- Email: [email protected]
Advances in hand biomechanics simulation
Advances in Hand Biomechanics Simulation David E. Thompson, PhD Professor, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, Louisiana.
William L. Buford, Jr., PhD Chief, Paul W. Brand Research Laboratory, C. W. Long National Hansen's Disease Center, Carville, Louisiana.
Loyd M. Myers, MD Deputy Chief, Paul W. Brand Research Laboratory, C. W. Long National Hansen's Disease Center, Carville, Louisiana.
David J. Giurintano, MSME Biomedical Engineer, Paul W. Brand Research Laboratory, C. W. Long National Hansen's Disease Center, Carville, Louisiana.
he current practices of surgery and therapy T for the hand are based on the experiences and observations of past clinicians. More often than not, little can be done to quantify the effects of surgery or therapy because there are no such methods available. In an attempt to rectify this condition, a real-time interactive graphical simulation of the human hand has been under development in the joint GWLHDC/LSU Laboratory for over ten years. This dynamic hand simulation is based on elementary principles of biomechanics. 8 •10,27,3o As new, more sophisticated graphics devices become available and the models we use to drive these simulations improve, the result will be more realistic, dynamic, and accurate simulations. This emphasis on graphics, however, is misleading. The real emphasis of this work is on (1) the underlying mathematical (biomechanical) models representing the functional behavior of the hand and its constituent sub-structures, such as muscles, tendons, sheaths, skin, and ligaments, (2) the anatomy of the hand, and (3) methods of interacting with the models, modifying the anatomy, and obtaining information about the behavior of an individual patient's hand. Modern imaging systems are providing hitherto unseen views into the living anatomy. These views are not just images, however, they represent the three-dimensional geometry of the hand. There is a direct relationship between the geometry of a biological structure and its function. Using the lanCorrespondence and reprint requests to David E. Thompson, PhD, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803.
142
JOURNAL OF HAND THERAPY
guage of mathematics, we can describe these relationships. The language of graphics allows us to visualize these same relationships.
Background Enormous amounts of information may be extracted from imaging data. This includes strictly geometric entities such as the paths of tendons, the curvature and rotational axes of joints, the mechanical lever arms of the individual tendons at each joint, interjoint distances, and other values. Magnetic resonance imaging offers another, different, view into the clinical evaluation of the hand. This instrument holds a great promise of future improvements in imaging techniques. Magnetic resonance imaging (MRI) provides a relative chemical density value in 3D space for the tissues based on measures of specific ion concentrations. We have only begun to use the wealth of information to be gleaned from this new measurement system. It is already clear that MRI scans provide much more information about soft tissues, a major deficiency in computed tomography (CT) scan data. By contrast, however, MRI today is restricted to measures of hydrogen ion concentrations and the hard, dense structure of the skeletal system has a paucity of these ions. For these tissues, CT scans, which are based on the relative x-ray absorption of tissues, are much more appropriate. Commercial systems are now being developed that actually combine these two imaging methods to provide much greater detail than was previously available. The three-dimensional data provided by current imaging technologies is of great value to the radiol-
fiGURE 1.
Raw, unprocessed data from CT scans.
ogist, physician, and therapist in a very visual sense. It may have hidden virtues, however, when this geo-
metric data is combined with the knowledge of the function of the hand to provide a mathematical model specifically tailored to each patient's hand. As an example, consider Figure 1. This image was derived from CT scans and represents stacked outlines of the skeletal system of a hand in three dimensions. Because the scanner does not know one bone from another, this presents all bones as one single composite structure. In Figure 2, Myers20 has implemented a graphics editing tool to allow each bone to be identified as a separate entity and its axes of rotation to be specified. This is combined with a mathematical model of the hand developed by BufordB to enable the individual joints of the hand to be manipulated. This is demonstrated in Figure 2. Articular Surfaces. The intrinsic quality of the imaging data from CT scans is amply demonstrated in Figure 3. Scherrer and Hillberry24 demonstrated that it is possible to accurately describe articular surfaces using mathematics. These mathematical curve forms may be readily analyzed to depict the instantaneous radius of curvature of the joint. In this manner, it may one day be possible to automatically define the principal axes for a joint with little or no manual intervention. Many problems remain, however, before this is a practical approach. Some of these include
fiGURE 2. Processed CT scan data showing multiple bone contours at varying z-values following segmentation and axis definition.
fiGURE 3.
The surface detail obtained through multiple CT
scans taken at 1 mm intervals. the need for higher resolution scanning at joints and greater detail of the cartilage surface. This may require scans taken at varying angles of obliquity to obtain sufficient detail at the joint. As MRI improves, this may actually provide sufficient detail to allow one to find areas where the cartilage surface has thinned or broken down completely. Muscles. As mentioned previously, geometric imaging data can be reduced to a mathematical model of the hand. If this model is coupled with a model of the tendons as was accomplished initially by OU 22 and then improved upon by Giurintano 13 and Thompson 28 , the requisite muscle / tendon excursions to provide the observed motion of a specific patient's joints may be predicted. These excursions are the functional requirements for the total extension and contraction of that patient's individual muscles. If this can be combined with clinical measures of the strengths of the individual muscles of a patient, models of the muscles may then be developed to discern how surgery or therapy might affect th~muscles and measure their ability to provide the necessary motion or torques at the joints they cross. Soft Tissue Effects. The measurement of the torque-angle characteristics of the joint of the hand in our laboratory have provided new insights into the tissues that surround the joints and moderate the functional range of the joint. Llorens 19 constructed a device to measure the passive torque-angle character of joints and Thompson et aU 9 presented a simplistic mathematical model by which one could interpret this data. Brandsma3A and others have used passive torque-angle information to judge the efficacy of treatment modalities and to predict the value of continued treatment to extend joint range of motion and flexibility. The use of dynamic measurements instead of the usual static measurements of passive joint torque-angle requirements will provide additional information April-June 1989
143
fiGURE 4.
The creation of a tendon transfer path for the thumb using a CAD program and a CT-derived database for the hand.
relative to the health of the joints and the soft tissues which affect them. As mentioned by Brand et aU some of the information provided by such a model will include measures of the viscous character of the muscle tissue or the tendon-sheaths of specific muscles. The variations in the parameters of the mathematical models of joints will provide quantification of edema, scarring, and other maladies. The importance of dynamic testing cannot be overstated, since large viscoelastic effects of soft tissues occur when joint angle changes are rapid. In the presence of high-protein edema, however, these effects are predominant even at very low joint rates. The "morning stiffness'" of joints is a clinical manifestation of the viscoelastic forces arising from edema within the soft tissues of joints and muscles. Tendon Path Planning and Analysis. The application of computer-aided design (CAD) methods to surgical or therapeutic techniques may be readily demonstrated. Yoon 34 developed a tendon path planning technique that permits the user to take images derived from CT or MRI scans of a patient's hand and to design the path of a tendon transfer procedure. This may be repeated at several different positions of the joints to determine the excursion required of the transferred muscle. Figure 4 depicts the display during this procedure. Although this has not been applied clinically, this demonstration indicates the directions of future trends in the synergistic application of math modeling, interactive computer graphics, and medicine. Giurintano and Thompsonls have described a method by which a mathematical model of a tendon may be logically integrated into the display of the three-dimensional geometry of a hand. This new tool allows one to model the various elements of tendons and their paths mathematically and then couple this 144
JOURNAL OF HAND THERAPY
model to the display of the hand in such a manner that the user may adjust the hand position interactively and analyze the biomechanics continuously. This capability is demonstrated in Figure 5.
THE MODELING CONCEPT The basic concept of using mathematical modeling is conceptually simple. If, for example, one measures the motion required of a tendon to move a simple hinge joint through various angles (refer to Fig. 6) and graphs the results, the relationship may be described as a linear one as shown in Figure 7. It is possible to approximate the behavior of the PIP joint using the mathematical formulation in Equation 1 where the excursion,S, is linearly related to the joint angle, (), by a constant of proportionality, r. (1)
5
=
r()
This identical relationship describes the excursionangle relationship of the wire wound on a cylinder. A simple model of a one-degree of freedom joint is, therefore, an equivalent cylinder with a radius equal
fiGURE 5. A coupled math model of the flexor tendons and a full geometric definition of a hand derived from electronic imaging.
PIP J 1 T
TE.!
('-J
a0
~
.... {Il
3C.I ~
o -
Experiment Cylinder Model
~
FIGURE 6. Two one-degree-of-freedom systems: a PIP joint and a wire wound on a cylinder.
to the distance between the joint axis and the point of closest approach of the tendon. Similarly, the torque, T exerted on such a joint by a tendon or the torque exerted on an equivalent cylinder by a force on the wire is given in Equation 2: (2)
T= Fr
There are some worthwhile points to consider from this simple mathematical model. It should be noted that pictures were used to portray the model and experimental data. This use of graphics, while restricted to static drawings, used the visual pathways and the past experience of the viewer to assist in the interpretation and assimilation of the model. The mathematics simply describe in symbols what is happening in nature. Pictures or graphics are powerful mechanisms for translating one's experience into an understanding of the basic phenomenon of hand biomechanics. Since both the graphics and the mathematics are portraying the phenomenon, it is proposed that using graphics will lead one to either understand the mathematics or, lacking mathematical skills, to obtain an experience-based understanding of the relevant relationships. If dynamic pictures of the simple structures in this example were to be employed, their understanding would occur more rapidly and the information would be easier to recall. This need for dynamically moving pictures is necessary when viewing threedimensional structures. Interpreting three-dimensional structures can be extremely difficult without motion. Dynamic graphics is an essential element in interpreting more complex mathematical models and their associated physical analogues. The general modeling concept used in the workstation research in our laboratories is shown in Figure 8. All of the basic elements are seen to be included. Basic experimental measurements lead to an understanding of the biomechanics and they are encoded into the language of mathematics. The three-dimensional geometry of the hand is obtained through electronic imaging and coupled to the mathematics to portray the hand and tendon structures dynamically. Tools for interacting with the geometry and the mathematics allow one to heuristically attain an understanding of the biomechanics without an in-depth knowledge of calculus or mechanics. The resulting workstation environment is felt to combine the visual interpretive skills of the user with the knowledge
Angle, e FIGURE 7. The relationship between tendon excursion and joint angle for flexion-extension motions of the PIP joint and a wire wound on a cylinder.
attained through experimental research and through mathematical modeling in a natural manner, thereby permitting the user to investigate ideas and to learn new concepts without the possibility of irreversible injury to patients.
SUMMARY The concepts and directions described in the previous sections are derived from the development of a hand biomechanics workstation for use by orthopedic surgeons and therapists that has been underway at the Paul W. Brand Biomechanics Laboratory for the past 12 years. This collaborative effort among engineers, surgeons, therapists, and physicians seeks to use math modeling, interactive graphics, and expert knowledge to build a workstation that provides natural, intuitive tools to be used in the treatment of hands. One goal of the project is to provide the surgeon with tools for planning and analyzing reconstructive surgical procedures and for analyzing certain functional abnormalities in hands. This new approach to planning reconstructive surgical techniques was designed to permit thE:! surgeon to base his procedures on quantitative methods rather than on the previous subjectively based methods. These tools are being designed to permit a surgeon to know in advance what excursions would be required based on the anatomy of a specific patient and the geometry of a chosen tendon path. He would also be advised of the mechanical advantage of the muscle at each joint it acts across and of the forces necessary for specific predetermined hand actions. In addition, the visualization of the anatomy provided by the workstation permits the surgeon to obtain new insights into the reasons for selecting specific paths for tendons. A second major goal of the workstation is to provide the therapist with new insights into the functional corrections being sought and methods of planning and analysis of external braces, splints, and prostheses. Models of soft tissue behavior and a selection of current treatment systems must be develApril-June 1989
145
oped and tested so that the information presented is accurate and can be used to devise acceptable therapeutic methods that are based on quantifiable measures of forces, pressures, and motions. The modeling of existing splints and other devices and their response to the forces resulting from their use will one day permit the evaluation of the efficacy of different treatments and provide a means to tailor them to the needs of specific patients. The past 3 years have seen an explosive growth in the number of computer graphics workstations. Parallel developments have occurred in networking and in the applications of computing in medicine. The power and capabilities of these workstations has also grown dramatically. Three years ago, a typical workstation was capable of executing approximately 0.5 million instructions each second (MIPS). This has risen to a value of approximately 10 MIPS today, a 20-fold increase in 3 years. On the medical imaging front, the availability of CT scanners has experienced a similar growth and a new wave of MRI scanners is appearing. Three years ago, these were not generally available or financially practical devices. Software programs to utilize the potential of such advances have not kept pace, however. There are singular successes, but the real power of the graphics workstation remains generally underutilized today. One hopeful sign is the emergence of a new standard for Macintosh-like windows that many manufacturers are embracing. This new standard seeks to make the graphics display vendor independent. Similarly, even the way computers communicate with one another is being standardized. Robust software development tools are finally becoming available for generating user-friendly applications so that the user does not have to be a computer expert to use the system. It is understandable, then, that much additional work remains before the current biomechanics workstation prototype is an acceptable system that can be placed into daily clinical use. A more complete toolbox of analytical methods is being designed in the joint biomechanics laboratories of GWLNHDC and LSU to evaluate the function of hands based on their form and on force and torque analyses. It will be imperative that this workstation present the user with the results of the mathematical analysis in a manner that is natural, realistic, and interactive. Only then will it be an acceptable tool for clinical application. The role of technology in medicine has always been to provide the best health care possible at the lowest possible cost and in the shortest time. In this triangle of factors, only two of these are generally achievable at any time. Thus, one might for example develop a device that will provide immediate health benefits and may even be cost effective, but such a device will usually require much more of a physicians' or therapists' time. Similarly, one might dramatically improve such a device and shorten the time of treatment, but this inevitably results in a higher device cost. It is hoped that the initiation of highly interactive computer workstations specifically developed for use by the medical practitioner will break this rule. Certainly the lessons have been learned and 146
JOURNAL OF HAND THERAPY
Musculo- Skeletal Geometiy, Axes of Rotation, Tendon Paths, Muscle strengths, Moment Arms
RESEARCH
TRAINING Interactive Computer Graphics and Visualiution Expert
CLINICAL APPUCATIONS
Knowledge Database
fiGURE 8. A block diagram of the modeling and display concept used in the hand biomechanics workstation.
the achievements made in this melding of mathematics, computer graphics, and medicine hold great promise. ACknowledgments The funding for this research was provided by the U.S. Public Health Service, Department of Health and Human Services under research contract 240-83-0060. Additional computing support was provided by the Interactive Modeling Research Laboratory, Department of Mechanical Engineering, Louisiana State University through a joint research program with Digital Equipment Corporation. Evans and Sutherland provided a PS 390 display system which was used to manipulate and view the images in this work. The image data for this research were provided by Digital Diagnostics, Inc. of Baton Rouge, LA (Dr. Charles Grieson, Director). They generously provided their time, materials, and scan time for this project.
References 1. Agee JM, Brand PW, Thompson DE: The moment arms of the carpometacarpal joint of the thumb: Their laboratory determination and clinical application. Proc. of the 37th Annual Mtg., Am. Soc. For Surgery of the Hand. 14, Jan 1982 [New Orleans, LA]. 2. An KN, Chao EY, Cooney III WP, Linscheid RL: Normative model of human hand for biomechanical analysis. J Biomechanics 12:775-788, 1979. 3. Brandsma JW: Pre- and post-operative evaluation of the hand with intrinsic paralysis. Proe.. IntI. Conf. on Biomechanics and Clinical Kinesiology of the Hand and Foot. Madras, India, LI.T., 1985, pp 69-70. 4. Brandsma JA, Brand PW: Quantification and analysis of joint stiffness. Proc. IntI. Conf. on Biomechanics and Clinical Kinesiology of the Hand and Foot. Madras, India, LI.T., 1986. 5. Brand PW, Beach RB, Thompson DE: Relative tension and excursion of muscles in the forearm and hand. J Hand Surg 6: 209-219, May 1981. 6. Brand PW (ed): Clinical Mechanics of the Hand. 5t. Louis, C.V. Mosby Co., 1985. 7. Brand PW, Thompson DE, Micks JE: The biomechanics of the interphalangeal joints. In Bowers WH (ed): The Interphalangeal Joint. New York, Churchill Livingstone Publishers, 1987, pp 21-54. 8. Buford WI Jr: An interactive three dimensional simulation of the kinematics of the human thumb. Ph.D. Dissertation, Dept. of Engineering Science, Louisiana State University, 1984; also Alln Arbor, MI, University Microfilms International, 85-15133, 1985. 9. Buford WL, Myers L, Thompson DE: A computer graphics sys-
10. 11. 12.
13. 14. 15. 16. 17.
18.
19. 20.
21.
tern for musculoskeletal modeling. Proc. 8th Annual EMBS Conference. Fort Worth, TX, 1986, pp 607-610. Buford WL, Thompson DE: A system for 3D interactive simulation of hand biomechanics. IEEE Trans Biomedical Engr BME 34:434-453,1987. Chao EY, Opgrande JD, Axmear FE: Three dimensional force analysis of finger joints in selected isometric hand function. J Biomechanics 19:387-396, 1976. Fischer CW: A treatise on the topographical anatomy of the long finger and a biomechanical investigation of its interjoint movement. Ph.D. thesis, Engineering Mechanics, Univ. of Iowa. Ann Arbor, MI, Univ. Microfilms, Inc. 1969. Giurintano DJ: A multi-joint model of the finger flexor tendons. M.s. thesis, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA, 1986. Giurintano DJ, Thompson DE: A kinematic model for the flexor tendons of the hand. Proc. IEEE/EMBS, Paper 40.330.4, November, 1987. Giurinatanq OJ, Thompson DE: A flexor tendon model of the hand. J Automedica 1989 (in press). Ketchum LD, Brand PW, Thompson DE, Pocock GS: The determination of moments for extension of the wrist generated by muscles of the forearm. J Hand Surg 3: Nov 1978. Ketchum LD, Thompson DE, Pocock GS, Wallingford D: A clinical study of the forces generated by the intrinsic muscles of the index finger and the extrinsic flexor and extensor muscles of the hand. J Hand Surg 3:571-578, Nov 1978. Ketchum LD, Thompson DE: An experimental investigation into the forces internal to the human hand. Appendix B. In Brand PW (ed): Clinical Mechanics of the Hand. St. Louis, c.V. Mosby Co., 1985, pp 325-331. Llorens WA: An experimental analysis of finger jOint stiffness. M.s. thesis, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA, May 1986. Myers LM, Buford WL, Thompson DE: A graphics editor for 3-D CT-scan data for musculo-skeletal modeling. Proe. Computer Assisted Radiology, Berlin, July, 1987, pp 477-483. Murphy SB, Kijewski PK, Simon SR, et al: Computer-aided simulation, analysis, and design in orthopedic surgery. Orthop Clin North Am 17:637-649, 1986.
22. Ou CA: The biomechanics of the carpometacarpal joint of th e thumb. PhD. Dissertation, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA. Dec. 1979. 23. Ross PD: An analysis of joint range of motion. Internal Report, Rehabilitation Research Department, GWL National Hansen 's Disease Center, 1982. 24. Scherrer PK, Hillberry BM: Piecewise mathematical representation of articular surfaces. J Biomechanics 12:301-311, 1979. 25. Stutts DS: A two-dimensional analysis of the extensor fibers in the human hand. M.s.M.E. thesis, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA, Dec. 1987. 26. Thompson DE, Hussein HM, Perritt RQ: Point impedance measurement of human soft tissues in vivo. In Marks R, Payne PA (eds): Bioengineering and the Skin. 1981, pp 103-11l. 27. Thompson DE: Biomechanics of the hand. Perspectives in Computing 3:12-19, Oct. 1981. 28. Thompson DE: Soft tissues: Their behavior in compressive loading. In Levin M, O' Neal LW (eds): The Diabetic Foot, 3rd I'd. St. Louis, C.V. Mosby Co., 1983, pp 148-161. 29. Thompson DE, Buford WL, Brewer JA, Myers LM: Simulating hand surgery: A work in progress. ASMEjSOMA 2:6-12, June, 1987. 30. Thompson DE, Buford WL, Myers LM, et al: A hand biomechanics workstation. Proc. ACM SIGGRAPH, Computer Graphics, 22:335-343, Aug 1988. 31. Thompson DE: The effects of stress on soft tissues. In Levin M, O'Neal LW (eds): The Diabetic Foot, 4th I'd. St. Louis, C.V. Mosby Co. 1988, pp 91-103. 32. Thompson DE, Giurintano OJ: A kinematic model of the flex or tendons of the human hand. J Biomechanics 22: 1989 (in press). 33. Vannier MW, Marsch JL, Warren JO: Three dimensional computer graphics for craniofacial surgical planning and evaluation. Proc. ACM/SIGGRAPH, 17:263-273, 1983. 34. Yoon I, Thompson DE: An interactive graphics based tendon path planning method. Proc. ASME WAM, Bioengineering Division, Paper BI0-9B, 1988.
April-June 1989
147
William L. Buford, Jr., PhD Chief, Paul W. Brand Research Laboratory, C. W. Long National Hansen's Disease Center, Carville, Louisiana.
Loyd M. Myers, MD Deputy Chief, Paul W. Brand Research Laboratory, C. W. Long National Hansen's Disease Center, Carville, Louisiana.
David J. Giurintano, MSME Biomedical Engineer, Paul W. Brand Research Laboratory, C. W. Long National Hansen's Disease Center, Carville, Louisiana.
he current practices of surgery and therapy T for the hand are based on the experiences and observations of past clinicians. More often than not, little can be done to quantify the effects of surgery or therapy because there are no such methods available. In an attempt to rectify this condition, a real-time interactive graphical simulation of the human hand has been under development in the joint GWLHDC/LSU Laboratory for over ten years. This dynamic hand simulation is based on elementary principles of biomechanics. 8 •10,27,3o As new, more sophisticated graphics devices become available and the models we use to drive these simulations improve, the result will be more realistic, dynamic, and accurate simulations. This emphasis on graphics, however, is misleading. The real emphasis of this work is on (1) the underlying mathematical (biomechanical) models representing the functional behavior of the hand and its constituent sub-structures, such as muscles, tendons, sheaths, skin, and ligaments, (2) the anatomy of the hand, and (3) methods of interacting with the models, modifying the anatomy, and obtaining information about the behavior of an individual patient's hand. Modern imaging systems are providing hitherto unseen views into the living anatomy. These views are not just images, however, they represent the three-dimensional geometry of the hand. There is a direct relationship between the geometry of a biological structure and its function. Using the lanCorrespondence and reprint requests to David E. Thompson, PhD, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803.
142
JOURNAL OF HAND THERAPY
guage of mathematics, we can describe these relationships. The language of graphics allows us to visualize these same relationships.
Background Enormous amounts of information may be extracted from imaging data. This includes strictly geometric entities such as the paths of tendons, the curvature and rotational axes of joints, the mechanical lever arms of the individual tendons at each joint, interjoint distances, and other values. Magnetic resonance imaging offers another, different, view into the clinical evaluation of the hand. This instrument holds a great promise of future improvements in imaging techniques. Magnetic resonance imaging (MRI) provides a relative chemical density value in 3D space for the tissues based on measures of specific ion concentrations. We have only begun to use the wealth of information to be gleaned from this new measurement system. It is already clear that MRI scans provide much more information about soft tissues, a major deficiency in computed tomography (CT) scan data. By contrast, however, MRI today is restricted to measures of hydrogen ion concentrations and the hard, dense structure of the skeletal system has a paucity of these ions. For these tissues, CT scans, which are based on the relative x-ray absorption of tissues, are much more appropriate. Commercial systems are now being developed that actually combine these two imaging methods to provide much greater detail than was previously available. The three-dimensional data provided by current imaging technologies is of great value to the radiol-
fiGURE 1.
Raw, unprocessed data from CT scans.
ogist, physician, and therapist in a very visual sense. It may have hidden virtues, however, when this geo-
metric data is combined with the knowledge of the function of the hand to provide a mathematical model specifically tailored to each patient's hand. As an example, consider Figure 1. This image was derived from CT scans and represents stacked outlines of the skeletal system of a hand in three dimensions. Because the scanner does not know one bone from another, this presents all bones as one single composite structure. In Figure 2, Myers20 has implemented a graphics editing tool to allow each bone to be identified as a separate entity and its axes of rotation to be specified. This is combined with a mathematical model of the hand developed by BufordB to enable the individual joints of the hand to be manipulated. This is demonstrated in Figure 2. Articular Surfaces. The intrinsic quality of the imaging data from CT scans is amply demonstrated in Figure 3. Scherrer and Hillberry24 demonstrated that it is possible to accurately describe articular surfaces using mathematics. These mathematical curve forms may be readily analyzed to depict the instantaneous radius of curvature of the joint. In this manner, it may one day be possible to automatically define the principal axes for a joint with little or no manual intervention. Many problems remain, however, before this is a practical approach. Some of these include
fiGURE 2. Processed CT scan data showing multiple bone contours at varying z-values following segmentation and axis definition.
fiGURE 3.
The surface detail obtained through multiple CT
scans taken at 1 mm intervals. the need for higher resolution scanning at joints and greater detail of the cartilage surface. This may require scans taken at varying angles of obliquity to obtain sufficient detail at the joint. As MRI improves, this may actually provide sufficient detail to allow one to find areas where the cartilage surface has thinned or broken down completely. Muscles. As mentioned previously, geometric imaging data can be reduced to a mathematical model of the hand. If this model is coupled with a model of the tendons as was accomplished initially by OU 22 and then improved upon by Giurintano 13 and Thompson 28 , the requisite muscle / tendon excursions to provide the observed motion of a specific patient's joints may be predicted. These excursions are the functional requirements for the total extension and contraction of that patient's individual muscles. If this can be combined with clinical measures of the strengths of the individual muscles of a patient, models of the muscles may then be developed to discern how surgery or therapy might affect th~muscles and measure their ability to provide the necessary motion or torques at the joints they cross. Soft Tissue Effects. The measurement of the torque-angle characteristics of the joint of the hand in our laboratory have provided new insights into the tissues that surround the joints and moderate the functional range of the joint. Llorens 19 constructed a device to measure the passive torque-angle character of joints and Thompson et aU 9 presented a simplistic mathematical model by which one could interpret this data. Brandsma3A and others have used passive torque-angle information to judge the efficacy of treatment modalities and to predict the value of continued treatment to extend joint range of motion and flexibility. The use of dynamic measurements instead of the usual static measurements of passive joint torque-angle requirements will provide additional information April-June 1989
143
fiGURE 4.
The creation of a tendon transfer path for the thumb using a CAD program and a CT-derived database for the hand.
relative to the health of the joints and the soft tissues which affect them. As mentioned by Brand et aU some of the information provided by such a model will include measures of the viscous character of the muscle tissue or the tendon-sheaths of specific muscles. The variations in the parameters of the mathematical models of joints will provide quantification of edema, scarring, and other maladies. The importance of dynamic testing cannot be overstated, since large viscoelastic effects of soft tissues occur when joint angle changes are rapid. In the presence of high-protein edema, however, these effects are predominant even at very low joint rates. The "morning stiffness'" of joints is a clinical manifestation of the viscoelastic forces arising from edema within the soft tissues of joints and muscles. Tendon Path Planning and Analysis. The application of computer-aided design (CAD) methods to surgical or therapeutic techniques may be readily demonstrated. Yoon 34 developed a tendon path planning technique that permits the user to take images derived from CT or MRI scans of a patient's hand and to design the path of a tendon transfer procedure. This may be repeated at several different positions of the joints to determine the excursion required of the transferred muscle. Figure 4 depicts the display during this procedure. Although this has not been applied clinically, this demonstration indicates the directions of future trends in the synergistic application of math modeling, interactive computer graphics, and medicine. Giurintano and Thompsonls have described a method by which a mathematical model of a tendon may be logically integrated into the display of the three-dimensional geometry of a hand. This new tool allows one to model the various elements of tendons and their paths mathematically and then couple this 144
JOURNAL OF HAND THERAPY
model to the display of the hand in such a manner that the user may adjust the hand position interactively and analyze the biomechanics continuously. This capability is demonstrated in Figure 5.
THE MODELING CONCEPT The basic concept of using mathematical modeling is conceptually simple. If, for example, one measures the motion required of a tendon to move a simple hinge joint through various angles (refer to Fig. 6) and graphs the results, the relationship may be described as a linear one as shown in Figure 7. It is possible to approximate the behavior of the PIP joint using the mathematical formulation in Equation 1 where the excursion,S, is linearly related to the joint angle, (), by a constant of proportionality, r. (1)
5
=
r()
This identical relationship describes the excursionangle relationship of the wire wound on a cylinder. A simple model of a one-degree of freedom joint is, therefore, an equivalent cylinder with a radius equal
fiGURE 5. A coupled math model of the flexor tendons and a full geometric definition of a hand derived from electronic imaging.
PIP J 1 T
TE.!
('-J
a0
~
.... {Il
3C.I ~
o -
Experiment Cylinder Model
~
FIGURE 6. Two one-degree-of-freedom systems: a PIP joint and a wire wound on a cylinder.
to the distance between the joint axis and the point of closest approach of the tendon. Similarly, the torque, T exerted on such a joint by a tendon or the torque exerted on an equivalent cylinder by a force on the wire is given in Equation 2: (2)
T= Fr
There are some worthwhile points to consider from this simple mathematical model. It should be noted that pictures were used to portray the model and experimental data. This use of graphics, while restricted to static drawings, used the visual pathways and the past experience of the viewer to assist in the interpretation and assimilation of the model. The mathematics simply describe in symbols what is happening in nature. Pictures or graphics are powerful mechanisms for translating one's experience into an understanding of the basic phenomenon of hand biomechanics. Since both the graphics and the mathematics are portraying the phenomenon, it is proposed that using graphics will lead one to either understand the mathematics or, lacking mathematical skills, to obtain an experience-based understanding of the relevant relationships. If dynamic pictures of the simple structures in this example were to be employed, their understanding would occur more rapidly and the information would be easier to recall. This need for dynamically moving pictures is necessary when viewing threedimensional structures. Interpreting three-dimensional structures can be extremely difficult without motion. Dynamic graphics is an essential element in interpreting more complex mathematical models and their associated physical analogues. The general modeling concept used in the workstation research in our laboratories is shown in Figure 8. All of the basic elements are seen to be included. Basic experimental measurements lead to an understanding of the biomechanics and they are encoded into the language of mathematics. The three-dimensional geometry of the hand is obtained through electronic imaging and coupled to the mathematics to portray the hand and tendon structures dynamically. Tools for interacting with the geometry and the mathematics allow one to heuristically attain an understanding of the biomechanics without an in-depth knowledge of calculus or mechanics. The resulting workstation environment is felt to combine the visual interpretive skills of the user with the knowledge
Angle, e FIGURE 7. The relationship between tendon excursion and joint angle for flexion-extension motions of the PIP joint and a wire wound on a cylinder.
attained through experimental research and through mathematical modeling in a natural manner, thereby permitting the user to investigate ideas and to learn new concepts without the possibility of irreversible injury to patients.
SUMMARY The concepts and directions described in the previous sections are derived from the development of a hand biomechanics workstation for use by orthopedic surgeons and therapists that has been underway at the Paul W. Brand Biomechanics Laboratory for the past 12 years. This collaborative effort among engineers, surgeons, therapists, and physicians seeks to use math modeling, interactive graphics, and expert knowledge to build a workstation that provides natural, intuitive tools to be used in the treatment of hands. One goal of the project is to provide the surgeon with tools for planning and analyzing reconstructive surgical procedures and for analyzing certain functional abnormalities in hands. This new approach to planning reconstructive surgical techniques was designed to permit thE:! surgeon to base his procedures on quantitative methods rather than on the previous subjectively based methods. These tools are being designed to permit a surgeon to know in advance what excursions would be required based on the anatomy of a specific patient and the geometry of a chosen tendon path. He would also be advised of the mechanical advantage of the muscle at each joint it acts across and of the forces necessary for specific predetermined hand actions. In addition, the visualization of the anatomy provided by the workstation permits the surgeon to obtain new insights into the reasons for selecting specific paths for tendons. A second major goal of the workstation is to provide the therapist with new insights into the functional corrections being sought and methods of planning and analysis of external braces, splints, and prostheses. Models of soft tissue behavior and a selection of current treatment systems must be develApril-June 1989
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oped and tested so that the information presented is accurate and can be used to devise acceptable therapeutic methods that are based on quantifiable measures of forces, pressures, and motions. The modeling of existing splints and other devices and their response to the forces resulting from their use will one day permit the evaluation of the efficacy of different treatments and provide a means to tailor them to the needs of specific patients. The past 3 years have seen an explosive growth in the number of computer graphics workstations. Parallel developments have occurred in networking and in the applications of computing in medicine. The power and capabilities of these workstations has also grown dramatically. Three years ago, a typical workstation was capable of executing approximately 0.5 million instructions each second (MIPS). This has risen to a value of approximately 10 MIPS today, a 20-fold increase in 3 years. On the medical imaging front, the availability of CT scanners has experienced a similar growth and a new wave of MRI scanners is appearing. Three years ago, these were not generally available or financially practical devices. Software programs to utilize the potential of such advances have not kept pace, however. There are singular successes, but the real power of the graphics workstation remains generally underutilized today. One hopeful sign is the emergence of a new standard for Macintosh-like windows that many manufacturers are embracing. This new standard seeks to make the graphics display vendor independent. Similarly, even the way computers communicate with one another is being standardized. Robust software development tools are finally becoming available for generating user-friendly applications so that the user does not have to be a computer expert to use the system. It is understandable, then, that much additional work remains before the current biomechanics workstation prototype is an acceptable system that can be placed into daily clinical use. A more complete toolbox of analytical methods is being designed in the joint biomechanics laboratories of GWLNHDC and LSU to evaluate the function of hands based on their form and on force and torque analyses. It will be imperative that this workstation present the user with the results of the mathematical analysis in a manner that is natural, realistic, and interactive. Only then will it be an acceptable tool for clinical application. The role of technology in medicine has always been to provide the best health care possible at the lowest possible cost and in the shortest time. In this triangle of factors, only two of these are generally achievable at any time. Thus, one might for example develop a device that will provide immediate health benefits and may even be cost effective, but such a device will usually require much more of a physicians' or therapists' time. Similarly, one might dramatically improve such a device and shorten the time of treatment, but this inevitably results in a higher device cost. It is hoped that the initiation of highly interactive computer workstations specifically developed for use by the medical practitioner will break this rule. Certainly the lessons have been learned and 146
JOURNAL OF HAND THERAPY
Musculo- Skeletal Geometiy, Axes of Rotation, Tendon Paths, Muscle strengths, Moment Arms
RESEARCH
TRAINING Interactive Computer Graphics and Visualiution Expert
CLINICAL APPUCATIONS
Knowledge Database
fiGURE 8. A block diagram of the modeling and display concept used in the hand biomechanics workstation.
the achievements made in this melding of mathematics, computer graphics, and medicine hold great promise. ACknowledgments The funding for this research was provided by the U.S. Public Health Service, Department of Health and Human Services under research contract 240-83-0060. Additional computing support was provided by the Interactive Modeling Research Laboratory, Department of Mechanical Engineering, Louisiana State University through a joint research program with Digital Equipment Corporation. Evans and Sutherland provided a PS 390 display system which was used to manipulate and view the images in this work. The image data for this research were provided by Digital Diagnostics, Inc. of Baton Rouge, LA (Dr. Charles Grieson, Director). They generously provided their time, materials, and scan time for this project.
References 1. Agee JM, Brand PW, Thompson DE: The moment arms of the carpometacarpal joint of the thumb: Their laboratory determination and clinical application. Proc. of the 37th Annual Mtg., Am. Soc. For Surgery of the Hand. 14, Jan 1982 [New Orleans, LA]. 2. An KN, Chao EY, Cooney III WP, Linscheid RL: Normative model of human hand for biomechanical analysis. J Biomechanics 12:775-788, 1979. 3. Brandsma JW: Pre- and post-operative evaluation of the hand with intrinsic paralysis. Proe.. IntI. Conf. on Biomechanics and Clinical Kinesiology of the Hand and Foot. Madras, India, LI.T., 1985, pp 69-70. 4. Brandsma JA, Brand PW: Quantification and analysis of joint stiffness. Proc. IntI. Conf. on Biomechanics and Clinical Kinesiology of the Hand and Foot. Madras, India, LI.T., 1986. 5. Brand PW, Beach RB, Thompson DE: Relative tension and excursion of muscles in the forearm and hand. J Hand Surg 6: 209-219, May 1981. 6. Brand PW (ed): Clinical Mechanics of the Hand. 5t. Louis, C.V. Mosby Co., 1985. 7. Brand PW, Thompson DE, Micks JE: The biomechanics of the interphalangeal joints. In Bowers WH (ed): The Interphalangeal Joint. New York, Churchill Livingstone Publishers, 1987, pp 21-54. 8. Buford WI Jr: An interactive three dimensional simulation of the kinematics of the human thumb. Ph.D. Dissertation, Dept. of Engineering Science, Louisiana State University, 1984; also Alln Arbor, MI, University Microfilms International, 85-15133, 1985. 9. Buford WL, Myers L, Thompson DE: A computer graphics sys-
10. 11. 12.
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tern for musculoskeletal modeling. Proc. 8th Annual EMBS Conference. Fort Worth, TX, 1986, pp 607-610. Buford WL, Thompson DE: A system for 3D interactive simulation of hand biomechanics. IEEE Trans Biomedical Engr BME 34:434-453,1987. Chao EY, Opgrande JD, Axmear FE: Three dimensional force analysis of finger joints in selected isometric hand function. J Biomechanics 19:387-396, 1976. Fischer CW: A treatise on the topographical anatomy of the long finger and a biomechanical investigation of its interjoint movement. Ph.D. thesis, Engineering Mechanics, Univ. of Iowa. Ann Arbor, MI, Univ. Microfilms, Inc. 1969. Giurintano DJ: A multi-joint model of the finger flexor tendons. M.s. thesis, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA, 1986. Giurintano DJ, Thompson DE: A kinematic model for the flexor tendons of the hand. Proc. IEEE/EMBS, Paper 40.330.4, November, 1987. Giurinatanq OJ, Thompson DE: A flexor tendon model of the hand. J Automedica 1989 (in press). Ketchum LD, Brand PW, Thompson DE, Pocock GS: The determination of moments for extension of the wrist generated by muscles of the forearm. J Hand Surg 3: Nov 1978. Ketchum LD, Thompson DE, Pocock GS, Wallingford D: A clinical study of the forces generated by the intrinsic muscles of the index finger and the extrinsic flexor and extensor muscles of the hand. J Hand Surg 3:571-578, Nov 1978. Ketchum LD, Thompson DE: An experimental investigation into the forces internal to the human hand. Appendix B. In Brand PW (ed): Clinical Mechanics of the Hand. St. Louis, c.V. Mosby Co., 1985, pp 325-331. Llorens WA: An experimental analysis of finger jOint stiffness. M.s. thesis, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA, May 1986. Myers LM, Buford WL, Thompson DE: A graphics editor for 3-D CT-scan data for musculo-skeletal modeling. Proe. Computer Assisted Radiology, Berlin, July, 1987, pp 477-483. Murphy SB, Kijewski PK, Simon SR, et al: Computer-aided simulation, analysis, and design in orthopedic surgery. Orthop Clin North Am 17:637-649, 1986.
22. Ou CA: The biomechanics of the carpometacarpal joint of th e thumb. PhD. Dissertation, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA. Dec. 1979. 23. Ross PD: An analysis of joint range of motion. Internal Report, Rehabilitation Research Department, GWL National Hansen 's Disease Center, 1982. 24. Scherrer PK, Hillberry BM: Piecewise mathematical representation of articular surfaces. J Biomechanics 12:301-311, 1979. 25. Stutts DS: A two-dimensional analysis of the extensor fibers in the human hand. M.s.M.E. thesis, Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA, Dec. 1987. 26. Thompson DE, Hussein HM, Perritt RQ: Point impedance measurement of human soft tissues in vivo. In Marks R, Payne PA (eds): Bioengineering and the Skin. 1981, pp 103-11l. 27. Thompson DE: Biomechanics of the hand. Perspectives in Computing 3:12-19, Oct. 1981. 28. Thompson DE: Soft tissues: Their behavior in compressive loading. In Levin M, O' Neal LW (eds): The Diabetic Foot, 3rd I'd. St. Louis, C.V. Mosby Co., 1983, pp 148-161. 29. Thompson DE, Buford WL, Brewer JA, Myers LM: Simulating hand surgery: A work in progress. ASMEjSOMA 2:6-12, June, 1987. 30. Thompson DE, Buford WL, Myers LM, et al: A hand biomechanics workstation. Proc. ACM SIGGRAPH, Computer Graphics, 22:335-343, Aug 1988. 31. Thompson DE: The effects of stress on soft tissues. In Levin M, O'Neal LW (eds): The Diabetic Foot, 4th I'd. St. Louis, C.V. Mosby Co. 1988, pp 91-103. 32. Thompson DE, Giurintano OJ: A kinematic model of the flex or tendons of the human hand. J Biomechanics 22: 1989 (in press). 33. Vannier MW, Marsch JL, Warren JO: Three dimensional computer graphics for craniofacial surgical planning and evaluation. Proc. ACM/SIGGRAPH, 17:263-273, 1983. 34. Yoon I, Thompson DE: An interactive graphics based tendon path planning method. Proc. ASME WAM, Bioengineering Division, Paper BI0-9B, 1988.
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