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Magnetic Resonance Imaging of Residual Soft Tissues for Computer-Aided Technology Applications in Prosthetics-A Case Study

Ricardo Torres-Moreno, PhD
Derek Jones, PhD
Stephan E. Solomonidis, MSc
Hamish Mackie, PhD

ABSTRACT

Stress analysis using finite element models is now being implemented in prosthetics to overcome empirical socket design procedures and to further improve computer-aided systems. This article describes the use of anatomical data from magnetic resonance images of a single subject to produce a generic mathematical model of the residual soft tissues and skeletal structure. The model, validated through experimentally measured parameters, was employed to theoretically evaluate the mechanical behavior of tissues, predict interface stresses, and aid in shaping the socket. Numerical analysis could improve socket design criteria and advance rehabilitation services to enhance the quality of life of individuals with amputations.

Key Words: Magnetic resonance imaging; prosthetic sockets; stress analysis.

Introduction

The lower-limb prosthetic socket is a mechanical interface that must provide adequate transmission of forces and moments generated under static and dynamic conditions of everyday living. This can be achieved successfully only by an appropriate socket fit. A comfortable socket fit, however, is subjectively assessed by the amputee while walking with the prosthesis. Although attempts have been made to employ objective techniques that could evaluate socket fit and residuum-socket interaction in-vivo,1,2 these are not clinically available.

The socket should comfortably encase the residual lower limb within a rigid or semirigid receptacle. In such an intimate mechanical environment, interface pressures, ranging from 0 to 400 kPa,3, 4 are of key importance to the tolerance of the socket fit. The presence of steep pressure gradients, shear stresses, and high peak forces can result in a restricted socket fit and breakdown or ulceration of the soft tissues at the interface and its immediate surroundings. The mechanical loading is of critical importance, irrespective of the type of socket being used; that is, from the patellar-tendon-bearing (PTB) to the ischial-ramus containment (IRC). Furthermore, factors such as subject fatigue, muscle activation, gait pattern, and prosthetic alignment can affect the magnitude and distribution of the interface pressures.

Although an optimal, three-dimensional (3-D) alignment of all the components of the prosthesis is essential, it is the socket fit that will dictate, to a great extent, the amputee's level of control, comfort, and mobility, as well as the usefulness of the artificial limb.

Current clinical prosthetic practice, although reasonably successful, relies on the personal experience and subjective judgment of the prosthetist to design the socket. The prosthetist obtains information by palpating the residual limb and predetermines the load transfer characteristics of the socket shape while reshaping the topography of the plaster mold during "cast taking." Rectification of the negative socket model obtained from the plaster mold leads to a more biomechanically acceptable socket shape. The prosthetic socket is then fabricated from this negative model through lamination or vacuum-forming methods.

Although advancements in socket design criteria are achieved at present by empirical means, further development must rely on scientific methods to achieve an improved understanding of the biomechanical parameters that govern a successful socket fit.

The relationship between the biomechanical behavior of the residual soft tissues and the prosthetic socket, however, has not yet been fully quantified or understood. Numerical relationships between socket modifications and successful socket fit-to form a scientific basis for socket design criteria-are unknown. In response to this need, and in an attempt to further enhance the use of computer-aided design and computer-aided manufacture (CAD/CAM) systems in the field of lower-limb prosthetics, 5,6,7 stress analysis methods recently have been implemented in these semiautomatic socket shape management systems.8,9 To aid further in developing a fundamental understanding of the biomechanical parameters of the residuum-socket interface, innovative numerical methods are now being considered more extensively.10,11

One stress analysis method, finite element analysis (FEA), has been widely employed in the study of the biomechanical behavior of biological tissues. Finite element (FE) models have been implemented to theoretically evaluate the stress distribution in bioprosthetic heart valves,12 the effect of axial loading on the behavior of intervertebral disc,13,14 the effect of bone remodeling as a function of the rigidity of the internal fixation plates, 15 the mechanics of head and neck injuries due to impact forces,16 and the application of orthopedic loading on the craniofacial complex.17

For the FEA to be valid and successful, a realistic 3-D geometrical description of the inner residual tissues under investigation is required. The objective of this case study was to obtain quantitative anatomical data of the internal soft tissues and skeletal structure of a single transfemoral residual limb to generate a first-generation 3-D generic FE model. The volunteer participant for the study was a 56-year-old male weighing 786 N, with a right-side traumatic above-knee (AK) amputation. The geometric description of the mature residual limb (26 years after amputation) was accomplished through digitization of cross-sectional images obtained with magnetic resonance technology.

Method

Magnetic resonance imaging (MRI) was selected as an ideal diagnostic and research tool to study the behavior of hydrogen atoms in the body tissues. The reaction of spinning hydrogen nuclei to radio frequency signals within a magnetic field produces the MRI phenomenon. As MRI reflects the local concentration of hydrogen atoms,18 it can facilitate tissue differentiation and ease the assessment of healthy and diseased tissue.19 For a more extensive and technical description of MRI procedure, please refer elsewhere.20,21

The MRI procedure has been used to provide basic data for the study of the biomechanics of the foot, using CAD/CAM technology for orthopedic footwear,22 as well as to predict the magnitude and distribution of normal stresses between individuals using wheelchairs and the supportive surface. Chung and collaborators23 employed MRI to determine the 3-D geometry of the human buttocks to be used in the generation of a FE model. MRI has also been used to record the position and cross-sectional areas of the musculature of the lumbar region to correlate these values to measurements of trunk dimension and body weight.18

This case study-the generation of a FE model to provide a theoretical basis for evaluating AK socket fittings-required that the geometric data of the residual soft tissues conform to that of the amputee standing with the residual limb unloaded. Since the MRI imager required the subject to lie horizontally, gravitational forces could distort the soft tissue distribution relative to the skeletal structure. To limit the distortion of the tissues, the residual limb was fitted with a plaster shell fabricated by an experienced prosthetist. The plaster shell was fabricated in a way that did not exert undue pressure on the tissues and that eliminated the need to fit an adjustable prosthetic quadrilateral brim. A strip of plaster-of-paris bandage was carefully placed along the vertical contour of the residual limb, just covering the distal apex. Distal shifting of the tissues was minimized by placing the bandages higher at the proximal end. Once the plaster cured, a new strip was placed adjacent to the first, and the routine was repeated until the complete residual limb was covered. Care was taken not to alter the shape of the residual limb but to conform to its anatomical and unloaded topography.

The MRI was carried out at the Institute of Neurological Sciences, Southern General Hospital in Glasgow, Scotland, using a Picker Vista resistive system whole body imager (Picker International). The subject, fitted with the plaster shell, was imaged while lying supine with hips extended within a flexible body coil to improve the signal-to-noise ratio around the lower extremities. Padding was placed around the pelvis and the plaster shell to ensure that the subject was comfortable and located centrally on the supporting semirigid surface of the imager and to avoid any unwanted tissue distortion. Although use of the plaster shell minimized tissue distortion due to gravitational effects, it was expected that the relative location of the distal end of the residual femoral bone would differ slightly from that of the subject in the upright position. Tissue distortion due to the physical limitations of the MRI imager is impossible to quantify and is considered minimal once the plaster shell is fitted.

During the MRI session, two multi-image, spin-echo sequences were required to complete the entire length of the residual limb. To ensure that the complete residuum was within the field of view of the imager, an initial coronal plane image was acquired before each transverse image sequence (Figure 1 ). Covering the proximal half of the residual limb (i.e., distal to the femoral head), 18 cross-sectional images were acquired for the first transverse image sequence (Figure 2 ). The spin-echo sequence was repeated with the image plane shifted 170 mm distally to the femoral head to locate it on the distal half of the residual limb for the second multiimage, spin-echo sequence, to obtain the final 16 cross-sectional images (Figure 3 ).

The images were acquired (viewing feet-to-head direction) with an image plane thickness of 10 mm, an image plane gap of 10 mm, 256 phase encoding steps, and a 400 mm field of view. The graphic display was 256 x 256 pixel matrix, 128 gray levels, and a pixel size of 1.56 mm. Sequence parameters were TE=60 ms and TR=1,600 ms (attenuation set to 29 dB), giving an imaging time of 10.2 and 8.5 minutes for the first and second transverse image sequence, respectively.

The information gathered from the MRI procedure, consisting of 2 coronal and 34 transverse images, was transferred to a magnetic disc and loaded on an Apollo 590-T 24-planes workstation. Each transverse image displayed on the computer screen described the location and type of various soft tissues within the right residuum and the left leg. Using the 8-bit color look-up table editor feature, it was possible to enhance regions of similar tissue density to differentiate tissue regions.

As the images were displayed individually on the screen, discrete points at the external contour edge of the skin, muscle mass, and femoral cortical bone were digitized interactively. Contour edges were detected visually at the approximate site where one type of tissue ended and the other began. A computerized graphic reconstruction of the digitized anatomical data allowed the adjacent tissue contours to be displayed simultaneously, as shown in Figure 4 . The software was capable of rotating, translating, hiding, and removing any of the displayed structures.

Further geometrical data manipulation also provided data files containing the Cartesian coordinates required for the construction of the geometrical entities of the generic 3-D FE model (Figure 5 ). The complete FE model of the transfemoral residual limb, constructed and graphically displayed with the PATRAN software program (version 2.4, PDA Eng. Int.), was comprised of: (1) 1,962 nodes, (2) 2,628 3-D solid isoparametric elements (2,380 triangular prisms and 248 hexahedrons), (3) 7,884 degrees of freedom, (4) 14,528 integration points, (5) a maximum wavefront estimated at 228, and (6) an RMS wavefront estimated at 208. Boundary conditions, mechanical properties, and loading function used in the mathematical model were obtained experimentallyl.24,25 The soft tissues were considered as nearly incompressible material with a Poisson's ratio of 0.45. The FE model was solved with the ABAQUS software program (version 4.9.1, Hibbitt, Karlsson & Sorensen Inc.) under nonlinear static analysis (i.e., large deflection), thus requiring a series of increments and iterations to reach a convergent solution. Completing the numerical analysis of the FE model required a total of 14 load increments, 47 iterations, and 3 hours, 57 minutes using a Silicon Graphics 4D/35 workstation.

Results

As the set of transverse cross-sectional images was displayed graphically on the computer screen, the inside view revealed the extent to which the residual tissues differed from those of the intact lower extremity. In the coronal image, it was clear that the ratio between adipose tissue and muscle mass increased toward the distal end of the residuum. Figure 1 shows that, although the atrophy of the muscle mass was relatively constant, the space covered by adipose tissue decreased as the distal end of the residuum was reached. Transversely, no apparent difference in thickness or relative distribution of the skin layer was noticed between the lower extremities.

Figure 2 shows the transverse residual soft tissue distribution and the relative location of the skeletal structure of the lower extremities at an image plane located 80 mm distal to the femoral head. Figure 3 , illustrating an image of the second imaging sequence, shows a marked atrophy of the residual tissues compared to the intact lower extremity. In general, functional muscular atrophy of the anterior and lateral muscle groups was observed along the entire length of the residual limb. Preservation of only the medial muscle group was noted.

Another important observation revealed that, due to atrophy of the anterior and lateral muscle groups, the femoral bone acquired an anterior-lateral position relative to the transverse cross section of the residual thigh. This position of the residual skeletal structure directly affects the design of the socket shape and the socket fit due to the pressure intolerance characteristics of bony prominences, particularly at the distal end. A larger cross-sectional area of the medullary cavity in the residual limb and a thinner femoral cortical layer were noted. This observation became more pronounced toward the distal end of the residual thigh. Figure 3 clearly shows the femoral cortical layer of the intact limb to be considerably thicker than that of the residual side. As shown in Figure 2 , a remarkable increase in connective tissue was observed in the deep muscular fascia, reaching the femoral diaphysis.

Discussion

For an amputee, the prosthesis represents an important aid that facilitates physical, social, and mental rehabilitation following the traumatic loss of a lower limb. With surgical procedures like osteomyoplasty and advanced prosthetic socket design philosophies (e.g., PTB and IRC), the shape of the residual limb has evolved from a simple passive conical stump to a more rounded dynamic structure capable of improving the amputee's weight-bearing capability, control, power, and proprioception. The extent to which the individual, the intact limb, and the residual tissues adapt to the new and challenging mechanical environment will be the result of tissue viability and the functional demands imposed. Under normal circumstances, the adaptation of tissue will involve atrophy and hypertrophy of the residuum and intact limb, respectively. Although the MRI data collected in this case study only allows differentiation between the two lower limbs without reference to normal or preamputation state of the tissues, it could represent an experimental method to facilitate research and development in the field of prosthetics.

The atrophy present in the anterior muscle group reflects the preservation mainly of the primary flexor of the thigh (rectus femoris). The remaining three muscles of the quadriceps femoris that extend the knee joint are no longer needed. To overcome muscular strength imbalance,26 functional demands to preserve the alignment of the residual limb are higher in the medial and posterior muscle groups. The mechanical demand on the adductor muscles could be partially the result of the need for medial counterpressure to act against the abductor muscles and the greater trochanter and prevent lateral displacement of the prosthetic socket.

The diameters of the transverse cross section of the soft tissues and femoral bone were systematically less on the residual side as shown in Figure 2 and Figure 3 . This is in agreement with the results of the radiology study by Baumgartner.27 The MRI revealed a decrease in the cortical bone wall thickness, with a corresponding rise in the width of trabecula bone and medullary cavity. This finding is possibly the result of decreased mechanical stresses exerted on the skeletal structure.

To explain the effect that uneven loading of the lower extremities has on skeletal structure, Wolff's law28 must be considered. According to Wolff's law, bone undergoes an adaptive remodeling process to optimize its mechanical function in response to the demands subjected. Wolff also stated that, under both static and dynamic conditions, bone remodels in the direction of the stress trajectory. If the sound femoral bone bears loads greater than normal, it adapts and becomes thicker (Figure 3 ) so as to reduce the stresses caused by the imposed mechanical loading. Following a lower-limb amputation, loading of the residuum is reduced on magnitude and duration and is transmitted to the prosthesis mainly via the soft tissues, rather than through the bones. The femoral bone remodels into a weaker structure. A similar result, called "stress-protection," has been observed following fracture stabilization with external fixation plates.15,29 Furthermore, the geometry and mechanical properties of the bone change as the loads on the bone vary in mean magnitude and peak force and as a function of time.30 Due to these intrinsic factors of the FEA technique used, the effect on the mathematical model, as a result of tissue distortion caused by gravity as the amputee was lying in the scanner with the custom-made plaster shell, becomes negligible.

Although the results in the study are based on data taken from only one transfemoral amputee, it is believed that similar features could be expected when imaging other amputees of similar characteristics. In general, these similarities will depend, to a lesser or greater extent, on factors such as age, physical activity, hours per day of prosthetic usage, cause of amputation, age at amputation, time since amputation, surgical procedure, flexibility of the socket, prosthetic alignment, and socket fit, as well as length and maturity of the residual limb.

The construction of the generic FE model of the transfemoral residuum was used in an attempt to theoretically predict the magnitude and distribution of pressures developed at the interface between the residual limb and the prosthetic socket using analytical methods. To validate the FE model, theoretical results were compared to experimentally measured interface pressures at discrete sites within the entity of the model, as shown in Figure 5 . Based on the nodal displacements of the outer surface elements obtained using FEA, the model also successfully predicted the socket shape that would conform to an acceptable socket fit as determined by traditional outcome measures in prosthetic fitting. A complete analysis and validation of the FE model (a topic beyond the scope of this paper) has been reported elsewhere.24,31,32 It should be remembered that the mathematical modeling of biological tissues is an oversimplification of the real situation. The results will be directly dependent on the mechanical properties, assumptions, boundary conditions, load function, and, most importantly, on the realistic 3-D geometrical data incorporated in the analysis.

This type of biomechanical study is an attempt to provide engineering solutions for the needs of the physically impaired in order to achieve functional recovery. This work is a clear example of research and development in human rehabilitation using MRI, analytical methods, and computer-aided technology.31,33

Conclusion

An MRI scanner was used to generate cross-sectional images of the internal structures of the above-knee residuum of a male amputee. The potential usages of MRI technology demonstrated by this case study were twofold. First, the images facilitated visualization of the extent to which residual tissues differed from those of the intact lower extremity. Second, quantitative geometrical data obtained from a single subject facilitated the generation of a generic FE model of the residual limb. The implementation of analytical methods in prosthetics can provide theoretical predictions of the pressure pattern at the residuum-socket interface. A better understanding of the load transfer characteristics between the residuum and the receptacle could lead to improved comfort, stability, and effectiveness of the socket fit.

Due to the high cost and time-consuming nature of the MRI procedure, its direct implementation as a shape-sensing technique in CAD/CAM systems for the design and fabrication of prosthetic sockets is not yet feasible. Application of MRI as a research tool, however, can facilitate the theoretical evaluation of the soft tissue response to mechanical loading. Further understanding of the mechanical behavior of the residual soft tissues through the use of FE models could improve socket design criteria and manufacture standards in clinical practice. The first generation of a generic FE model from a single subject, as described in this case study, permits the quantitative evaluation of a virtual fitting of different socket shape without the need to fabricate the actual socket. The clinical application of engineering principles, computer-aided technology, and numerical methods may help to advance the field of prosthetics and ultimately improve the functional independence of individuals experiencing lower-limb amputation.

Acknowledgements

The authors wish to express their gratitude and appreciation to the single volunteer amputee subject who participated in the imaging process, to Mr. N. Govan for the fabrication of the plaster shell, and to Dr. B. R. Condon and Dr. G. Macreath for permitting the use of the MRI facilities at the Southern General Hospital in Glasgow, Scotland.


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