stress reduction in the residual limb of a transfemoral...

Stress Reduction in the Residual Limb of a TransfemoralAmputee Varying the Coefficient of Friction

Vanessa Restrepo, BSc, Junes Villarraga, PhD(c), Jose Pavon Palacio, PhD

AbstractA finite element computer model was used to validate the relationship between coefficient of friction (COF) and the shearstresses and pressures obtained at the socket/residual limb interface for four individuals with transfemoral amputation. Thismodel simulated the process of donning the socket and application of loads during the stance phase of gait cycle. The residuallimb was modeled as a solid multilayer (skin, fat and muscle) with hyperelastic properties. An experimental design was madeto calculate the significance of hairiness, sweating, and texture factors in measuring the COF between polypropylene andskin with the help of a sclerometer; values were obtained from 0.188 to 0.545. It was demonstrated that the surface textureis significant when measuring the COF. On the results of the simulation, a horizontal strip where the greatest stressesand pressures occurred was identified; in this strip, the COF was varied from 0.2 to 0.6 to observe its effect on the distributionof stresses. The average shear decreased up to 25%, whereas the pressures did not vary significantly and the results do notexceed the value of 70 kPa, from which values are potentially harmful to the skin. (J Prosthet Orthot. 2014;26:205Y211.)

KEY INDEXING TERMS: socket-limb residual interface, finite element analysis, dynamic simulation, stress distribution

The socket is the element of the prosthesis that is in directcontact with the patient. For this reason, its design isfundamental for the patient’s perception of comfort with

his/her prosthesis. Several authors have demonstrated thatshear stresses and excessive pressures in the socket-residuallimb interface are responsible for damage to the patient’s softtissue, whereas the normal and tangential forces applied to theresidual limb when it interacts with the socket produce circu-latory problems.1Y3 However, the worst conditions that lower-limb amputees experience according to Meulenbelt et al.4 arepressure ulcers, followed by infections and wounds.

The experimental pressure and stress measuring methodsin the socket-residual limb interface provide only approxima-tions to the real values because of the complexities associatedwhen implementing these methods and do not account forall of the surfaces in contact.5,6 The finite element methodserves as a complement to the experimental measurementswhile these validate the method.7,8 To date, the models used fortransfemoral amputees are based on suppositions and simpli-fications that do not recreate donning the socket and defor-mation of soft tissues.9 There are various factors that affectthe distribution of stresses on the residual limb, such as var-iability in the anatomy of persons, skin types, sweating, pres-ence or absence of hair, and others. The aim of this study wasto obtain the stress distribution on the residual limb for atransfemoral amputee varying the coefficient of friction (COF)in the socket-residual limb interface to

1. aid the designer in the design process;2. decrease stress values and reduce injuries to patients, in-

creasing their quality of life and facilitating their reinte-gration into society; and

3. assist the prosthetist to an easier adaptation of the patientto his/her prosthesis.

Coefficient of friction was selected as a study variable be-cause it is easily quantifiable and measurable. So far, therehave been no studies that aim to answer the question posedin this research.

This study was conducted on four individuals with differentphysiological characteristics, making a distinction in the phys-ical and mechanical properties of the constitutive layers ofthe residual limb (skin, fat, and muscle).10,11 A dynamic explicitsimulation was performed to represent the socket donningprocess and initial support during the gait. The model was di-vided into three analysis stages, which included the donningphase. This stage accounted for the vertical motion of the socketduring donning from a configuration in which there is nocontact with the residual limb to its final configuration, inwhichit contains all of the soft tissue and bone. The relaxation phase isconsidered as a transition phase between the donning phaseand the exertion of the load phase, when the most critical loadof the gait phase is applied.

It has been demonstrated that the COF directly affects themagnitude of stresses generated by the socket on the residuallimb.12 For this reason, the COF between the residual limb andthe socket was varied from 0.5 to 1.0 to determine the stressand pressure distributions. The stress concentration zone wasidentified from these values where the COF was altered todetermine if the stresses could be reduced. An experimentalvalidation was carried out to determine the influence of socketsurface texture on the COF in the socket-residual limb inter-face to prove the viability of optimizing the socket surface. Thefactors accounted for in the experimental measurements were

VANESSA RESTREPO; JUNES VILLARRAGA, PHD(c); and JOSE PAVONPALACIO, PHD, are affiliatedwith theUniversidad de Antioquia, Calle 67Numero 53-108, Medellın, Antioquia, Colombia.

Disclosure: The authors declare no conflict of interest.

Copyright * 2014 American Academy of Orthotists and Prosthetists

Correspondence to: Vanessa Restrepo, 152 East Stadium, Apt 5 WestLafayette, IN 47906; email: [email protected]

Volume 26 & Number 4 & 2014 205

Copyright @ 2014 by the American Academy of Orthotists and Prosthetists. Unauthorized reproduction of this article is prohibited.

mailto:[email protected]

hirsuteness, skin sweatiness, and the surface texture of thepolypropylene because their significance has been demon-strated in previous works. Upon completion, it was determinedthat the COF considerably affects shear stresses because themagnitude was reduced up to 25%.

METHODS

CHARACTERIZATION OF THE SUBJECTSParticipating in the study were four individuals with trans-

femoral amputation who varied in age, sex, and amputationlength. In the absence of a formal institutional review board,the principles outlined in the Declaration of Helsinki werefollowed. Informed consent was verbally obtained from re-search subjects before they were involved with the study. Thesubjects’ data are presented in Table 1. Forces and momentswere calculated from data obtained from the gait laboratoryat Maria Cano University.

MODEL GEOMETRYTo produce the models, a three-dimensional scanner was

used for the socket and the residual limb, whereas the bonewas modeled from a reconstructed computed tomography (CT)image of each individual. The parameters used for the scanwere as follows: Siemens Emotion 6 Scanner, 112 mAs, 130 kV,512 � 512 pixel matrix, pixel size 0.758 mm, gantry tilt 0.00,and slice increment 1 mm. The components were assembledaccording to each subject’s biometrical configuration, and the

anatomical positions were obtained from the CT. To date, thesetechniques are being used to design and fit the socket.13 Thepatient’s residual limb model was produced as a multilayermodel including the skin, fat, and muscle. According toGeerligs10 and Portnoy et al.,14 the skin and fat have a thicknessof 2 and 4 mm, respectively, and the remaining volume cor-responds to the muscle.

FINITE ELEMENT MODELFor solving the model, ABAQUS version 6.9 was used. A

dynamic explicit simulation was the solution strategy becauseof large displacements of the socket and the large strain ofskin and fat. Also, the capacities of this type of analysis al-low the simulation of the hyperelastic and damping behaviorof the soft tissues and define complex contact conditions.A tetrahedron C3D4 element was used to mesh all elementsof simulation, and 310320 was the average of elementsused; default convergence criteria of the simulation softwarewere used.

The initial considerations taken into account when pro-ducing the model included the amputee’s donning of thesocket, shown in Figure 1A, and its analysis under the mostcritical loads during gait. The femur is fixed in the acetabu-lum, as shown in Figure 1B, to restrict movement in any di-rection and rotation. This attachment occurs at the initialsupport; there is no relative displacement of the acetabulumwith the hip. Owing to action of the muscles on the femur, thisrestriction of movement makes the transmission of load to thehip joint possible.

Table 1. Subject information

Code of the subject Height, m Body weight, kg Residual limb length, m Normal F, N Shear F, N Moment, N m

Sub 1 1.53 53.2 0.24 567 207 100Sub 2 1.75 75.0 0.24 807 295 172Sub 3 1.65 88.7 0.30 961 352 167Sub 4 1.63 63.5 0.29 682 249 119

Figure 1. A, Fitting of the socket; B, fixing of the acetabulum.

Restrepo et al. Journal of Prosthetics and Orthotics

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The donning procedure was divided into three phases toproduce an accurate model of the procedure.

DONNINGIn this step, the amputees facilitate the fitting (sliding) of

the socket using a thin sock or a liner that reduces the frictioncoefficient and therefore allows for smoother donning. Thisstage was considered as an independent stage because it hasspecific characteristics differing from the other two stages.Moreover, the greatest relative socket movement with respectto the residual limb occurs during this stage.

During the donning step, the soft tissue must deformconsiderably to be contained by the socket, which has a specificgeometry. Figure 1 shows the socket fitting procedure.

RELAXATIONIn this step, a 3-second interval was established to allow

the soft tissue to adjust to the socket’s geometry and to dis-sipate the changes occurring as waves or creases in the skinbecause of the considerable deformations that occurred duringthe motion step.

LOADThis load is located on the rigid part of the socket, where

it joins the rod of the thigh. It can reach magnitudes of upto 120% of the individual’s body weight and is produced atthe beginning of the initial support phase and at the end ofthe initial and final support phases, with a horizontal loadrepresenting 7% to 10% of the individual’s body weight.This step is applied after the relaxation phase and lasts for0.1 seconds because it is the average duration of this stancephase. In this phase, the relative motion between the socketand residual limb is not considered.

The main consideration accounted for when this investi-gation was performed was the fact that soft tissues, such asskin, fat, and muscle, were treated as hyperelastic, homoge-neous, and isotropic materials. Using the Mooney-Rivlin gen-eralized deformation (Equation 1), the constitutive parametersC10, C11, and D1, shown in Table 2, were introduced into theABAQUS version 6.9.2 software.

w ¼ C10 I1j3ð Þ þ C11 I1j3ð Þ I2j3ð Þj 1D1

ð Jj1Þ2: ð1Þ

The bone and the polypropylene of the socket were assumedas lineal, homogeneous, and isotropic materials. The completeproperties of the materials used in the simulation are shownin Table 2.12,14Y17

In addition, reference models were produced for each in-dividual by varying the COF from 0.5 to 1.0 to determine thezones where stresses were concentrated. Once the area of in-terest was identified (Figure 2), the socket was modified toallow for the change of the COF on a 10-cm-wide horizontalstrip located 2 cm below the ischial support. This change wasmade to observe the effect of varying COF over stress distri-bution. The rest of the model had a global COF set to 0.9.14

EXPERIMENTAL DESIGNA 2k factorial type experiment was performed with three

factors (hirsuteness, sweatiness, and texture) in two levels(high and low). To test the high hirsuteness level, the subject’sarm was not altered; for the low hirsuteness level, the testarea was shaved. The high sweatiness level was tested withan artificial sweat solution prepared according to the NTC5221 standard; a spray in the area of interest was applied. Forthe low level, the skin was tested in dry conditions. Finally,to test the high texture levels, the polypropylene coatings ofthe indenters were molded with a nylon stocking, simulatingthe socket fabrication process; for the low level, the surface of thecoatingswas left smooth. The experimentdesign results requiredeight measurements, with a replica (16 measurements total) toincrease the reliability of the results.

The primary roughness profiles of the coatings for the in-denters used in the experiment were obtained with a MitutoyoSV-3000 M surface roughness tester, distinguishing the sur-face topography of the coatings with high and low texture. Themeasurements where performed at a speed of 0.1 mm/s, witha 0.5 Km pitch and an 8 mm test length.

RESULTS

SIGNIFICANCE OF THE FACTORSTo determine the COF between the polypropylene and the

skin, pertinent measurements were taken with a sclerometeron the same individual’s moisture levels (with no clinicalconditions on the skin) to prevent skin tone, body mass index,physical activity, and all other factors inherent in the individual

Table 2. Properties of the materials

Material Young modulus, GPa Poisson coefficient C10, kPa C11, kPa D1, MPaj1

Elastic Polypropylene socket17,24 1.5 0.3 NA NA NACortical bone15 15 0.3 NA NA NA

Hyperelastic Skin14,16 NA NA 9.400 82 0Fat14,16 NA NA 0.143 0 70.2

Muscle14,16 NA NA 8.075 0 1.243

NA indicates not applicable.

Journal of Prosthetics and Orthotics Stress Reduction in the Residual Limb

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from affecting the results. Other factors that could not be con-trolled included relative humidity and temperature; because ofthese, the tests were performed on the same day. Also, theequipment was calibrated before use to ensure that the data wereas precise as possible.

A total of 16 measurements were taken, and the value of theCOF was calculated for each one. These are presented in Table 3.

A significance analysis of the studied factors was accom-plished with MINITAB 16 software. For a value to be signifi-cant, its p value must be below 0.05; for this experiment,p values of all the factors were less than 0.05.

REFERENCE MODEL STRESSESThe shear stresses presented a high concentration gradient that

is not desirable because it increases the occurrence of soft-tissueinjuries. The highest stress concentrations occurred on a 10 cm-wide strip located 2 cm below the ischial support. It must be notedthat this stress distributionwas consistent for all the study subjects.

Table 3. Values of the friction coefficient

MeasurementFrictioncoefficient Replica

Frictioncoefficient

Factors

Hirsuteness Sweatiness Texture

1 0.361 9 0.240 Low High Low2 0.522 10 0.545 Low Low Low3 0.349 11 0.345 High Low Low4 0.229 12 0.232 High High High5 0.188 13 0.186 High High Low6 0.266 14 0.396 Low Low High7 0.242 15 0.270 High Low High8 0.261 16 0.250 Low High High

Figure 3. Stress distribution on the reference model for subject.

Figure 2. Residual limb Von Mises surface stress distribution.


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OPTIMIZED MODEL STRESSESAfter modifying the socket in the previously identified strip,

the simulations were solved with a fixed (0.9) global COF be-tween the skin and the polypropylene14 and a variable stripCOF ranging from 0.2 to 0.6. The shear stress distributionsobtained on the skin for a strip COF of 0.2 was similar to thatshown in Figure 3.

The results for the optimized model are presented inFigure 4A; there is a small variation in the average pressuresafter modifying the COF.

The optimized model was considered as the definitive com-ponent (with a strip COF of 0.2 and a global COF of 0.9) becauseit produced lower values for the resulting shear stress. A com-parison of the average pressure and shear stress for the opti-mized model and the reference model without the strip with aglobal COF of 0.9 in the entire socket-residual limb interface ispresented in Table 4.

DISCUSSION

SIGNIFICANCE OF FACTORSThe data analysis served to identify the significance of the

factors in the experiment. Particularly, the surface roughnessincreased the apparent contact area and therefore reducedthe maximum pressure and shear stress in the material.18 Thethree factors studied (hirsuteness, sweatiness, and texture)

account for 90.56% of the data (R2). This study presents thestatistical analysis that determines the influence of the socket’ssurface texture on the COF between the polypropylene and theskin, which had not been previously ascertained.

REFERENCE MODEL STRESSESShear stress values tend to be linear and proportional to the

COF. This behavior is similar to the one reported by Li et al.19

and Zhang et al.9 for a transtibial amputee and Zhang et al.12

for a transfemoral amputee.The average pressures did not portray a similar behavior to

that of the shear stresses. These show a more stable tendencywith no significant change when modifying the COF. Zhanget al.9 reported a different behavior from the one presentedin this work. However, it must be noted that the model usedin that investigation was simpler; soft tissues were treated aselastic and there have been no further studies that validate thetendency or the results. The shear stresses presented a highconcentration gradient, which may be attributed to the use ofhyperelastic materials in the simulation that better accom-modate the socket’s geometry. It has been previously shownthat skin breakdown associated with formation of skin lesionsoccurs when applying shear stresses higher than approxi-mately 70 kPa on the skin surface20; the results obtained areunder this rank.

OPTIMIZED MODEL STRESSESThe optimized model shows a similar tendency to that of

the reference model, with a shear stress and pressure con-centration in the same location forming a horizontal stripbelow the ischial support. Figure 4B presents the same be-havior of the reference model, which corroborates the con-cept that the COF directly affects the value of the resultingshear stresses.

When using the optimized model with the strip, consider-able reductions were obtained for the stresses and pressures onthe skin in the area in contact with the socket. The 25%

Table 4. Stress reduction percentage

Code of the subjectAverage

pressure, %Averageshear, %

Sub 1 4.75 20.69Sub 2 4.58 18.67Sub 3 7.39 14.65Sub 4 2.68 25.61

Figure 4. A, Average pressures; B, average shear stress versus friction coefficient (reference model).


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reduction is expected to diminish injuries to patients anddiscomfort, thus increasing their level of comfort.

One of the main limitations in this type of study is obtainingan adequate characterization of the tissues composing theresidual limb because existing models involve simplificationswith behaviors veering off from real ones.21 Moreover, it isrecommended to include a larger number of subjects to per-form a more adequate statistical analysis of the data.

The most recent international studies on transfemoralamputees date back to the 1990s. Because of recent develop-ment of computational resources and the evolution of softtissue models,21Y23 new simulations involving these advance-ments are needed to better understand the socket-residual limbinteraction and propose optimized designs to improve ampu-tees’ perception of comfort.

CONCLUSIONSThe selection of soft tissues (skin, fat and muscle) as

hyperelastic materials proved to be a valid procedure, as thesebehaved like the real materials. The results are strictly com-parable with those found in similar works.2,23,24 Also the de-formation process of the real tissue is physically compatibleto that observed in the simulation.

A horizontal strip was identified below the ischial support,where the pressures and shear stresses concentrate. These largestress concentrations occurred because the soft tissues weretreated as hyperelastic materials because these more effectivelyduplicate the socket geometry when they deform.

It was demonstrated that the COF between the polypro-pylene and the skin directly affects the value of the shearstresses, upon which the socket was modified by reducing theCOF in the proposed horizontal strip. When the shear stressesare decreased, the risk of soft tissue damage is reduced. Theseresults are consistent with investigations.8,9,12,24

The multilayer model is the most adequate to mimic stressdistribution in the residual limb with respect to the entiremodel because the physical properties of the soft tissues aredifferentiated. This allows the simulation to deform in a waysimilar to the real phenomenon.

The COF between the polypropylene and the skin wasmodified by varying the surface texture of the coatings. Fromthe analysis of the results, it can be concluded that the tex-ture indeed affects the average value of the COF. Therefore,a detailed study is proposed which deals with the influenceof the tribological parameters Ra, Rq, HSC, and others mea-sured on the internal surface of the socket on the COF.

The average shear stresses were reduced up to 25% aftervarying the COF on the strip. This proves that when changingthe surface texture on the proposed strip, a considerable im-provement of the stress distribution can be obtained.

The models developed serve as a basis for future studiesusing more complex models that account for the interactionbetween the muscle and the bone and simulate stress distri-bution in the residual limb when negative pressure is applied tothe sockets with a suction valve.

ACKNOWLEDGMENTSThe authors thank Universidad de Antioquia for the technical supportprovided and the use of equipment, licenses, and infrastructure, andUniversidad Nacional de Colombia Medellın Campus for the access toits measuring equipment and licenses.

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17. Hendriks FM, Brokken D, Oomens CWJ, Baaijens FPT. Influenceof hydration and experimental length scale on the mechanicalresponse of human skin in vivo, using optical coherencetomography. Skin Res Technol 2004;10:231Y241.

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