‘%V‘,) Department ofVeterans Affairs

Journal of Rehabilitation Researchand Development Vol . 31 No . 2, 1994

Pages 111—1 19

Three-dimensional computer model of the human buttocks,in vivo

Beth A. Todd, PhD and John G. Thacker, PhDUniversity of Alabama, Tuscaloosa, AL 35487-0278; University of Virginia, Charlottesville, VA 22903

Abstract —In an effort to reduce the incidence ofdecubitus ulcers among wheelchair users, current work incushion design concentrates on minimizing the pressure atthe buttock-cushion interface . Finite element analysis canshow the stress levels throughout the soft tissue betweenthe cushion and the ischial tuberosity and give designers abetter indication of the effects of a particular cushion.Finite element models were generated of the tissuesaround the ischial tuberosities of male and femalesubjects . Linear three-dimensional models were generatedusing a 386 computer and solved with infinitesimaldeflection theory. The resulting minimal principal stresseswere 17 kPa and 15 kPa at the buttock-cushion interfacefor seated male and female subjects, respectively . Compu-tational results were verified experimentally with magneticresonance imaging and interface pressure measurements.

Key words : biomechanics, computer models, decubitusulcer, feasibility studies, magnetic resonance imaging,mechanical stress, pressure, wheelchairs.

INTRODUCTION

Development of decubitus ulcers is a seriousproblem for wheelchair users, who sometimes sit intheir chairs from 12 to 16 hours per day . For thosewith insensate skin, such as some individuals withparaplegia and quadriplegia, the first indication ofulcer formation is redness on the skin surface.However, surgeons have found evidence that ulcers

Address all correspondence and requests for reprints to : Beth A . Todd,PhD, The University of Alabama, 210 Hardaway Hall, Box 870278,Tuscaloosa, AL 35487-0278 .

form internally and spread toward the surface of theskin (1) . By the time surface damage is noticed,subcutaneous necrosis may already have occurred.

Producers of wheelchair cushions use interfacepressures between the buttocks and the cushion toassist in determining if adequate pressure relief isprovided. If interface pressure is directly propor-tional to the internal pressure at the site of decubitiformation, pressure at the interface will provideenough information for cushion design . If the twopressures are not directly proportional, more infor-mation must be gathered to effectively designpressure relieving cushions.

Previous work has been performed by severalinvestigators in this area. Reddy, et al., created anexperimental buttock model from a semicircular slabof PVC gel (13 .9 cm in diameter and 3 .8 cm thick).The gel was placed around a 5 .7 cm-long woodencore that represented the ischial tuberosity . Thepurpose of their experiments was to investigate thestress distribution in the buttock resulting fromseveral common cushion materials . Four differentfoam cushions and a PVC gel cushion, each 38 mmthick, were investigated under a vertical load of 20 .2N applied to the buttock . In general, high stressregions occurred beneath the wooden core . Thelowest normal stresses were caused by the mediumdensity foam cushion . The shear stresses generatedby the gel cushion were approximately twice thosefrom the medium density foam cushion (2).

Brunski, et al . generated pressure sores inYorkshire pigs using cylindrical indenters with sur-face radii of curvature of 8 cm and 3 cm . The

111

112

Journal of Rehabilitation Research and Development Vol . 31 No . 2 1994

affected tissues were modeled with axisymmetricfinite elements to calculate the stress distributionsaround the indenters . In the model, the tissue wasassumed to be linear, elastic, and isotropic . Resultsshowed an approximately Hertzian surface stressprofile for the 3 cm radius of curvature indenter.The other indenter created a non-Hertzian profilewith large peaks near the contact radius . Maximumoctahedral stresses occurred in the skin layer (3).

Chow and Odell created an axisymmetric, three-dimensional finite element model of a human but-tock . The purpose of their work was to determinethe three-dimensional stress state within the softtissues due to different loading conditions. A but-tock was modeled as a homogeneous hemisphere oflinear elastic isotropic soft tissue with a rigid core torepresent the ischial tuberosity. It was assumed thateach buttock bore a load of 300 N . The six loadingconditions considered were floating on water, float-ing on mercury, sitting on a rigid frictionless flatsurface, applying a modified cosine pressure distri-bution, sitting on a foam cushion, and sitting on afoam cushion with a lubricated interface . In allcases, the highest stresses occurred under the rigidcore. Results showed that hydrostatic pressure pro-duced minimal distortion and that gradient pressurewas the main cause of von Mises stress (4).

Kett and Levine developed a model based onthe premise that pressure sore etiology could bebetter related to tissue distortion or deflection thanseating interface pressure . The bond-graph tech-nique was used to analyze their one-dimensionalnonlinear mechanical model . The authors felt thattheir model provided insight into the significance oftime dependence in the formation of decubitusulcers (5).

The purpose of the research presented in thispaper is 1) to show that a finite element model couldbe developed that gave results consistent withexperimental data and 2) to begin to relate buttock/cushion interface pressures to internal pressures atthe ischium. The finite element method can be usedto calculate relationships between displacements andpressures or stresses for complex structures madefrom several materials . Thus, it can be used toexamine different designs or prototypes of a device,such as a wheelchair cushion (6).

Wheelchair cushion design is usually performedin small business or clinical settings that do not haveaccess to CRAY or large mainframe computers .

Particularly in light of the need to design andgenerate devices at minimal costs, it was decided togenerate the models in this project using IBM-compatible 386 and 486 computers . The finiteelement package PRIMEGEN" was donated byGeometrics, Inc . and used to generate and solve themodels.

METHOD

Models were generated of two ambulatorysubjects : a 58-kg female and a 74-kg male . Modelswere created to represent seated and supine positionsfor each subject on a custom-contoured cushion . Togenerate the models, their geometries were defined,material properties determined, and loading andboundary conditions prescribed.

The objectives of this project were to show thatthe finite element method can be used in cushiondesign and to compare stresses throughout the softtissue. To participate in this project, the experimen-tal subjects had to undergo several different experi-ments . Once the techniques for generating a modelhave been developed, members of specific popula-tions may be recruited to determine the characteris-tics of a particular group. For establishing the initialprotocols, young ambulatory subjects were chosenfor their availability and agility.

GeometryA number of assumptions regarding all aspects

of the model were made to keep the size of themodel manageable for a desktop computer. Theischium is cited as the location where wheelchairusers are most likely to develop pressure sores (7).Bilateral symmetry was assumed, so only the tissuesaround the right ischial tuberosity were included inthe model.

The geometry of each subject's anatomy wasgenerated noninvasively using nuclear magnetic res-onance imaging (MRI) (8) . Each subject was placedin a supine position inside the tube of a SiemensMagnetom 1 .0 Tesla whole-body MRI imager . Theimager measured the hydrogen content of differenttissues of each body and generated a two-dimen-sional map with a 1 mm resolution of the geometryof transverse abdominal slices . A typical slice of atransverse abdominal cross-section is shown in Fig-ure 1 . Information from each slice was digitized and

113

TODD and THACKER : 3-D Buttocks Computer Model

Figure 1.Typical MRI image of a transverse cross-section of the pelvis.

used as the basis for generating the finite elementgeometry . By combining the information fromseveral parallel slices spaced 8 mm apart, a three-di-mensional model was created.

A cross-section of the finite element model isshown in Figure 2 . The half-cushion shown is 221mm wide and 73 .6 mm deep. For the male subject,the ischial tuberosity is located 64 .4 mm from theplane of bilateral symmetry, 109 mm above thebuttock-cushion interface, and 94 mm from thelateral surface . For the female subject, these dis-tances are 60.8 mm, 111 mm, and 97 mm, respec-tively. Both models were generated with eight-nodedthree-dimensional isoparametric brick elements . Themale model contains 1008 elements : ischial tuberos-ity 36, cushion 433, elastic foundation 84, and softtissue 455 . The female model contains 1008 ele-ments: ischial tuberosity 120, cushion 337, elasticfoundation 83, and soft tissue 468.

The geometries for the models were generatedby placing the subjects in "free-hanging" positions.The back and thighs of each subject were elevated

Figure 2.Cross-section of finite element model of male subject.

and supported by foam cushions while the buttockstissues were maintained in their undeformed shape.For model verification purposes, both subjects werereimaged while reclined on custom-contoured cush-ions with their tissues under body weight loading.Both of these positions are presented pictorially inFigure 3.

The tube in the MRI imager has an openingslightly larger than the average adult's shoulderwidth. This small diameter precluded the generationof geometry for the subjects in a seated position.The supine geometry was used in both cases, and thematerial properties were adjusted to account for thepostural change. The change in orientation of themuscles in the supine position led to the overalltrend of the tissues around the ischial tuberositybeing less stiff or having a smaller Young's modu-lus, as shown in Table 1 .

114

Journal of Rehabilitation Research and Development Vol . 31 No. 2 1994

Figure 3.The loading conditions used for imaging.

Table 1.Material properties used in models.

Material Young's ModulusE (kPa)

Poisson's Ratiov

Bone 17000 0 .31

Cushion 10 .2 0 .1

Soft TissueSeated Female

47.5 0 .49

Soft TissueSupine Female

11 .9 0 .49

Soft TissueSeated Male

64.8 0.49

Soft TissueSupine Male

15 .2 0 .49

Elastic FoundationSupine Female

1 .19 0.49

Elastic FoundationSupine Male

25 .3 0 .49

As a person sits down, the contact area betweenthe buttocks and the seating surface changes . Tomodel this situation, many cushion geometries wouldrequire the use of sophisticated contact-gap elementsto allow change in contact surface between loadedand unloaded conditions . The use of a custom-contoured cushion prevented the introduction of thatadditional complication into the model . Commonnodes were used between the elements representingthe buttocks and those representing the cushion.

Material PropertiesFour different materials were included in each

model: bone, soft tissue, cushion, and elastic foun-

dation. Average values of Young's modulus ofelasticity and Poisson's ratio for bone were takenfrom the literature (9-17) . Material properties of thecushion material were determined from load-deflec-tion tests described in the literature (7).

Material properties for each subject in bothseated and supine positions were determined experi-mentally by a process similar to that described bySteege, Schnur, and Childress (18). A custom-contoured cushion made from uncoated, open cell,HR 55 polyurethane foam was cut for each subjectin both seated and supine positions . A hole was cutin each cushion under the subject's right ischialtuberosity, and the cushion was placed on a woodenchair especially designed for measuring these mate-rial properties . The contour gage developed byGordon was used to record the data (19,20) . Thegage consisted of a stepper motor that drove athreaded shaft containing a strain gage to measureaxial compression. As the motor drove the shaftupward in one mm increments, the axial force wasrecorded until a predetermined force was measuredor exceeded . A Keithley data acquisition system wasused to record the relationship between the positionof the shaft and the force on the gage . These datawere transformed into a force deflection curve asshown in Figure 4 . The equation associated with thecurve in Figure 4 is

F= - 0.112 + 0 .967x+ 10(- 0 .908 +0 .0704x)

To maintain the manageability of the model,several assumptions were made regarding the mate-

Figure 4.Force-displacement relationship for female subject in seatedposition.

115

TODD and THACKER : 3-D Buttocks Computer Model

rial properties of the soft tissue . While biologicaltissue is nonlinear, anisotropic, and viscoelastic, dueto the lack of knowledge of the particularmicrostructure of the tissue, it was assumed that thesoft tissue in the buttocks was linear, isotropic, andtime independent . Therefore, the initial linear por-tion of the force-deflection curves was used tocalculate four moduli of elasticity, one for eachsubject in each position . Material properties used inthe models are shown in Table 1.

Applied LoadingMany investigators have pondered the transfer

of load through the tissues of the body (21,22).Most of the load is carried through the skeletalstructure, but it is not clear how it is transferredthrough the soft tissue of the buttocks whensomeone sits . To maintain a manageable model, asimple form of loading was applied . A singleconcentrated force was applied downward at a nodein the center of the top surface of the elementsrepresenting the ischial tuberosity . This type of loadapplication creates a region of stress concentrationin the ischial tuberosity . Since the region of interestis the soft tissue between the cushion and the bottomof the ischial tuberosity, this region of fictitious highstress can be ignored.

The magnitude of the force applied to eachmodel was based on each subject's weight . For thesupine position, half of the weight of the pelvis wasused. For an average male, this is 6 .7 percent of thetotal body weight or 48.4 N for the 74 kg subject(23) . For an average female, the right pelvis com-prises 8 .6 percent of the total body weight or 48.5 Nfor the 58 kg subject.

For the seated position, half of the weight ofthe upper body was used . For an average male, thisis 29 .2 percent of the total body weight or 211 N forthe 74 kg subject . For an average female, the righthalf of the upper body contains 29.7 percent of thetotal body weight or 167.5 N for the 58 kg subject.

Boundary ConditionsBilateral symmetry was assumed so that only a

portion of the right buttock was included in themodel . To represent this symmetry, all of the nodeson the plane of symmetry or centerline boundarywere constrained from horizontal motion.

In normal use, a wheelchair cushion is placedon top of a hard, flat surface . To represent that

surface, all of the nodes on the bottom plane of thecushion were constrained from vertical motion.

The other planes of the model represent sur-faces that have been cut from other tissues of thebody. These surfaces cannot be accurately repre-sented by either free or fixed surfaces . In acompromise between accuracy and model size, thetop plane of the model was constrained by an elasticfoundation. The front and back surfaces of themodel remained free . The elastic foundation wasmodeled by a series of semi-infinite elements con-strained on the end that is not attached to the softtissue. Material properties for the elastic foundationare given in Table 1.

RESULTS

Displacements were calculated with the pro-gram PRIMEGENTM for each subject under bodyweight loading in both the seated and supinepositions . A graphical representation of the verticaldisplacements for the seated male subject are shownin Figure 5 . Note that the figures containingdisplacement and contour plots are black and whitesketches of the color computer plots . The outline ofthe elements may not exactly match that shown inFigure 2 . A vectorial sum of the y- and z-displace-ments (downward and forward) for the seated malesubject are shown in Figure 6 . In all cases, theischial tuberosity had translated as the soft tissueunder it was compressed and pushed outward . Asexpected, the models of the seated position showedmore deflection (y- and z-directions) than the mod-els of the supine position . Deflection of the soft

-0 .26

0 .25 -052 em

f---I 0.52-0.77 ,M

077-100 ".

100

11 I. =;1z9-155-

1155- ! 80~m

1.80- 2 06 c,,

205-Z

232-2523

2 .58-283.

2 .03 - 3.09 em

Figure 5.Vertical displacements for seated male subject .

116

Journal of Rehabilitation Research and Development Vol . 31 No. 2 1994

the minimum principal stresses, a3, which areanalogous to the pressures which are often measuredclinically . Von Mises stresses were also calculated.An example of the stress contour plots for the seatedmale subject are shown in Figures 7 and 8 . Theseplots show there is little difference in the buttock-cushion interface stresses between the seated andsupine positions for both subjects. The values inthese plots are somewhat misleading because thestresses are in units of N/cm2. One N/cm 2 isapproximately equivalent to 75 mm of Hg which arethe units normally used in clinical studies . In thosestudies, changes in pressure of 25 to 40 mm of Hg

Figure 6.y- and z-displacements for seated male subject.

tissue directly under the ischial tuberosity was calcu-lated. Comparisons of the computational deflectionswith those determined from the digitized imagesgenerated with the MRI are shown in Table 2.

For both the male and female subjects, thecomputational displacements are within 5 percent ofthe displacements that could be measured experi-mentally with the MRI. The displacements in Table2 are vertical displacements . Note that the femalesubject shows greater vertical displacement in thesupine position than in the seated position . In theseated position, the z-displacement is much greater(approximately 6 cm) than it was in the supineposition. This large displacement is partly due to thefact that the front and back surfaces of the modelare free.

The computer program PRIMEGENTM is capa-ble of calculating stresses in the directions of the x,y, and z axes, the three principal stresses, and vonMises stress. The stresses of primary interest were

Table 2.Displacements under the right ischial tuberosity .

Position ComputationalDisplacement (cm)

ExperimentalDisplacement (cm)

Male—supine

Male—seated

Female—supine

Female—seated

1 .8

3 .34

3 .81

3 .00

1 .7

Not available

3 .9

Not available

Figure 7.Minimum principal stresses for male subject in seated position.

Figure 8.von Mises stresses for seated male.

011E]1 5 -3 "km'

3-4 .5 'h,s'

f.5-7.5"km,'

EEI 75- /O.

10 .5-15 '/em'

117

TODD and THACKER: 3-D Buttocks Computer Model

Table 3.Buttock/cushion interface stresses.

Position a3 (Pa) °von Mises(Pa)

OxfordPressure

Monitor (Pa)

Male—supine 2,978 2,487 4,100

Male—seated 16,921 16,981 not available

Female—supine 4,667 4,384 2,800

Female—seated 14,955 12,465 not available

have appeared to be quite significant (24) . Specificstress values in the soft tissue at the buttock-cushioninterface are given for each loading condition inTable 3 . Some experimental data generated at thebuttock-cushion interface measured with an Oxfordpressure monitor are also given in Table 3 . Thecomputational principal stresses are approximately50 percent different from the experimentally deter-mined pressures . As more information about materi-als, large deformations, and nonlinearities is intro-duced into the model, the results will improve.

DISCUSSION

The main objective of this study is to show thatfinite element analysis can be used as a tool incushion design . To be truly useful, the model mustbe capable of being used in a desktop computingenvironment . Some limitations were placed on thesize of the model and the complexity of analysisused so that it could be handled in this environment.

Material Properties of the Soft TissueWhile the material properties of the soft tissue

exhibit nonlinear behavior, they were modeledlinearly in this model as a first approximation . Dataare available to expand this model into the range ofnonlinear materials . This type of analysis willbecome more practical as computers continue tobecome more powerful.

Experimental vs . Computational ResultsDeflection of the soft tissue under the right

ischial tuberosity was determined experimentallywith MRI by imaging subjects in both free-hangingand body weight loading conditions .

Buttock-cushion interface pressures in certainloading conditions were measured experimentallyusing an Oxford pressure monitor. These pressureswere compared with the minimum principal stressescomputed for the interface. Stresses and displace-ments are consistently higher in the seated positionthan in the supine position throughout the softtissue. This is due not only to the increased loadsapplied in the seated cases but also to the differentmaterial properties used.

While buttock-cushion interface pressures areused in cushion design, surgical evidence suggeststhat decubitus ulcers form within the internal tissuesand progress toward the surface . The stress contourin Figure 7, for example, shows the change in stresswithin the soft tissues . Stresses at the buttock-cushion interface and in the tissues surrounding theischial tuberosity are shown in Table 4 . For the malesubject in the supine position, the stress increases bya factor of 3.5 from the buttock-cushion interface tothe element beneath the ischial tuberosity . In theseated position, the stress increases by a factor of4.5 . For the female subject in the supine position,the stress increases by a factor of 11 from thebuttock-cushion interface to the element beneath the

Table 4.Interface and internal stresses.

Position Interface a3 (Pa) Ischial Tuberositya3 (Pa)

Male—supine 2,978 10,631

Male—seated 16,921 74,112

Female—supine 4,667 51,526

Female—seated 14,955 204,850

118

Journal of Rehabilitation Research and Development Vol . 31 No . 2 1994

ischial tuberosity . In the seated position, the stressincreases by a factor of 13 .5.

Literature discussing the formation of decubitusulcers gives ranges of interface pressures associatedwith their onset (7,24,25) . This diverse range ofvalues indicates that other factors, such as internalstress, may be better predictors of formation ofdecubiti . Results from this initial model are notadequate to suggest any relationship between inter-face pressures and internal stresses . A study withmore subjects and a more advanced model would benecessary to begin to define that relationship.

CONCLUSION

Although the model contained many approxi-mations regarding material properties and loading,the difference between computational and experi-mental results indicate that this is a feasible ap-proach for modeling healthy buttocks tissue on acustom-contoured cushion . Magnetic Resonance Im-aging can be used to generate the geometry of amodel of an anatomical structure although moreautomation could greatly reduce the tedium in thisprocess. Introduction of an elastic foundationboundary condition led to computational results thatapproached the experimentally measured results.

The clinical significance of the stress results isthat there is no clear correlation between interfacepressures and the internal stresses . Variation in thechange in stress from the buttock-cushion interfaceto the ischial tuberosity may explain the citation ofdifferent stress values in the literature for theinitiation of decubiti . The correlation between themagnitudes of stress in the internal tissues andformation of ulcers is unknown at this time.

REFERENCES

1. Rosen JM, Hentz VR, Perkash I . The plastic surgicalmanagement of pressure sores . In: Proceedings of the39th Annual Conference on Engineering in Medicine andBiology. 1986:281.

2. Reddy NP, Brunski JB, Patel H, Cochran GVB. Stressdistributions in a loaded buttock with various seatcushions . Adv Bioeng 1980 :97-100.

3. Brunski JB, Roth V, Reddy N, Cochran GVB . Finiteelement stress analysis of a contact problem pertaining toformation of pressure sores . Adv Bioeng 1980 :53-6 .

4. Chow WW, Odell EI . Deformation and stresses in softbody tissues of a sitting person . J Biomech Eng1978 :100 :79-87.

5. Kett RL, Levine SP . A dynamic model of tissue deflectionin a seated individual . In : Proceedings of the 10th AnnualRESNA Conference, 1987 June ; San Jose, CA, Washing-ton, DC : RESNA Press, 1987 :524-6.

6. Cooper R, Ward C, Ster J . Characterization and develop-ment of a resistive sensor for measuring cushion interfaceforce . In : Proceedings of the RESNA International '92Conference, 1992 June, Toronto, ON, Washington, DC:RESNA Press, 1992 :210-2.

7. Chung KC. Tissue contour and interface pressure onwheelchair cushions (Dissertation) . Charlottesville, VA:University of Virginia, 1987.

8. Protz PR, Chung KC . Implementing magnetic resonanceimaging for the quantification of load-bearing buttockstissues . In: Proceedings of the 13th Annual RESNAConference, 1990 June, Washington, DC : RESNA Press,1990 :109-10.

9. Bentzen SM, Hvid I, Jorgensen J . Mechanical strength oftibial trabecular bone evaluated by X-ray computedtomography . J Biomech 1987 :20 :743-52.

10. Jastrzebski ZD . The nature and properties of engineeringmaterials . 2nd ed . New York : Wiley, 1977.Fung YC. Biomechanics : mechanical properties of livingtissues . New York : Springer-Verlag, 1981.Fleming DG, Feinberg BN . Handbook of engineering inmedicine and biology . Boca Raton, FL: CRC Press,1976 :254.Reilly DT, Burstein AH . The elastic and ultimate proper-ties of compact bone tissue . J Biomech 1975 :8 :393-405.McElhaney JH, Fogle JL, Melvin JW, Haynes RR,Roberts VL, Alem NM. Mechanical properties of cranialbone . J Biomech 1970 :3 :495-511.Vannah WM, Childress DS . An investigation of the three-dimensional mechanical response of bulk muscular tissue:experimental methods and results . ASME Symposium onComputational Methods in Biomechanics, 1988.Cowin SC, Van Buskirk WC, Ashman RB. Properties ofbone. In: Skalak R, Chien S, eds . Handbook ofbioengineering . New York : McGraw-Hill, 1987:2 .1-27.Reilly DT, Burstein AH, Frankel VH. The elastic modu-lus of bone . J Biomech 1974 :7 :271-5.Steege JW, Schnur DS, Childress DS . Prediction ofpressure at the below-knee socket interface by finiteelement analysis . In: Stein JL, ed . ASME Symposium onBiomechanics of Normal and Prosthetic Gait . Boston,MA. B10-7B, BED-4, DSC-7 :1987:39-43.Gordon JR . Control algorithms and mechanical compo-nents for an automatic body contour measurement system(Thesis) . Charlottesville, VA: University of Virginia,1989.Brienza D, Gordon JR, Thacker JG . A comparison offorce transducers suitable for an automatic body supportcontouring system . In: Proceedings of the 12th AnnualRESNA Conference, 1989 June; New Orleans, LA,Washington, DC : RESNA Press, 1989 :238-9.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20 .

119

TODD and THACKER : 3-D Buttocks Computer Model

Kenedi RM, Cowden JM, Seales JT . Bedsorebiomechanics . London : University Park Press, 1976.Bush CA. Study of pressures on skin under ischialtuberosities and thighs during sitting . Arch Phys MedRehabil 1969 :50 :207-13.

21 . Bennett L . Transferring load to flesh—part II . Analysisof compressive stress . Bull Prosthet Res Fall 1971 :45-63 .

24.

22 . Bennett L, Patel H . Transferring load to flesh—part IX.Cushion stiffness effects . Bull Prosthet Res 1979 :10 :31 .

25.

23 . Anthropometric Source Book, Volume I : anthropometryfor designers. NASA Reference Publication 1024.1978 :IV-31-9.