Link to Figures Show Figures
	Article Text Figures References
	Send Link Send HTML Article

Surface Curvature-Based Modification as a Practical CAD/CAM Rectification for Transtibial Limbs

William M. Vannah, PhD
David M. Harning, CPO
Jeffrey A. Hastings, MS
Joseph A. Stand
David M. Drvaric, MD

ABSTRACT

Prosthetic socket digitization creates a quantitative record of the limb shape. From this record, the curvature of the limb's surface at any point can be calculated. The report describes a modification that is based on the limb's surface curvature. Convex areas are relieved and pushed in on, each in proportion to the magnitude of the curvature. Because bony prominences are strong convex shapes (such as the tibial crest), these prominences are relieved. In blinded check-socket testing with 14 subjects, the modification provided a noticeably more comfortable fit (p < .05). The magnitudes of the modifications involved were small; all were <2.0 mm. Although this modification is not a complete rectification, it can provide an improvement in socket fit without cost or other apparent disadvantage. It is necessary to have a quantitative record of the limb shape, such as that available when a computer-aided design/computer-aided manufacturing (CAD/CAM) system is used.

Key Words: prosthesis, artificial limb, rectification, computer-aided design, mechanics, tissue mechanics

Digitizing a residual limb makes a quantitative record of the limb shape that is stored on a computer. This quantitative record of the shape can then be analyzed mathematically. Among other things, one can calculate the curvature of the limb's shape at any point on the surface. The investigators found that modifying the shape by relieving areas with convex curvature and pushing in on areas with concave curvature allows a noticeably more comfortable socket fit. This is not a complete rectification, only one modification that can be added to CAD/CAM rectification styles to make the socket more comfortable. This modification comes without cost or apparent disadvantage.

In mathematical terms, this modification is a function of the three-dimensional curvature (3DC) of the limb's shape. For present purposes, 3DC is calculated as follows. The limb's shape record is transformed into an elevation map in which the elevation at each point represents the limb's radius at each point. An example of this transformation is shown in Figure 1 . Curvature is the change in angle as we proceed along the surface of the elevation map. A bony prominence typically has a negative curvature because the slope of the surface becomes less positive as the surface is traversed. The 3DC at any point is calculated by adding the curvatures in any two perpendicular directions. To illustrate the calculation of 3DC, some basic shapes can be examined. Consider a saddle point. A saddle point (Fig. 2 ) is similar to a notch or pass in a mountain range. A road passing through the notch would have a negative curvature. The ridgeline of the mountain range passing through the notch would have a positive curvature. These negative and positive curvatures might cancel each other out, resulting in a zero 3DC at the saddle point itself. A monadnock, a mountain that stands by itself, has a negative curvature in both directions; therefore, its 3DC is more strongly negative. A bowl has a positive curvature in both directions; therefore, its 3DC is more strongly positive.

The modification is calculated by multiplying 3DC by a negative constant coefficient: modification = 3DC × coefficient.

In this way, areas of negative 3DC are given reliefs; that is, bony prominences are relieved. Areas of positive 3DC are pressed in upon. The 3DC of the limb's outer surface is slightly amplified.

Methods

To date, 14 subjects have been test-fitted with surface curvature-based (CB) modified devices--12 with transtibial limb deficiency (age range, 10 to 20 years) and two full-limbed persons (age 43 and 48 years). Subject data are given in Table 1 . The patients were a convenience sample from our pediatric lower-limb clinic; all were experienced prosthesis wearers with healthy limbs. The full-limbed persons were investigators. Informed consent was obtained.

A passive plaster cast of the limb was taken and digitized. The fineness of the recording mesh was 3.175 mm vertically and 5 degrees tangentially. Curvature at a given point was calculated as the difference between that point's elevation and the average elevation of the adjoining two points. Note that this is an approximation of the curvature. Specifically, this is a central difference approximation to the second derivative of the elevation map at this point. There are several other methods of calculating curvature that are mathematically more precise, but this method was found to be the most trouble-free in actual use. Curvature was calculated in two directions, tangentially and vertically, and the results were added to produce the value of 3DC at that point. 3DC was then multiplied by the coefficient to generate the modification for that point. Coefficients of between 0.5 and 5.0 were trialed.

The sockets were evaluated in the usual clinical manner, using clear plastic check sockets. The prosthetists who evaluated the fittings were blinded as to the rectification method, and sockets based on a variety of rectification methods from other research were usually tested at the same time. These other rectification methods included manual rectification, rectifications based on a soft-tissue stiffness map of the limb¹ and rectification templates from a commercial CAD/CAM package. A thin nylon stocking was put on, then the socket was donned. In three cases, an additional, thicker stocking was necessary to achieve a good fit. Check-socket fit was evaluated in our usual clinical manner. The clinician grasped the socket with two hands and attempted to force it in the anterior-posterior and medial-lateral directions, applying varying levels of proximally-directed force. The amount of laxity observed in this testing indicated whether the socket was too loose in any plane. The surface pressure was assessed by observing the motion between the stocking and the socket. A simplified statement of the assessment rules is as follows: If the stocking moved relative to the socket, the surface pressure in that area was low. If the stocking did not move and the weave of the stocking was visibly crushed against the socket with blanched skin showing through, the pressure was too high. Proper rectification in areas for which load bearing was desired prevented the stocking from slipping against the skin or the socket, but did not cause crushing of the stocking weave or skin blanching.

Socket fit was similarly evaluated during weightbearing by resting the distal end of the socket on an adjustable-height stool. Significant vertical motion of the patella within the socket when the socket was loaded indicated insufficient vertical support and stabilization. Full-limbed subjects used a partial socket/leg device to allow weight bearing (Fig. 3 ).

Results

The CB-modified socket was preferred to the unrectified socket by all clinicians and subjects with three exceptions. This difference was statistically significant (p < .05; chi-squared test). The most noticeable change when rectified and unrectified sockets were compared was an absence of pain around bony prominences. A typical result is shown in Figure 4 .

Observations on the three exceptions were as follows, with details presented in Table 1. One less bony subject, a 17-year-old woman, found any socket without a patellar tendon-bearing (PTB) indentation to be very painful during weightbearing. A 20-year-old man who was relatively bony preferred the unrectified socket during weightbearing. This second subject pointed to two areas as needing relief; these areas were the fibular head and a prominent medial aspect of the tibial crest. Paradoxically, the CB-modified socket was relieved precisely in these areas. This subject was eventually well-fit in a socket with explicit PTB indentations. The CB-modified socket did not have a PTB indentation or other explicit means of vertical load transmission. A third subject who was obese, an 11-year-old boy, was quite insensitive to modifications. For this subject, it was difficult for the investigators to assess fit or to determine that one socket was clearly better than another. The subject found the unrectified and CB-modified sockets to be comfortable fits along with several other sockets with various rectifications.

The optimum modification magnitudes were in the range 0.0 mm to 2.0 mm. Coefficients ranging from 0.5 to 5.0 were trialed. Coefficients that produced modifications of >2.0 mm did not appear to improve comfort; actually, they decreased it and quickly led to cosmetically noticeable bumpiness because of noise amplification. For digitizing resolutions of 5 degrees tangentially and 3.175 mm vertically and the curvature approximation used, the best coefficient was ~1.0.

After CB modification, the sockets typically felt loose and it was necessary to decrease the volume of the socket by 1% to 3% (a 1.0 mm to 1.8 mm decrease in radius applied globally). This decrease was necessary even though the CB modification had virtually no effect on socket global volume; otherwise, the sockets felt loose. Note that the modification increased the distances across opposing bony prominences because bony prominences were relieved. The volume decrease tightened these important dimensions and presumably also increased hydrostatic weightbearing.

CB modification also amplifies any inadvertent bumpiness or "noise" in the shape record. On noisy shape maps (some hand-held digitizers and/or bumpy casts), it was useful to limit the magnitude of negative modifications. Large negative modifications in sensitive areas could be felt by the patient. Filtering the shape map by an 11 Hz low-pass filter² before calculating 3DC improved the results.

Discussion

The CB modification provides a noticeable improvement in comfort without cost. It is necessary to have a quantitative record of the limb shape such as that available when a CAD/CAM system is used. The CB modification relieves bony prominences and thus works best for lean persons in whom the bony contours are evident from the surface shape.

We made check sockets with only the CB modification simply to isolate the modification's effects; this was not a complete rectification. In particular, we observed that provisions for vertical load transmission (such as PTB indentations or indentations at the lateral and medial tibial flares) were often too small. Both of the poor fits during testing were noticed only during weightbearing. The best use of this modification may be to simply add it to whatever style is currently being used.

The CB modification is an experimental procedure and any clinical application of it should be carefully monitored by an experienced, certified prosthetist. The CB modification should be added to a passive total-contact cast before other modifications are applied. If other modifications are applied first, the CB modification will amplify them. When the CB modification was applied to an existing PTB rectification, it amplified it such that the socket was unwearable. After CB modification, many modifications made for bony prominences such as the tibial crest can be eliminated. Other modifications, particularly those for vertical load transmission or for relief of sensitive points that are not reflected in surface prominences (as in some fibular heads that are not prominent) should be maintained.

The optimum modification coefficient was ~1.0 for digitizing resolutions of 5 degrees tangentially and 3.175 mm vertically; the coefficient will be different for other digitizing resolutions, increasing for higher resolutions.

After applying the CB modification, we found it was usually necessary to decrease the global volume of the socket slightly. The volume decrease was achieved by decreasing the radius by an equal amount (typically 1.0 mm to 1.8 mm) at every point. The curvature modification increases the diameters across the limb where there are opposing bony prominences causing the looseness. This global volume decrease, which we believe beneficially increases hydrostatic, soft-tissue weight bearing, is possible because the CB modification relieves all bony prominences.

Many investigators have suggested using finite element stress analysis to solve for the ideal socket shape around a bony prominence.^3-13, One plausible optimization criteria is to minimize the peak shear strains in the soft tissues. The CB modification is a result of earlier theoretical work in this area^{9, 14} and articles by Murphy¹⁵ and Pritham¹⁶ discussing the concept of hydrostatic containment. Curvature amplification is a simplified method that attempts to replicate some of the character of a finite element-based modification without the expense of the finite element analysis. When a bony prominence is relieved, the loading in areas about the prominence is slightly increased, creating narrow containment. This is analogous to the application of tension about the proximal brim of an above-knee socket.

Conclusions

Surface curvature-based modification provided a noticeable improvement in comfort (p < .05), by relieving bony prominences. The magnitude of modification involved was small; the maximum modification applied was ~2.0 mm. This modification is not a complete rectification, but it can provide an improvement in socket fit without apparent drawbacks. It is necessary to have a quantitative record of the limb shape, such as that available when a CAD/CAM system is used.

Acknowledgements

The investigators gratefully acknowledge the support of the Shriners Hospitals for Children Office of Research Programs Grant # 8510.

References:

1. Vannah WM, Drvaric DM, Hastings JA, Stand JA, Harning DM. A method of residual limb stiffness distribution measurement. J Rehabil Res Dev. 1999;36:1-7.
2. Hastings JA, Vannah WM, Stand JA, Harning DM, Drvaric DM. Evaluation of below-knee residual limb shapes for frequency spectrum. J Prosthet Orthot. 1998;10:2-6.
3. Krouskop TA, Dougherty DR, Vinson FS. A pulsed Doppler ultrasonic system for making noninvasive measurements of the mechanical properties of soft tissues. J Rehabil Res Dev. 1987;24:1-8.
4. Krouskop TA, Muilenberg AL, Dougherty DR, Winningham DJ. Computer-aided design of a prosthetic socket for an above-knee amputee. J Rehabil Res Dev. 1987;24:31-38.
5. Steege JW, Schnur DS, Childress DS. Finite Element Prediction of Pressure at the Below-Knee Socket Interface. Biomechanics of Normal and Prosthetic Gait. New York: American Society of Mechanical Engineers; 1987.
6. Reynolds D. Shape Design and Interface Load Analysis for Below-Knee Prosthetic Sockets [doctoral thesis]. London: University of London; 1988.
7. Michael JW. Reflections on CAD/CAM in prosthetics and orthotics. J Prosthet Orthot. 1989;1:116-121.
8. Houston VL. Automated fabrication of mobility aids (AFMA): Below-knee CASD/CAM testing and evaluation program results. J Rehabil Res Dev. 1992;29:78-124.
9. Dresens EP. A Method for Evaluating AK Prosthetic Socket Designs [master's thesis]. Medford, Mass. Tufts University; 1993.
10. Mak AFT, Lui GHW, Lee SY. Biomechanical assessment of below-knee residual limb tissue. J Rehabil Res Dev. 1994;31:188-198.
11. Silver-Thorn MB, Steege JW, Childress DS. A review of prosthetic interface stress investigations. J Rehabil Res Dev. 1996;33:253-266.
12. Vannah WM, Childress DS. Indentor tests and finite element modeling of bulk muscular tissue. J Rehabil Res Dev. 1996;33:239-252.
13. Torres-Moreno R, Jones D, Solomonidis SE, Mackie H. Magnetic resonance imaging of residual soft tissues for computer-aided technology applications in prosthetics--A case study. J Prosthet Orthot. 1999;11:6-11.
14. Vannah WM, Childress DS. Modelling the mechanics of narrowly contained soft tissues: The effect of specification of Poisson's ratio. J Rehabil Res Dev. 1993;30:205-209.
15. Murphy EF. Sockets, linings, and interfaces. Clin Prosthet Orthot. 1984;8:4-10.
16. Pritham CH. Biomechanics and the shape of the above-knee socket considered in light of the ischial containment concept. Prosthet Orthot Int. 1990;14:9-21.