Although the fabrication of above-knee prosthetic sockets has taken place throughout history, in modern times relatively few major improvements have been made in the methods of fitting or in prosthesis design. With the advent of computer-aided design and computer-aided manufacturing (CAD/CAM), it is now possible to reevaluate current designs, and to replace some of the burden of tedious and time-consuming fitting procedures with computerized processes.
Several groups worldwide are involved with developing systems for this activity. Notably, the Mechanical Engineering Research Unit system developed by Saunders, Foort, et al. (1985), and the University College London system of Dewar and Reynolds, and their colleagues (1986), have been clinically successful in fitting below-knee amputees. These systems seek to imitate the activities of the prosthetist, using the computer instead of plaster and other traditional tools. In general, these systems use simple measurements to predict the socket shape. The basic socket design can be altered for a personalized fit, and the resulting cast shape is milled.
The work described in this paper is aimed at the development of a practical system to not only aid in the day-to-day prosthetic fitting process in the clinic by imitating current practice, but also to improve the basic fitting techniques. This will be achieved by basing new designs on measurable parameters, including tissue properties, interface pressures, and limb shape. Once these are better understood, higher quality prostheses can be made available as more efficient and convenient methods of fitting come into practice.
Many researchers have studied the specific variables related to fit. Shape measurement methods are among the most common research topics, since every system, no matter what its goal, must be able to record the shape of the residual limb. Those studies interested in measuring the limb in its deformed state often must use intermediate materials, such as a plaster cast to achieve the desired shape, or must load the residual limb in a specific manner.
More common are studies which record the shape of the unloaded limb. Crawford (1985) has developed a "silhouette" system which builds a three-dimensional shape from several two-dimensional images. This has some use in below-knee applications, but seems to be insufficient for objects with concavities in their horizontal cross-sections and use is limited.
Fernie (1985) developed a laser system for shape sensing in which TV cameras record the distortion of a beam of light. This distortion reveals the shape of the limb. Though successful with below-knee amputees, the system is fairly large and requires the purchase of several cameras and a computer, as well as the laser device.
Other shape sensing devices are being investigated by Faulkner (1986) using ultrasound, computerized tomography, and digitization. The use of Moire contourographs was studied by Saunders (1982). Other stereometric techniques were investigated by Zuniga (1977).
In other areas, Childress, et al. (1987) use a plunger device to obtain general stiffness measurements of limb tissue. The plunger depresses the tissue with known force and deflection is recorded. This deflection is proportional to the stiffness.
Interface pressures in prosthetic sockets have been measured by several investigators (Naeff, 1980; Van Pijkeren, 1980; Pearson, 1973; and Rae, 1971). Krouskop (1987) used thin, flexible fluid-filled pressure transducers to find that comfortable pressures in above-knee prostheses ranged between 110-l5OmmHg.
To combine all these factors, Childress' group (1987) has developed a finite element system to predict socket pressures inside the socket for below-knee amputees. The ultimate goal of their system is to base alignment on anatomical factors for production of a "prealigned" device.
Similarly, the basis of this project is that the behavior of the tissues of a residual limb can be theoretically modelled using computerized techniques and the behavior of these tissues when loaded, as inside a socket, can be predicted. By doing this, not only can current prosthetic methods be imitated and facilitated, they can also be improved upon by determining what type of behavior is desirable. Our better understanding of the system will in turn lead to more comfortable socket configurations, better socket materials, and a consistent, quantitative method to analyze and evaluate the performance of many types of devices.
The system developed in this project consists of a shape sensor, stiffness measurement device, and various computer programs to process the data. These parameters: the shape, loading and tissue stiffness, are used then as input for a finite element analysis to define the rectified socket shape. The undeformed shape of the residual limb is measured so that all needed dimensions and contours are collected. Information about the mechanical properties of the limb are desired in order to predict the deformation of the tissue when it is fit into a socket. Earlier studies concerning interface pressures of above-knee sockets (Krouskop, 1987) and limb shape and volume measurement (Krouskop, 1979) are used along with this data in several computer programs. These include the finite element program to model the resultant form of residual limb when inside a socket, as well as several programs which incorporate the traditional fitting principles used by the prosthetist for intricate and customized features such as brim fitting or accommodation of limb abnormalities. This rectified socket shape is sent via modem to a numerical milling machine for fabrication. The resultant cast is used by the prosthetist to construct the final socket. A description of each component of the system follows.
To measure the undeformed shape of the patient's residual limb, a shape measurement device was developed. The initial specifications set up for this task were:
The process should take no more than seven minutes to complete;
The measurements should at least match the current circumferential measurement error of 0.63cm;
Vertical measurements should be accurate to 0.25cm; and
Measurements should be reproducible within 2%.
The device constructed to meet these needs consists of two stainless steel probes mounted on a round base. The probes travel horizontally toward and away from the limb as it hangs vertically. The base rotates 360° in 10° increments. At each location, the probes move inward until they make contact with the limb. The position of the probe tips is electronically recorded and stored via computer (an Apple lle). The probes then retract, the base rotates, and the process repeats until data have been collected all the way around the limb. The level of the probes is then adjusted to a new height, and the process repeated. The number of levels depends on the length of the residual limb, and as many levels as are necessary are measured to create an accurate picture of the limb sur- face. The device also can collect data, using only one probe, from 180° and 270° rotations. This allows data collection above the hip joint.
The shape sensor has met the design criteria adequately. The probe tips are 0.63cm in diameter allowing for the proper vertical resolution. Currently, a vertical resolution of 2.5cm over the main part of the limb, and 1.3cm on the proximal and distal ends has been found to be sufficient. If it should become necessary to have a higher resolution than 0.63cm, it will be possible to produce smaller probes.
The highest radial resolution that the hardware is capable of is 0.625°. However, this resolution would take approximately 10 minutes per level to complete; total collection time for 10 levels would then be well over an hour. However, the resolution is adjustable and at this time, through comparison of the outputs from various settings, it has been determined that data collection at 20° resolution provides enough detail to show bumps and depressions of the skin surface and does not take an exceedingly long time to complete. Each resolution of the leg takes approximately 10 seconds. Time between height adjustments is about 20 to 30 seconds. For a complete data collection of 10 or 12 levels, then, approximate time for testing is five to seven minutes.
In clinical trials of 100 above-knee amputees, shape characterizations were obtained over time to determine shape changes during the adjustment period. In sockets which "fit well," according to traditional clinical evaluation and patient comfort criteria, it was found that the proximal 30% of the socket must have a volume between 5-8% less than the corresponding unloaded limb for a good-fitting socket. (Further information on the testing of the device is in publication, Krouskop, et al., in press.)
To characterize the mechanical behavior of the residual limb, an ultrasonic method has been devised which calculates the Young's Modulus (a measure of the stiffness) of the limb's tissue. Analytically, this method is founded on basic physical equations of motion and through a rigorous derivation, a relatively simple equation has been developed:
Details of this derivation have been published (Krouskop, 1987).
The hardware consists of a steel bracket placed around the subject's residual limb. Mounted on opposite sides of the bracket are two cylindrical, plastic platforms, each approximately 5cm in diameter. One platform is stationary; its purpose being to hold the limb still during collection. The other vibrates the subject's tissues in a cyclic perturbation with frequency of 8Hz. The moving piece contains the ultrasound transducer, which serves to measure the displacement occurring at depths throughout the tissue. The transducer is computer controlled; the depth and frequency of measurement are automatically accomplished. The result is a displacement versus depth graph. An example of this is shown in Figure 1 .
In preliminary studies, the data points from this graph were directly used in the modulus calculation. Since only three points are required for the calculation, the choosing of the points had an effect on the outcome of the modulus. Therefore, preliminary data from 20 subjects varied widely and results were difficult to interpret. As a result, the data are now smoothed to fit an exponentially decaying curve before modulus calculation. An exponential was chosen because this is the form of the curve which would result if all materials and procedures were ideal. The data are divided into two sections: a superficial region and the tissue beneath it. The moduli from these two sections are used to calculate a weighted average to give a general modulus value over the entire tissue depth measured.
In the second testing period of the stiffness equipment, nine male above-knee amputees were tested. Modulus values were obtained at four different regions on each person: anterior, posterior, medial, and lateral. The results of this test showed that the posterior readings were significantly higher than the other areas; that is, this region would be expected to behave more stiffly (see Table 1 ). This result is being investigated at this time to determine if this is an acquired stiff- ness distribution of amputees, attributed to an abnormal gait pattern, or if this is the normal stiffness profile for all subjects.
The superficial tissue (0 to 0.8cm deep) was found to have a higher modulus than the tissue measured beneath it (0.8 to 2.5cm) (see Table 2 ). Although the muscular tissues of the leg were expected to have higher elasticity, the skin has a very high tensile strength and may have a confining effect on the upper tissue layers, giving it the apparently higher stiffness. This behavior is important to consider when fitting prostheses since generally the superficial tissues are affected the most.
The data were found to be repeatable. Modulus readings were within 15% of the average. Generally, mechanical testing methods have an error of about 10%. Thus, this method is not as repeatable. However, it is not unreasonable and it is much more convenient than conventional methods. Also, as the equipment is further developed, it is expected that this variance will be eliminated. Additionally, the preliminary results of ultrasonic testing were compared to values obtained by Instron mechanical testing machines (Krouskop, 1987). The results showed good agreement with the Instron results (within 7%).
To collect shape and stiffness data, a method was necessary to hold the limb of the subject both vertical and stationary. Early data have been confusing due to the motion of the amputees as they tried to balance. A sling which is secured to the parallel bars in the clinic was devised (Figure 2) so that the subject could be seated during the testing. This sling eliminated swaying motions which had caused the earlier problems. A hole in the sling accommodates the residual limb and isolates it for testing. The subject leans forward onto a board which is placed on the parallel bars in front of the subject. This position is comfortable enough to be maintained for at least 15 minutes at a time by most subjects, enough time for either of the measurement procedures.
Using the ANSYS Finite element code, a three-dimensional isoparametric solid model of the residual limb was developed. The grid for the model consists of five layers radially, 1" elements over the length of the limb, and nodes every 10° circumferentially. Shape and stiffness data as measured from each subject is input, as well as tissue density (1.OOg/cm3), estimated bone location and diameter, and pressure profiles which had been previously determined to be desirable in comfortable sockets (Krouskop, 1987). Bone is considered to be a rigid boundary for this analysis, since the soft tissue is several orders of magnitude softer. The output of interest from this program is the deflection at the surface of the limb.
The deflected form of the limb is then "fit" with a brim according to the principles used normally in the clinic. For example, for a Normal Shape Normal Alignment (NSNA) socket the prosthetist chooses a brim with a specific anterior-posterior to medial-lateral diameter ratio based on the circumference of the limb. This information is used in the automated version also, a NSNA brim being constructed numerically by the computer, using the data collected. At this time, these algorithms are being expanded so that the user can customize brim types, brim size, flare of the brim, and other aspects which are normal considerations of a prosthetist during a fitting session. The result of these advances will be an interactive routine which constructs and displays the socket cast in a scientific manner, without the time and expense of building trial sockets.
The final step of the process is to transfer the output from the finite element and other programs to a numerically controlled milling machine. This machine carves the desired shape from a cylindrical plastic foam blank. The carved model is then used by the prosthetist to make the socket, which is then aligned in the usual manner.
In addition to the preliminary stiffness testing, the entire procedure is now being used to fit amputee patients. The third subject is in the process of being fit and during this time, the entire system is being further refined so that the subsequent fittings will proceed rapidly and efficiently. Fourteen additional subjects are expected to be fit using the system.
Further work on this project will have several goals. First, the system will be made clinically viable so that it can be used immediately for fitting patients. This will also provide the important adjustment period for the prosthetists to become familiar with the equipment and proficient in its use so that new research and technique development is more easily integrated.
Secondly, the system may be used to fabricate several types of prostheses for use in evaluation of design. Measurable parameters will be monitored for each design technique. This will pave the way for rational and scientifically based choices for new prostheses.
Finally, the equipment used in this system will be further developed to give more insight into the characteristics of the tissues being measured. Of particular interest will be the stiffness distribution over the residual limb and its changes over time, tissue property measurements at other body locations, tissue packing inside the socket, and the relationship of these variables to the fit of the socket.
Although the system has not yet been sufficiently tested in routine clinical fittings, as it is further refined, it will provide several significant advantages.
First, because the system predicts the deformed shape of the limb inside the socket, the limb need not be measured in the configuration in which it will be fit. That is, it is perfectly acceptable to directly measure the undeformed shape of the limb without having to be concerned with plaster casts or other intermediate devices.
Secondly, this system provides a quantitative measure of the stiffness of the limb. This has been a highly qualitative parameter up to this point, with the prosthetist judging the quality of the tissue by feel. As this variable is investigated further, correlations between tissue condition, muscle tone, and comfort will become quite useful to the prosthetist.
Finally, the main advantage of this system and the reason this technique has been pursued, is that it provides a scientific, quantitative base for developments in the area of prosthetics. Rather than being based on what is already accepted and currently practiced, this system will help to determine which new ideas are feasible. The finite element feature will allow analysis of many types of sockets and will help to determine which of these provides the most desirable socket stresses, interface pressures, and tissue deformations. In this way, the design process will advance beyond trial and error methods so that innovative sockets can be evaluated prior to use and changes can be made based on the analysis provided.
Though potentially very useful, the major drawback of this system is that at this time it is in need of further testing and refinement. Although it has been used to fit several patients successfully and over 100 patients have participated in various measurement studies, many changes have been made to each part of the system, necessitating more testing prior to clinical use. Also, since the equipment has been used for research up to this point, some of the procedures must be revised for clinical convenience. For example, at this time the shape sensor must be adjusted manually between readings. Eventually, this adjustment will be done automatically. Also, more feeble or elderly subjects may have difficulty using the sling apparatus, so an alternate measurement configuration is needed. These and other minor refinements must be completed before extensive clinical trials begin.
A computerized system has been developed for use in above-knee prosthetics fitting and research and has been successful in preliminary trials. Further refinements are taking place currently to enable clinical use of the system.
This project is aimed at providing not only a convenient tool for the clinician, but also a means for future developments in prosthetics technology. In order to do this, we have chosen to predict the behavior of a complex system, so our computer methods are correspondingly complicated. Many people have expressed the idea that the problem of prosthetics fitting does not warrant such a detailed approach. However, we feel that by modelling the three-dimensional object, rather than using two-dimensional cross-sectional representations, and by taking into consideration material characteristics (both tissue and socket) and loading variability, this method will eventually allow for practical advancement of prosthetics design and practice based on scientific principles. It can provide a valuable means to test and evaluate innovative designs efficiently, an outcome which has yet to be achieved using less sophisticated methods.
This work was sponsored in part by a grant from the Veterans Administration Rehabilitation Research and Development Service to the Houston VA Medical Center.