass [kg] 71.4 10.3 51.8 99.1 Table 2.1: Basic subject anthropometry

2.3 Experimental Design

The independent variable was sternopelvic angle. This was a measure of trunk angle quantified as the rotational displacement of the sternum relative to the pelvis. The levels of sternopelvic angle tested were 0, 10, 20, and 30 degrees, which covered a range of upright and slouched postures. The zero degree condition was the subject’s upright, neutral seating posture, and the other values are degrees of flexion from the neutral position. The dependent variables were the coefficients of a polynomial that was fit to the shape of the lumbar skin profile. The sternopelvic angle measurement was one of several inputs used to create a regression to predict the polynomial coefficients. These coefficients allowed for a re-creation of the predicted lumbar skin profile.

2.4 Procedure

Upon arriving at the laboratory, consent was given by the subject and anthropometry was recorded. Included in the anthropometric measures were height, weight, skinfold at the level of the L4 spinous process, and spine length from the C7 spinous process to the L5 spinous process. Age and gender were also recorded.

An OptiTrack optical motion capture system (NaturalPoint, Corvallis, Oregon,

USA) was used to record the positions of markers placed on the body. The system used

14 infrared cameras to triangulate the position of retroreflective markers (B&L

Engineering, Santa Ana, California, USA) inside the capture volume. This system was calibrated to an accuracy of 0.3 mm which corresponded to a sternopelvic angle error of

±0.68 degrees. The markers were 6.4 mm in diameter and were attached to the skin with double-sided tape.

Two sets of markers were used in this study (Figure 2.1). One marker set was used to measure the lumbar skin profile and consisted of markers placed over the midline of the spine, shown in Figure 2.2. In this set, an inferior spine marker was placed at the level of the L5 spinous process. A superior spine marker was placed at the level of the xyphoid process which corresponds to the level of T10 (Moore, Dalley and Agur 2010).

Two or three spine markers (dependent on spine length) were placed between the inferior and superior markers. This spacing arrangement allowed the highest degree of fidelity without surpassing the ability of the optical system to differentiate between markers.

The second set of markers consisted of those used to measure the sternopelvic angle and were applied in such a way as to ensure they were visible when the subject sat in a chair with a back. Two markers were placed over the right iliac crest, 5 cm apart, and one marker was placed over the left iliac crest. One marker was placed over the sternum immediately inferior to the suprasternal notch and another marker 5 cm inferior to the suprasternal notch. A final marker was placed on the right clavicle (Figure 2.3).

Figure 2.1: Marker placement schematic with maker set 1 (black), marker set 2 (gray), and sternopelvic angle (θ)

Figure 2.2: Marker set 1 over the spine from T10 to L5/S1

Figure 2.3: Sternum markers belonging to marker set 2; the clavicle marker was not used in calculation of the sternopelvic angle

Subjects sat on a flat-surfaced laboratory stool during the study to enable simultaneous recording of all markers (Figure 2.4). Using an adjustable footrest, the lower limbs were set such that the thighs were parallel to the ground and the shanks perpendicular to the ground. Subjects were unshod and kept their knees and feet shoulder-width apart. A standardized arm position was used where the hands were placed on the knees.

Figure 2.4: Sitting protocol used by the subjects .

Subjects assumed 0, 10, 20, and 30 degrees of trunk flexion as measured by the two sternal markers and the two markers on the right iliac crest. Each posture was held for three seconds while the marker positions were recorded at 100 Hz with the ARENA software package (NaturalPoint, Corvallis, Oregon, USA). Angular feedback was provided to the subjects via a monitor placed in front of them. This feedback system 12 required the inputs of all markers in the second set, but only the two markers on the right iliac crest and two on the sternum were used to calculate the sternopelvic angle. Each posture was repeated eight times, and the trial order was randomized for each subject.

Two additional types of trials were recorded with each subject. In one task, the subject was instructed to sit up straight and a 30-second trial was recorded without angular or temporal feedback. Subjects also performed an untimed dynamic motion where they were instructed to flex and extend the trunk to maximum comfortable limits.

2.5 Data Analysis

Data were exported from ARENA and analysis of the postures was performed in

MATLAB (MathWorks, Natick, Massachusetts, USA). Marker positions were smoothed with a forward and reverse 20 ms sliding window filter, and a sagittal projection was taken. The coordinates of the markers were rotated to counteract any antero-posterior pelvic tilt. The coordinates were then translated to place the marker over the L5 spinous process at the origin of the reference frame. This position corresponds to the level of the

L5/S1 interspace during flexion and thus was a convenient spinal origin point (Chaffin,

Schutz and Snyder 1972). The marker coordinates were averaged over the three second trial. A quadratic polynomial representing the lumbar skin profile was fit to the set of markers over the lumbar spine. The characterizing coefficients of that polynomial were recorded as the dependent measures.

A linear multiple regression analysis was performed using the SAS software package (SAS Institute, Cary, North Carolina, USA). This regression was used to predict

13 the polynomial coefficients based on several regressors: sternopelvic angle, an average neutral coefficient value, and several anthropometric measures.

2.6 Validation

Data from eight subjects (four males, four females) were collected in addition to the

39 subjects on whom the regression was based. The data from these eight subjects were not used in creating the regression and were used as an independent validation dataset.

The anthropometry for these subjects is shown in Table 2.2. All validation subjects completed the same trials as in the main study: eight repetitions of 0, 10, 20, and 30 degrees of sternopelvic angle; 30-second held trial; dynamic flexion/extension trial. In addition, two sets of tasks were performed to test the robustness of the model for tasks on which the model was not based.

Standard Mean Minimum Maximum Deviation Age 23.4 2.3 21 26

Stature [cm] 175.3 9.3 162.8 190.9

Mass [kg] 73.5 12.9 59.1 97.7 Table 2.2: Basic anthropometry for validation subjects

For the additional conditions, the subject sat on the same laboratory stool and a padded support was added to mimic a chair back in different configurations. The support structure was weighted such the subject could lean against it without discretion. The first condition used support the level of the middle of the scapula while keeping the spine

14 markers visible below the support. Five subjects performed 20 and 30 degrees of flexion, and three subjects performed 0, 10, 20 and 30 degrees of flexion. The second condition used lumbar support in the form of two supports at the level of the L3 spinous process, 10 cm lateral to the midline. Two supports were used to maintain visibility of the spine markers. One subject performed 20 and 30 degrees of flexion, and three subjects performed 0, 10, 20, and 30 degrees of flexion while supported. Four repetitions of these supported trials were conducted, and the trial order was randomized within each section

(main trials, scapular support, and lumbar support).

Chapter 3: Results

A quadratic polynomial was fit to the markers over the spine to provide a geometric description of the lumbar skin profile. As seen in Table 3.1, this polynomial approximated the shape of the lumbar skin profile very well throughout the range of flexion over which the subjects were tested. The square of Pearson’s correlation coefficient (r2) combined with the average absolute error (AAE) provides a clear picture of the accuracy of the polynomial in representing the lumbar skin profile. The standard deviation of the r2 measure relies on the assumption that the data is normally distributed, which is not the case since it has an upper bound of 1. Of the trials included in these calculations, 94% had r2 values greater than 0.90. Ten trials were removed from this dataset due to a skin profile marker dropout. In these cases, the polynomial r2 was exactly

1 and the AAE was exactly 0. These trials were removed because they would have artificially biased these measures.

r2 of polynomial fit AAE of polynomial fit [mm] All subjects (n = 39) 0.98 ± 0.07 0.60 ± 0.39 Table 3.1: Fit of polynomial to lumbar spine markers (mean ± standard deviation)

Based on previous studies, it was expected that the sternopelvic angle would be correlated with the polynomial coefficients that describe the shape of the lumbar skin

16 profile. The results of this linear correlation test are shown in Table 3.2. The values reported are the averages of the linear correlation coefficients for all subjects. These results support the notion that the polynomial coefficients could be predicted by linear means. The values for the polynomial coefficient could easily be predicted for intra- subject trials, but it was expected that a regression with additional variables would be needed to account for postural variations among the subjects.

x2 coefficient x coefficient All subjects (n = 39) 0.94 ± 0.04 -0.89 ± 0.09 Table 3.2: Pearson correlation coefficients (r) for the linear relationship between sternopelvic angle and lumbar skin profile polynomial coefficients (mean ± standard deviation)

A linear multiple regression was created to predict the lumbar skin profile polynomial coefficients from several regressors including sternopelvic angle. Data regarding these regressions is shown in Table 3.3 through Table 3.5. Additional regressors were chosen to create a model applicable across a wide range of subjects.

Average neutral coefficient value, gender, spine length from L5 to C7 [cm], skinfold thickness at L4 [mm], and body mass index (BMI) were included in the regression.

x2 coefficient regression x coefficient regression All subjects (n = 39) 0.87 0.91 Table 3.3: r2 values for the linear multiple regressions predicting polynomial coefficients

Variable Parameter Estimate Standard Error Pr > |t| Intercept 0.00088373 0.00021295 <0.0001

Sternopelvic Angle 0.00005295 7.893997e-7 <0.0001

Average 0 Value 0.81717 0.01697 <0.0001

Gender -0.00017243 0.00002810 <0.0001

L5-C7 Spine Length 9.08802e-7 0.00000257 0.7239

L4 Skinfold 0.00000625 0.00000233 0.0074

BMI -0.00003439 0.00000701 <0.0001 Table 3.4: Regression data for x2 coefficient

Variable Parameter Estimate Standard Error Pr > |t| Intercept 0.05651 0.03400 0.0967

Sternopelvic Angle -0.00635 0.00012665 <0.0001

Average 0 Value 0.95065 0.01212 <0.0001

Gender 0.00934 0.00454 0.0401

L5-C7 Spine Length -0.00290 0.00041330 <0.0001

L4 Skinfold -0.00166 0.00037390 <0.0001

BMI 0.00361 0.00113 0.0014 Table 3.5: Regression data for x coefficient

The regression analysis used six input variables to predict the coefficients of the polynomial describing the shape of the lumbar skin profile. All variables except sternopelvic angle were chosen to enhance the subject-specific nature of this study and allow the equations to be applied to any individual. Of the variables chosen, all were significant at α = 0.05 except for L5-C7 spine length for x2 coefficient prediction. A plot of fitted values versus residuals did not show any systematic deviations. 18

The validation dataset was used to test the regression equation. The regression was used with trials similar to the main dataset as well as the trials involving lumbar and scapular support to test the robustness of the regression model. The mean square prediction error (MSPR) from the validation dataset was compared to the mean square error (MSE) from the regression model. These results are presented in Table 3.6. The

MSPR will always be greater than the MSE, but if the values are fairly close, the predictive capability of the model is well-represented by the MSE (Kutner, Nachtsheim and Neter 2004).

x2 coefficient x coefficient

MSE – Regression Model 9.16 x 10-8 0.00236

MSPR – Validation, 9.88 x 10-8 0.00790 Main Trials MSPR – Validation, 4.87 x 10-7 0.0388 Lumbar Support MSPR – Validation, 2.91 x 10-7 0.0232 Scapular Support Table 3.6: Comparison of MSPR and MSE values to test the appropriateness of the regression model for the validation dataset

As was expected, the best prediction occurs for the main trials which are the types of trials on which the regression model is based. The MSPR values are rather close to the values for MSE of the model. The MSPR values for the trials with lumbar and scapular support are higher than those for the main, unsupported trials. This shows that the predictive capability of the model diminishes with these types of trials, but the MSPR

19 values are still relatively close to the MSE values, indicating some level of generalization is possible.

This test illustrates the predictive capability of the regression model regarding the polynomial coefficients, but a more meaningful comparison is that of the skin profiles created by reconstructing the polynomial represented by these predicted coefficients. For each of the eight validation subjects, the lumbar skin profiles were re-created from the predicted coefficients and compared to the measured polynomial created from the skin markers over the spine. The results are shown in Table 3.7 where the square of the

Pearson correlation coefficient (r2) and the average absolute error (AAE) are used in concert to determine the level of fit of the predicted skin profile to the measured skin profile.

Main Trials Lumbar Support Trials Scapular Support Trials Validation Subject r2 AAE [mm] r2 AAE [mm] r2 AAE [mm]

1 0.94 4.4 X X 0.98 8.1

2 0.58 6.1 X X 0.52 13.3

3 0.81 4.1 X X 0.99 2.5

4 0.90 2.1 X X 0.99 4.7

5 0.98 2.2 0.99 3.9 0.99 2.2

6 0.99 2.9 0.72 9.5 0.85 7.4

7 0.96 9.0 0.93 15.0 0.99 6.2

8 0.86 12.1 0.64 21.8 0.41 16.6

Mean 0.88 5.4 0.82 12.6 0.84 7.6 Table 3.7: Comparison of measured and predicted skin profiles for validation dataset 20

Overall, as foreshadowed by the coefficient prediction results of Table 3.6, the predicted profile fits best for trials similar to those on which the regression model was based. The lumbar and scapular support trials showed decreased r2 and increased AAE, but the errors are still relatively small. A comparison of the profiles is most useful because it is an indication of how different the two inputs (measured and predicted) would be to a model which predicts vertebral geometry based on skin profile.

The measured and predicted skin profiles were used as inputs to a model that predicts IV angles in the lumbar spine from the lumbar skin profile (Sicard and Gagnon

1993). Table 3.8 shows the results for IV angle from the measured and predicted profiles for all validation subjects over the range of sternopelvic angle. At increasing levels of flexion, the IV angles become increasingly positive, showing the amount of flexion at each level of the lumbar spine. In addition, the IV angles decrease with increasing spinal level, indicating higher levels are in a more extended arrangement.

Average differences between measured and predicted IV angles from the unsupported, lumbar support, and scapular support trials are shown in Table 3.9 and are yet a further indicator of the viability of the skin profile prediction regression. The difference in angle was lowest for the main trials, indicating better predictive capabilities for the types of trials with which the regression was created. For the lumbar and scapular support trials, the angles were generally increasingly overpredicted at superior levels of the lumbar spine. The average absolute errors are reported to show the level of absolute error found between the measured and predicted angles.

SP L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 Avg Subj ang M P M P M P M P M P M P Diff 0 -0.13 -1.26 -2.67 -1.68 -2.39 -2.09 -2.75 -2.45 -2.98 -2.69 -3.17 -2.90 -0.17 10 1.20 0.66 1.66 0.46 1.25 0.25 1.03 0.04 0.80 -0.16 0.59 -0.34 0.94 1 20 2.25 1.66 2.59 1.55 2.31 1.41 2.12 1.25 1.86 1.06 1.62 0.90 0.82 30 3.76 3.37 3.39 3.25 3.32 3.07 3.05 2.79 2.67 2.44 2.33 2.12 0.25 0 7.56 -3.47 6.67 -4.12 5.50 -4.69 4.10 -5.07 2.61 -5.16 1.24 -5.12 9.22 10 3.11 -0.98 2.37 -1.28 1.48 -1.56 0.60 -1.81 -0.25 -1.97 -1.03 -2.11 2.67 2 20 0.52 0.37 0.20 0.22 0.10 0.08 -0.06 -0.06 -0.20 -0.20 -0.33 -0.32 0.02 30 1.74 1.61 1.29 1.50 1.28 1.39 1.13 1.24 0.96 1.07 0.80 0.91 -0.09 0 2.18 2.04 1.93 1.73 1.24 1.41 0.62 1.06 0.04 0.71 -0.47 0.39 -0.30 10 2.25 2.57 2.46 2.45 2.19 2.29 1.97 2.07 1.70 1.81 1.46 1.56 -0.12 3 20 1.75 2.61 2.01 2.61 1.80 2.53 1.64 2.34 1.44 2.07 1.25 1.81 -0.68 30 2.87 4.24 2.87 4.41 2.73 4.36 2.52 4.03 2.23 3.49 1.95 2.97 -1.39 0 0.62 -0.34 0.36 -0.72 -0.38 -1.09 -0.98 -1.45 -1.51 -1.73 -1.99 -1.98 0.57 10 0.81 0.68 0.99 0.55 0.76 0.41 0.62 0.27 0.46 0.14 0.33 0.01 0.32 4 20 1.64 1.63 1.74 1.53 1.57 1.42 1.42 1.28 1.23 1.10 1.06 0.95 0.12 30 3.15 3.34 3.08 3.30 2.96 3.16 2.74 2.91 2.41 2.55 2.12 2.22 -0.17 0 -1.78 -1.52 -2.75 -1.97 -3.09 -2.42 -3.48 -2.80 -3.69 -3.06 -3.84 -3.26 -0.60 10 0.68 0.42 0.11 0.17 -0.06 -0.08 -0.32 -0.34 -0.56 -0.56 -0.78 -0.77 0.04 5 20 1.92 1.60 1.32 1.47 1.32 1.32 1.14 1.15 0.94 0.95 0.76 0.78 0.02 30 2.92 2.89 2.21 2.77 2.26 2.61 2.05 2.37 1.79 2.07 1.55 1.81 -0.29 0 1.66 2.50 2.77 2.22 2.01 1.92 1.67 1.59 1.31 1.23 0.98 0.91 0.01 10 1.56 2.70 2.43 2.59 1.93 2.44 1.72 2.22 1.47 1.94 1.25 1.69 -0.54 6 20 2.59 3.81 3.06 3.80 2.73 3.68 2.50 3.41 2.21 3.01 1.93 2.62 -0.89 30 3.54 4.78 3.61 4.93 3.44 4.84 3.17 4.46 2.80 3.86 2.44 3.28 -1.19 0 -0.92 0.85 1.38 0.58 0.22 0.31 -0.08 0.03 -0.35 -0.23 -0.58 -0.47 -0.23 10 1.27 1.41 1.90 1.31 1.53 1.19 1.36 1.04 1.16 0.88 0.98 0.73 0.28 7 20 3.32 3.08 3.61 2.95 3.36 2.76 3.10 2.50 2.73 2.17 2.37 1.88 0.52 30 3.65 4.35 3.77 4.24 3.61 3.96 3.34 3.54 2.94 3.01 2.56 2.56 -0.30 0 -2.76 -2.23 -3.54 -2.78 -4.04 -3.31 -4.44 -3.74 -4.58 -3.97 -4.62 -4.13 -0.63 10 -0.84 -0.23 -2.00 -0.44 -2.02 -0.65 -2.25 -0.85 -2.36 -1.01 -2.42 -1.15 -1.26 8 20 1.40 0.74 0.20 0.63 0.42 0.52 0.27 0.39 0.12 0.27 -0.01 0.15 -0.05 30 3.69 1.95 3.28 1.84 3.34 1.70 3.10 1.53 2.74 1.32 2.40 1.14 1.51 Table 3.8: Measured (M) and predicted (P) values of IV angle for all levels of the lumbar spine for validation subjects [degrees]

Absolute L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 Average Main 0.38 0.40 0.30 0.24 0.18 0.13 0.27 Trials Lumbar -0.28 -0.22 -0.57 -0.79 -0.94 -1.04 0.64 Support Scapular 0.39 0.52 0.19 -0.03 -0.24 -0.42 0.30 Support Table 3.9: IV angle errors for the lumbar spine [degrees]

Chapter 4: Discussion

This study attempted to provide a means for predicting the geometric shape of the lumbar skin profile based on measurements taken from the anterior and lateral aspects of the body. In order to characterize the shape of the lumbar spine, it was necessary to indirectly measure the ends of the lumbar spine by measuring the thorax rotation relative to the pelvis. Any movement of the pelvis relative to the trunk brings about changes in lumbar spine geometry, similar to the thorax moving relative to a stationary pelvis

(Sprigle, et al. 2002, Delisle, Gagnon and Sicard 1997). The pelvis was used as the base of the lumbar spine since trunk motion consists of that of the pelvis and that of the vertebral column (Vanneuville, et al. 1996, Vanneuville, et al. 1997, Kuo, Tully and

Galea 2009). By also monitoring the thorax, the superior end of the lumbar spine was indirectly measured. The rib cage lends stability to the thoracic spine making it less mobile and mechanically stiffer than the other spine sections. Sagittal mobility of the thoracic spine beings to significantly increase around the level of T10 which is the superior end of the skin profile measured in this study (White and Panjabi 1990). The measurement taken in this study is of the sternum, which is part of the rigid thoracic cage structure and moves concordantly (Hirose 2005).

Many previous studies have measured lumbar lordosis, and a simple angular measure is very commonly used (Gracovetsky, et al. 1995, Vergara and Page 2000, Kuo, Tully and Galea 2009, Tully, Fotoohabadi and Galea 2005, Singh, Bailey and Lee 2010). 24

These simple measures of lordosis are not descriptive enough to use for complex biomechanical modeling and cannot be used as the input to a skin profile model. Rather, some sort of geometric profile description is required. This study showed that a quadratic polynomial was sufficient to describe the shape of the lumbar skin profile over 0 to 30 degrees of trunk flexion as measured by sternopelvic angle. Extending the profile to the level of T10, as in this study, shows that a large part of the spine can be represented by this low order polynomial. The coefficients of a quadratic polynomial are readily understood, and this simple measure adds no undue complication and can be used to characterize the shape of the lumbar skin profile with much more fidelity than a simple angle. It also provides an input to a separate model predicting internal vertebral geometry from such a profile.

Several attempts have been made at predicting and characterizing the lumbar skin profile based on measurements taken from other areas of the body. Two previous studies found that when using one measure to predict lumbar skin shape, the results could not be generalized across subjects (Hirose 2005, Leitkam, Bush and Li 2011). The present study incorporated several additional regressors to provide a prediction equation that would be applicable across subjects to address this issue. Leitkam and colleagues achieved r2 values of 0.27 to 0.43 when using a one-variable prediction model, compared to 0.87 and

0.91 for the current study. The coefficients for the neutral sitting position were averaged and included in the regression to help account for normal postural variation across the subjects. All subjects were instructed to sit up straight for the zero degree condition and this, coupled with variation in normal spine shape, precipitated the need to use such a

25 measure to ensure the results would cover a wide range of possible subjects. Several anthropometric measurements were also included in the regression in an attempt to account for the variations in spine shape (Sprigle, et al. 2002, Singh, Bailey and Lee

2010). The spine length from L5 to C7 was included since subjects with longer spines would have a relatively shallower profile compared to subjects with shorter spines. This variable was significant only in x coefficient prediction. A possible reason for this is that the x2 coefficient in the quadratic polynomial is largely a measure of the degree of curvature of the profile which is affected much more strongly by the sternopelvic angle.

The skinfold thickness at the level of L4 and BMI were used to account for different body dimensions and their influence on the shape of the skin profile. The skin profile was not normalized based on body dimensions to prevent any undue manipulation. Instead, these anthropometric measures were used as additional regressors to account for the variation seen across body types. Gender was also included to keep the model as general as possible and since there are known gender differences in spine shape and motion profiles

(O'Sullivan, et al. 2006). Without creating a regression that is applicable to a wide array of subjects, the goal of enabling subject-specific biomechanical spine modeling is not furthered.

The geometric profile created by applying the predicted polynomial coefficients matched the measured skin profile rather well. Errors generally increased towards the superior end of the profile. This can be attributed to the origin placement at the L5 spinous process marker. Error also generally increased at higher degrees of flexion. This indicates a loss of predictive ability as subjects move further away from the neutral sitting

26 posture, but the errors were still small (4.75, 4.73, 7.04, 8.70 mm average for 0, 10, 20,

30 degrees of unsupported sternopelvic angle for the validation subjects). The sternopelvic angle regressor bore the sole responsibility for the changes in skin profile over the flexion range, reducing accuracy at larger flexion angles. However, it was desirable to keep the model as simple as possible, and this is accomplished through using a minimum of regression variables. As seen in Table 3.7, several validation subjects had low r2 values for profile matching. One reason for this is that the profile is rather shallow and featureless. Thus, any disagreement will be magnified when correlating the measured and predicted profiles. When a slight lordosis was measured but is absent from the predicted curve, the correlation is poor, resulting in low values for r2. This was usually manifested at low flexion angles where the subject’s skin profile was linear or nearly so. Because the absolute error values are still generally in agreement with other subjects, the profiles still tend to match quite well.

The model robustness was tested in several ways. The lumbar and scapular support trials were used to observe any errors that might arise when using this prediction model with a subject in a seat with a back. Since these trials were different than those on which the model was based, higher errors were expected, but they were still minimal. One source of error is the small amount of translation that is possible in the vertebral joints

(Harrison, et al. 2002). By applying a translational force on the support, the thorax is displaced anteriorly. This motion was not measured and is not reflected in the model, but the errors for these trials are comparable to those found in the unsupported trials.

Deformation of the skin, especially during lumbar support trials, could be another source

27 of increased error. The supports were much smaller than a typical chair back, leading to increased pressure on the soft tissues surrounding the spine. This deformation at the inferior end of the lumbar skin profile would have a negative effect on the prediction capabilities.

The robustness of the model was also tested by applying the model to postures taken from the dynamic maximum flexion/extension trials. The model sensitivity to dynamic motions as well as to interpolation was tested by comparing the skin profiles of the validation subjects at 5, 15, and 25 degrees of sternopelvic angle in flexion and return during the dynamic trials. Hysteresis effects were evident, showing low x2 coefficient prediction in flexion and high prediction in return. MSE values from the regression and

MSPR values from the data were fairly close, suggesting good coefficient predictability in this situation. The fit of the skin profiles was also comparable to that of the unsupported trials, showing that the model is still viable in dynamic and interpolative situations.

In order to calculate spinal loading patterns from the data in this study, the skin profile must be used in a model to predict IV angles. The resolution of spinal force into compressive and shear components is dependent on the angular orientation of the vertebrae relative to one another. It is these values that are compared to tissue tolerance limits, so proper calculation is essential to determining injury risk for a given task. The measured and predicted skin profiles produced IV angles that were an average of 0.27 degrees different. This is comparable to previous results of 0.22 degrees (Lee, et al.

1995) and 1.98 degrees (Chen and Lee 1997) from other studies predicting internal

28 geometry. It is also much lower than the reported accuracy of the model used to calculate the IV angles, 2.1 degrees, indicating that the differences found in the skin profiles are minimal (Sicard and Gagnon 1993). The values obtained for IV angles indicate a rather straight spine when sitting in a neutral posture. The tilt of the pelvis and change in center of gravity that occurs when moving from a standing posture to a sitting posture is the main reason for this loss of lumbar lordosis. As the subjects flexed, the degree of kyphosis in the lumbar region increased, which is evident in the increasing IV angle at each vertebral level.

The overall effect of skin distraction is to be noted in any study involving skin markers. These effects were minimized in the current study by using appropriate landmarks. The sternum is an excellent choice due to limited skin distraction and the low level of tissue between the skin and bone (van Niekerk, et al. 2008, Kuo, Tully and Galea

2009). The iliac crest location has similar properties and offers limited skin distraction when observing the motion of the pelvis (Lamoreux 1996, Vanneuville, et al. 1996,

Vanneuville, et al. 1997). The midline of the spine also is not prone to significant skin distraction, and any distraction occurs longitudinally (Lundberg 1996, Moga 2010). This is not of concern in this study since geometric lumbar skin profiles are compared and not absolute spine marker locations. One subject in this study had a BMI greater than three standard deviations above the mean. Extra adipose on this subject prevented accurate palpation of the bony landmarks; thus, his results were removed from the analysis.

Several limitations to the current study should be noted. Firstly, motion was only analyzed in the sagittal plane. However, a goal was to provide an input for models which

29 predict vertebral orientation from skin profile, most of which exist only for the sagittal plane. Also, the measurement of the thoracic cage as an analogue for the thoracic spine may have introduced undesired artifacts especially of translation and rotation motion during respiration. To investigate this, the breathing cycles of the validation subjects were analyzed using the 30-second trials. Gross torso motion was estimated by using a heavily-filtered signal, and deviations from this signal were observed. The average absolute error for all subjects was 0.46 degrees, comparable to the maximum error of the motion capture system. Additionally, this study used static postures in characterizing the shape of the lumbar skin profile. Seated tasks are generally static by their nature, and prolonged seating is a commonly cited risk factor for LBP. The data from the interpolation tests show that very little error was introduced when using the current regression model to study dynamic trials. It is likely that this approach will therefore be applicable to tasks involving sit-to-stand, vehicle ingress/egress, or occupational work with a back apparatus in addition to static seating tasks.

Chapter 5: Conclusions

In this study, the lumbar skin profile was predicted using torso angle as measured from the anterior and lateral aspects of the body. Additional measures were used to allow for a subject-specific regression. This approach will allow for the prediction of the lumbar skin profile when the back his hidden from view, such as during seating tasks.

This is a first step in allowing subject-specific biomechanical modeling of tasks where it is currently difficult or invasive to do so. These biomechanical models can be used to predict spinal loading patterns and determine injury risk for a given task.

Future work in this area should concentrate on reducing the number of models needed to produce these spinal loading results. The model from the current study requires the use of a further model to predict internal geometry; combining these to predict internal geometry directly from anterior and lateral torso measurements is a logical next step. Also, expanding the prediction model to three-dimensional movement would enable the modeling of complex tasks at a similar level of fidelity and would allow for spinal loading prediction for virtually any task.

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