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3 Biomechanical Models Interest in the biomechanical properties of the human body has evolved along with mathematical sophistication. The early works of Leonardo da Vinci (O'Malley and Saunders, 1952), Galileo Galilei (1638), and Giovani Alfonso Borelli (circa 1679) demon- strate man's curiosity ~d desire to describe the human in quan- titative terms. Even though hundreds of years have passed since these early attempts, biomechanical modeling of the human mus- culoskeletal system remains one of the most challenging tasks known to man. This chapter evaluates biomechanical modeling knowledge and its significance to ergonomics. Prior to such a review, however, the concept of modeling as used here should be discussed first. A mode} can be defined as any set of equations that describe phys- ical events or phenomena. Sinclair and Drury (1980) described a mode} as a paradigm view of science. They proposed two defini- tions of models. First, they defined a mode! as "the result of using theoretical understanding to present a particular aspect of the real world. This definition represents a normative model, which de- scribes the idealized behavior of the system. Second, they defined another type of descriptive mode] that used Statistical techniques to relate theoretical variables present in a collection of data. This type of model typically employs regression analysis to describe the dynamic behavior of the human body. In the context of this review of biomechanical models, only 19

20 models according to Sinclair and Drury's first definition will be considered. Consideration must be given to the objective of a biomechan- ical mode! used for ergonomic purposes. A biomechanical mode] should facilitate the basic understanding of the system. Morris (1967) noted that modeling should be a process of enrichment and enhancement. He pointed out that one should begin with a mode! that is distinct from reality and, in an evolutionary manner, move toward a more elaborate mode! that reflects the complexity of the actual situation. Little (1970) stated that the objective of the mode} should be to provide intuition. It is apparent that these two objectives are complementary. Through a process of under- standing the components of a system, the mode! is expanded and a greater understanding of component interaction is gained. To achieve these objectives, a mode! should display several qualities. The model should be robust. It should display the essence of the system under a variety of circumstances. A biome- chanical mode! should also represent reality and have clinical rel- evance or workplace applications. The significance of these objectives and requirements applied to ergonomics means that biomechanical models should provide insight into the interaction of people and their environment. Ide- ally, an ergonomic mode} should predict both long- and short-term results of human work, and the effects on people, particularly if a risk exists for both traumatic and cumulative injuries. The discussion on biomechanical models is limited to those models that may be useful to ergonomists. Hence, impact, physim logical, and psychophysical models are not included in this review, nor are all existing models of the musculoskeletal system. Instead, examples are presented that concern bones, joints, body segments, and the whole body. HISTORY OF BIOMECEANICAL MODELS As noted in Chapter 2, Anthropometric Models, the early models of the 1960s assumed that the body is a series of rigid links. These models were limited in the number of links, usually one, two, or three. Most of the models were two-dimensional, based on kinematic information, with some dynamic data. The objective was to look at the forces, torques, and moments around

21 the various articulations and then to track the links to determine what type of loading or motion occurs. Some of the models were then extended, but none predicted any of the internal loadings on the body. Most of the early models worked in some way with the external loadings, based primarily on kinematic types of information and characteristics of torque and force generated by the link motions. Some models, like that of SIote-Stone (1963), were used in predicting power and some, like that of Ayoub et al. (1974), were used in predicting position during work. These models provider! the basic context of understanding in the programs. Many of the later models are based on the work of Chaffin (1969), who joined seven or eight different links of the body. Ex- tending the previous principles, he calculated torques and forces around the joint, and then tracked the whole body in a kinetic chain. Most of the later models are two-dimensional static models that represent, to a limited extent, forces and moments acting at each particular articulation to generate internal loading informa- tion. More recent versions of this model are built on the same basic logic but use dynamic data and three dimensions. Ayoub and El-Bassoussi (1976) used optimization to predict a lifting model, and in the early 1980s, Schultz and Andersson (1981) and Schultz et al. (1982) developed a different type of model that no longer considered the body as a set of rigid links. This was a three-dimensional model that represented active analysis of the stresses imposed on the body under working conditions. This two- part analysis can be used to analyze the net reaction which must be resisted by the internal forces of the body. Several methods have been used for this type of analysis. One is to assume that the antagonist muscles are silent (which may or may not be a correct assumption, depending on the circumstances), and another is to use optimization, particularly linear programming with upper and lower bounds. Another class of new models is that described by Hatze (1976, 1977~. This is a complex model that accurately predicts forces in the leg when a person takes a step with a weight tied onto the leg. It represents advanced techniques that may be useful for future ergonomic modeling.

22 REVIEW OF BIOMECHANICAL MODELS One of the more basic evaluations that occur in biomechani- cal modeling is the analysis of moments and forces that act on a body segment in a work environment. Chaffin (1982) performed an analysis of such forces for single- and two-body segments un- der static planar conditions. In these cases Newtonian mechanics were applied to the segments and the system was evaluated in a state of static equilibrium. When multiple body segments were involved, each body segment was evaluated as a separate link in a kinetic chain system. A two-link model of the arm was devel- oped by Pearson et al. (1961, 1963~. It computed the forces and torques present at the elbow and shoulder caused by the motion of arm, forearm, and hand in the sagittal plane. This analysis required data obtained from stroboscopic photography to caTcu- late the instantaneous position, velocity, and acceleration of the arm, forearm, and hand system. Together with the known values of mass ant] length of the body segments, these data were used to compute the forces and torque present caused by the motion. Extensions of this mode! were developed by Plagenhoef (1966), who modeled whole-body motion based on kinematics. Predictive equations for hand motion in workspace design have been developed by Kattan and NadIer (1969), and SIote and Stone (1963) modeled acceleration patterns of the upper extremity. Ay- oub et al. (1974) also developed a two-segment, three-dimensional motion mode! of the upper extremity. This mode! was unique, however, in that it used optimization (dynamic programming) for a solution to perform a movement. It predicted hand position in space during certain movements. However, Ayoub and coworkers (1974) stressed the need for more detailed evaluation of mode! assumptions. This work demonstrated the feasibility of using oh timization techniques to mode} the external loading factors of a biomechanical system. Several biomechanical models that evaluate stress caused by external loads during lifting have been presented in the litera- ture. Models by Chaffin (1967) and Chaffin and Baker (1970) are static, sagittal plane extensions of the major body segments and were expanded to predict the compressive forces sustained by the lumbar spine. They demonstrated how predicted moments gener- ated about the body articulations could be compared with human strength characteristics, and suggested that this method be used

23 to evaluate the physical strength capability and requirements of manual materials-handling activities. This model assumed that lifting occurs slowly and smoothly, so that the effects of accel- eration are negligible. This approach has been adopted by the National Institute for Occupational Safety and Health (NIOSH, 1981) for evaluation of the workplace. A three-dimensional static strength evaluation analysis was described by Garg and Chaffin (1975~. Chaffin and Andersson (1984) also discussed how multiple-link static models could be used to evaluate reactive moments of the body in both coplanar and nonplanar analyses, how modeling techniques assess the moments experienced by joints during motion, single- and multiple-segment dynamic modeling techniques, and how biodyna~nic analysis tech- niques could be used to assess pushing tasks. Aunts et al. (1980) developed a method to estimate moments about the elbow during maximum flexion. These techniques employed high-speed photo- graphic techniques to predict angular velocities and acceleration. Inertial forces and resistance moments that must be produced by the muscles could then be calculated. Ereivalds et al. (1984) used this technique to study dynamic lifting. The models that have been described take into account the stresses and loads caused by an external load or motion imposed on the body. Some of these models also evaluate internal forces. These assumed that the body is composed of several rigid links which are joined by articulations. The analyses usually consist of evaluations of the motions and loads imposed on these structures via traditional Newtonian mechanics. Recently, some optim~za- tion techniques have been used and represent a promising area of endeavor. Chaffin (1969) developed a seven-link, two-dimensional static model to calculate joint forces and moments during material- handling activities. The model also computed the spinal compres- sion force during lifting. This model was later expanded to include three-dimensional static strength prediction (Chaffin et al., 1977; Garg and Chaffin, 1975~. Freivalds et al. (1984) also expanded this model to evaluate the sagittal plane kinematic activity. All of these models consider the effects of both external and internal loading when considering the compressive forces on the spine. El-Bassoussi (1974) and Ayoub and El-Bassoussi (1976) de- veloped a model which predicts stresses on the muscuToskeletal system by infrequent tasks in the sagittal plane. The mode! used predicted movement dynamics based on the findings of Slate and

24 Stone (1963~. This mode! is dynamic and considers subject move- ment and the forces that are generated because of these mover meets. Ayoub et al. (1980) compared the virtues of these lifting models. They pointed out that the limitation of most lifting mod- els for ergonomic purposes is that they only estimate stresses within the body when work is performed in the sagittal plane and few of them consider motion. Gruver et al. (1979) developed a five-link, two-dimensional mode! of the human body to simulate manual lifting tasks. These models just described are limited by the fact that most are two-dimensional planar models. These models help us to un- derstand the loading of the body in sagittally symmetric exertions. Many of the more challenging ergonomic concerns, however, in- volve loading of the body in three dimensions. For many tasks the body is loaded in a torsional fashion. Assessment techniques are required to evaluate these situations. Another limitation of existing models concerns the ability to assess the consequences of motion. Many of the analysis techniques are static and do not consider the effects of velocity or acceleration of the body part or load when assessing the biomechanical cost to the system. Some models have been reported in the literature that consider motion; however, the motion assessment is usually limited to the sagittal plane, and often, the effects of load weight are not considered. Basic research is required which addresses the question of whether a kinetic link system portrayal of the biomechanical sync tem is appropriate. Some assumptions regarding the shape and length of link elements are necessary for simplification purposes. Freivalds et al. (1984) pointed out that the spine could be better represented by some semiflexible arrangement. Thus, a rigid beam link analogy may not be the best method of modeling the human system. This is also evident from the previous discussion regarding bone modeling. The models described in this section describe techniques for assessing the reactive moments and forces at each articulation that must be exerted by the muscles. These reactive moments and forces are necessary to overcome the forces imposed on the biomechanical system by external loads and body weights. These models have been used successfully to match worker capabilities to the demand of the task. They provide insight into worker selection rationale.

25 Ergonomic models should be capable of assessing the trau- matic ejects as well as the cumulative effects of the work. To achieve this objective, ergonorn~c models should be able to evalu- ate the loading of the articulation and skeletal structures caused by the external and internal loadings. Internal loading refers to the forces supplied by the muscles and ligaments that react to the ex- ternal loads; thus, both external and internal forces load the body. The significance of internal forces to the loading of the body has been discussed by Cailliet (1968) and Tichauer (1978~. Knowledge of the effects of internal and external forces is necessary to predict the instantaneous loading of the body articulations and skeletal structures. Models that include internal forces are usually much more difficult to use since there are often more unknown muscle forces than there are independent equations available to solve the problem. Thus, a unique solution is not possible, and the problem becomes statically indeterminate. Models of Bones Work on the biomechanics of bone and load-bearing capability of bone dates back over three centuries to Galileo Galilei (1638) and has progressed to modern stress analysis techniques (Burstein et al., 1970; Minns et al., 1977; Piotrowski and Wilcox, 1971; Toridis, 1969~. Others (Brown et al., 1980; Hayes et al., 1978; Huiskes et al., 1981; Olofsson, 1976; Piziali et al., 1976; Rohimann et al., 1982; Rybicki et al., 1972; Scholten et al., 1978; Valliap- pan et al., 1977, 1980) used finite-element models of the femur which assume that bone is an isotropic and homogeneous mate- rial, even though it is nonhomogeneous and is described as being transversely isotropic. The femoral model described by Vallia~ pan et al. (1977, 1980) used a finit~element analysis to compare the stress distribution in the femur for both a prosthesis mode! and a normal femur. The stresses were computed both with and without the anisotropic assumption of transverse isotropy, and two loading conditions were used, walking and one-legged stance. The stress distribution was found to change significantly when the anisotropic assumption was used for cortical bone; however, no val- idation of results was mentioned. Others (Goe! et al., 1978; Hayes et al., 1982; Oonishi et al., 1983; Snyder et al., 1983; Williams and Lewis, 1982) developed finite-element models for other bones, such as the pelvis, patelIa, and trabecular bone. A summary of

26 the merits of many of the finite-element models used in orthopedic biomechanics was prepared by Huiskes and Chao (1983) and elan orates on the details of the models. It does not include a discussion of a finite-element mode! of a lumbar vertebra. Hakim and King (1979) subjected a bilaterally symmetric finite-element model of a lumbar vertebra to static and dynamic loads. The cortex and plates and spongy bone of the vertebral body were modeled with thin plate and shell elements and three- dimensional isoparametric elements. The pedicle, lamina, and articular facets were represented with brick elements, and the facets were modeled to provide articulation such as that in a true facet joint. Plate elements were used to represent the processes. Material properties data from the literature were used, and input load distribution was taken from experimental data (Hakim and King, 1976~. Validation efforts showed a favorable comparison between computed and measured strains. Balasubramanian et al. (1979) extended this mode} to simulate a unilateral laminectomy and bilateral asymmetric loading. Vibration data have been used to determine in viva elastic properties of long bones, another area of bone modeling. Jurist and Kianian (1973), Orne (1974), Orne and Mandke (1975), Orne and Young (1976), and Viano et al. (1976) have all studied the elastic property of bone in this manner. Models of Single Joints In viva internal forces and moments at a joint are both difficult to measure and calculate, largely because of the involvement of many muscles and ligaments, which results in more unknowns than there are equations. Electromyogram (EMG) data, minimum total muscular force and/or moment, and minimum total mechanical or metabolic energy are used to reduce the number of unknowns. Equations in dynarn~c models are usually nonlinear differential equations. They are reduced to algebraic equations by electing to solve the "inverse dynamic problems in which kinematic data are supplied as input to eliminate the derivatives. Models of the Hip and Enee Joints The knee has been modeled in various ways by Bresler and Franke! (1950~; Kettelkamp and Chao (1972), Engin and Korde

27 (1974), Crowninshield et al. (1976), Harrington (1976), Andriacchi et al. (1977), Hight et al. (1979), Chand et al. (1976), Wismans (1980), Wismans et al. (1980), and Minns (1981~. Morrison (1968, 1969) computed muscle and ligament forces for a normal gait, while eliminating forces in muscles with quies- cent EMG data and eliminating ligament forces that become slack during the specific phases of gait. Experimental force plate data were used along with photographic identification of the hip, knee, ankle, and foot to provide joint displacement and rotation data. EMG data of principal muscle groups were acquired from bipolar surface electrodes. Six equations of motion were used to determine the net re- action force and moment at the knee. When solving for bone contact force components and the muscle and ligament forces, the problem became indeterminate. Use of EMG data eliminated the antagonistic muscle forces and ligament functions and allowed calculations of bone contact or joint force. The results were com- parable for repeated tests of the same subject but varied from subject to subject. Another method of reducing indeterminacy is to compute the forces in the ligaments across the knee joint as a function of knee flexion angle. A ligament mode! developed by Wismans et al. (1980) assigned stiffness values to the ligaments. This mode! also considered three-dimensional kinematics of the knee joint and ar- ticular surface geometry, which established the conditions of con- tact on medial and lateral surfaces. With this information, 16 unknowns were calculated, including relative joint location, con- tact points and forces medially and laterally, relative abduction and rotation, and the magnitude of the joint constraint moment. The results were principally kinematic and did not provide kinetic data, which would have been helpful. In a more complete work by Wismans (1980), kinetic data were also not provided. Rheo- logical models of the knee by Moffatt et al. (1976) arid Pope et al. (1976) were based on oscillatory tests that described the knee as a Maxwell fluid or a Kelvin solid. Hip joint models were developed in much the same way as those for the knee (Crowninshield et al., 1978; Noel and Svensson, 1977; Williams and Svensson, 1968~. Paul (1967) assumed that the hip joint transmitted a contact force and that no more than two muscles were active at any instant of gait. Kinematic and force plate data were required by this model.

28 For the ankle, t~vo-~unensional models were developed by Brewster et al. (1974), Stauffer et al. (1977), and Wynarsky and Greenwald (1983~; and a three-dimensional model was developed by Procter and Paul (1982~. Models of Joints of the Upper Extremity With assumptions of a hinge joint with three major flexors, the elbow becomes simple to simulate. Based on the work of MacConaiD (1967), Yea (1976) used linear progrmnming to com- pute the total forces generated in the muscles. Because the mode! results contradicted experimental data that show that ad three muscles are active during flexion, Yea claimed that the Minimum principle" was not valid. Cro~vninshield (1978) defined maximum allowable tensile stress in each of three muscles, and his objective function was minimum total tensile stress. The mode} correlated wed with experimental data for both isometric and isokinetic con- tractions. This approach was extended by An et al. (1983) to compute joint contact forces. Modeling efforts for the shoulder include the work of DeLuca and Forrest (1973), who used isometric abduction. Models of :Intervertebral Joints Schultz and Andersson (1981) developed a practical threw dimensional, statically indeterminate mode} which calculated loads placed on a lumbar vertebra during physical activity. This mode} functioned in two parts, similar to the knee model, and consid- ered the action of both the spinal musculature and the abdominal muscles. The net reaction across a lumbar vertebra, derived from equilibrium considerations, formed the determinate portion of the problem. Linear programming was used to determine the resultant spinal loads and muscle forces while minimizing spinal compress sign. Large spinal compression forces were predicted for minor activities and were validated with myoelectric activity indicating muscular tension. This mode} was later modified by Schultz et al. (1982), who changed the objective function to specify minimum ~ ,, ~ intensity or stress. Other researchers developed models of ~ single intervertebral joint (Belytschko et al., 1974; Kulak et al., 1976; Lin et al., 1978~. They were able to determine the responses of the intervertebral

29 disc. The cIann that such a mode} could be used to predict mate- rial properties of the joint using optimization was a new concept. These disc models were loaded axisymmetrically, which is a phys- iologically incorrect assumption. Redundancy and validation continue to be the major problems encountered in the modeling of joints. The use of optimization to solve the redundancy problems is now acceptable; however, the choice of an objective function remains an unresolved problem. This difficulty ~ linked to the inability to validate the predic- tions of the models. Reliable methods and transducers have not been developed at this time to achieve the goal. Pedotti et al. (1978) proposed the use of nonlinear optimization schemes that had closer correlations with EMG data than did linear schemes, and Crowninshield and Brand (1981) proposed a mode! that re- quired a minnnum muscle stress and that correlated with EMG activity. These approaches, however, did not reduce the difficulty in the choice of an objective function. An et al. (1983) opined that linear optimization tenth inequality constraints was superior to a nonlinear scheme. Models of Multiple Body Segments and the Whole Body This class of models can be divided functionally into models of five groups: (1) the fingers and thumb; (2) the lower extremities, including gait; (3) the spinal column; (4) the thorax; and (5) the whole body, excluding gait. Modem of Fingers and the ThnTr~h Many researchers have developed modem of the fingers and thumb, from kinematic models (Landsmeer, 1961) to two-dimen- sional models (Hirsch et al., 1974; Smith et al., 1964) to three- dimensional thumb models (Cooney and Chao, 1977; Taft and Berme, 1980~. Other models were developed by Chao et al. (1976), Spoor and Landsmeer (1976), Berme et al. (1977), Chao and An (1978a,b), and An et al. (1974~. There are many problems encountered in the modeling of a finger, as discussed in a series of papers by Chao et al. (1976), Chao and An (1978a,b), and An et al. (1974~. These models were thre~dimensional and were indeterminate because of the large

30 number of tendons and intrinsic muscles that could be active dur- ing a given activity. Before a mechanical analysis could begin, all unknowns had to be identified and simplifying assumptions had to be made to determine the degree of indeterminacy. In many cases, antagonistic muscles were assumed to be inactive, yet in the isometric function of the finger, they participated in the stabilization of the joints, which is known as the pylon concept. Thus, other justifications were needed to determine simplifying assumptions. A frictionIess cable and pulley system for tendons and tendon sheaths enables the tensile force in the tendons to be transmitted undiminished across joints. Other anatomic reasons have been used to yield constraint equations that reduce the num- ber of unknowns. The equations for the mode] are obtained from a free-body analysis of all joints of the finger. The problem was solved by linear programming with a variety of objective functions that determined joint forces caused by a unit pinch force between the tips of two fingers or between finger and thumb. One objective function was the minimization of the sum of muscle forces or the sum of constraint moments. An et al. (1974) developed a three-dimensional kinematic mode! of the human hand based on cadaver measurements. These measurements included tendon location and orientation for all four fingers in a neutral position expressed in coordinate systems nor- malized against the middle phalanx of each specific finger. Tendon geometry was computed from a force and moment potential. Models of the Lower Extremities Models of the lower extremities take on many forms, from a one-legged comprehensive static mode! (Seireg and Arvikar, 1973) to human gait models of the lower limbs (Cappozo et al., 1975; Beckett and Chang, 1968; Geh! et al., 1975; Hardt, 1978; Seireg and Arvikar, 1975~. The most comprehensive dynamic lower limb mode! was de- veloped by Hatze (1976), who verified it experimentally. This two-dimensional mode! tracked the motion of a weighted foot as it attempted to hit a target on the floor in minimum time. The action was fully voluntary with no ground interaction. The results compared well with volunteer data. Models of human gait involving the head, arms, and torso (HAT), in general, try to determine joint reactions and moments

31 during gait. If the kinematic variables of displacement, velocity, and acceleration are not independent of each other, the number of unknowns exceeds the number of equations by the number of joint moments, thus rendering the problem indeterminate. By assum- ing known ground reactions and specifying kinematic variables, the problem can become determinate and can be solved as an inverse dynamic problem (IDP). The kinematic variables are assumed to be functions of time, reducing the differential equations of motion to algebraic equations. A direct approach can be taken if the differential equations are solved for unknown kinematic variables and/or joint loads. The problem is generally indeterminate, re- quiring an optimization scheme with identification of an objective function to create extra equations. HAT models of the IDP type have been proposed by Townsend and Seireg (1972), Chao and Rim (1973), Cappozo and Pedotti (1973), Townsend and Tsar (1976), Aleshinsky and Zatsiorsky (1978), and Hardt and Mann (1980~. Direct solutions of the motion equations include a model by Nubar and Contini (1961), who pioneered the optimization approach by proposing a minimum energy principle for muscular effort. This generated a dynamic two-dimensional, five-link model of the skeleton. However, only a static stance solution was provided. It was then extended to an optimal control model (Chow and Jacobson, 1971~. Hatze (1977), likewise, extended his earlier lower-limb model (1976) into a whole-body musculoskeletal control model. An IDP model developed to solve for ground reactions dur- ing bipedal gait was formulated by Thornton-Trump and Daher (1975~. This model generated seemingly reasonable ground forces, but did not account for a period of double support and therefore had questionable validity (Paul, 1978~. A model by Hardt and Mann (1980) corrected this deficiency. Autogeneration models of gait were proposed by Onyshko and Winter (1980) and Nakhla and King (1983~. The autogeneration models were two-dimensional HAT models which applied appropriate muscle moments to the ankles, knees, and hips, enabling the linkage system to move over level surfaces at different speeds and cadences. The models also accounted for double support. Recently, Nakhla and King (1985) formulated a three-dimensional model for the autogeneration of human gait. Limb kinematics were computed from joint moment inputs, 18 of which were required for a seven-segment HAT model. Experimental gait data were used to compute the moment time

32 histories to ensure that the input was realistic. Gait was then gen- erated by solving the differential equations of motion by using an existing three-dimensional human link model which was developed originally by Calspan Corporation for the simulation of occupant kinematics in an automobile crash. It is also known as the artic- ulated total body (ATB) model, a more complete description of which can be found in the section by that title in Chapter 4. The ATE model was modified to accept joint moments as input. Models of the Spinal Column An early three-dimensional static mode! of the spine proposed by Schultz and Galante (1970) generated complex equations that were not solved. A geometric mode! resulted from the use of fixed- length elements. This was followed by work by Panjabi (1973), who developed a general formulation for a three-dimensional discrete parameter mode! of the spine that could simulate responses to static and dynamic loading. No specific mode} was proposed. Belytschko et al. (1973), however, developed a three-dimensional structural mode! of the entire spinal column with responses to three loading cases. This mode! simulated vertebrae, ligaments, and soft tissue and provided resistance against axial, torsional, bending, and shear loads. The results were validated against experimental data. Panjabi (1978) has since proposed a model of a functional spinal unit which could simulate coupled motion. The disc and soft tissue were represented by a deformable element such as a viscoelastic body, but because of the lack of material properties, no model of either a spinal segment or the spinal column was proposed. Koogle et al. (1979), attempted a three- dimensional finite-element mode! of the lumbar spine based on the mesh developed by Balasubramanian et al. (1979), with no conclusive results. Preliminary results, however, from a finite- element model of a functional spinal unit formulated by Yang and King (1984) indicate that it is able to accurately predict intradisc pressures. Models of the Thorax A three-dimensional, bilaterally symmetric, elastostatic, and finite-element moclel of the human thorax, developed by Roberts and Chen (1977), was able to reasonably predict rib displacement

33 under loading conditions. The ribs were simulated by beam ele- ments, and geometric and physical rib properties were included. Sundaram and Feng (1977) developer} both a full thoracic ant] a skeletal finite-element mode} of the thorax. The former models simulated the soft tissues and organs of the rib cage, the thoracolumbar spine, the sacrum, the coccyx, the ribs, and the sternum. The results of stresses and displacements from 11 static loading conditions compared favorably with experimental data. Models of the Whole Body While several investigators have proposed whole-body mod- els of human motion not involving gait, many were inspired by the simulation of movements in space. Kane and Scher (1970) and Passerello and Huston (1971) formulated models of people in space and simulated yaw, pitch, and roll maneuvers. Huston and Passerello (1971) went further to simulate lifting, swimming, and kicking with one leg. A lumped-parameter mode! of a seated human (Muskian and Nash, 1974) simulated the head and torso, which were subjected to sinusoidal excitation at the seat level. Heart and diaphragm ac- tivity was also simulated; and responses of the head, back, torso, and other masses as a function of frequency was given for ~30 Hertz (Hz). Muskian and Nash (1976) proposed a simpler three- mass mode! which simulated dual load paths from the head to the pelvis, the spinal column, and the abdominal viscera. Non- linear frequency-dependent damping was used to simulate actual responses. DISCUSSION King and Marras prepared an extensive table of biomechan- ical models for this study (Table 3-1) that presents an extensive overview and summary of the specific variables and parameters of existing models. They listed the mode} type, input and out- put variables, mode! characteristics, and the assumptions made in mode! development. This table is a unique contribution to the literature and should prove valuable to those who do research on biomechanical models. The ultimate goal of biomechanical models should be to create

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37 LE6FND FOR TABLL OF BIOHECHANICAL HODElS ABO ABDUCTION OR ABDOMINAL ANISOTROPIC THE MATERIAL DOES NOT HAVE THE SAHE RFSPONSE ro lOADS fROH DIFFERENT DIRECTIONS ANNUlUS TNE FIBROUS OUTER RIN6 OF AN INTERVERTEBRAl DIS! ANrAGON ANTAGONISTIC AUTO 6EN AUTO-6ENERATION AVAIL AVAlLABlE AX AXIAL AXISYH AXIAL SYHHEIRY IS ASSUMED BEAH THEORY SIMPLIFIED THEORY OF ElASTICITY APPLIED ro ONE- DIHENSlONAl PROBLEMS, SUCH AS BEAMS BILAT BILATERAl CALC CALCUlATE OR CAlCUlATED CART CARTIlAGE CLOSED SOlUTION SOLUTIOH ro A SET ~F DIFFERENTIAL EQUATIONS c`R,rEe our ANAlYTICALLY IN [ERHS OF A HATHEHATICAL EXPRESSION COHB COMBINED OR COMBINATION COMB / PE RH COHB I NAT ION/ PERMUTATION COHP COHPRESS1ON OR CO8PRESSIYE COND CONDITION CONf OR CONfI6 CONfI6URATION CONST H OF I THE HASS HOHENT OF INERTIA OF BODY SE6HENTS IS ASSU8ED ro REMAIN CONSTANT DURIN6 LOCOHOllON CONTACT HODEl A TECHNIQUE IN ElASTICITY TO COMPUTE CONTACT STRESSES BETIEEN r~o BODIES rN CONTACT CORT CORTICAL D DYNAMIC DAHP DAHPIN6 DEFl DEFlECTION DIFF EQS DIFFERENTIAL EOUAllONS DOF DE6REES OF FREEDOM DYN EQUIL PRINClPlES OF DYNAMIC EQUILBRIUH dERE USED ro FORMULATE HODEl ElASTIC PROPERTIES THE PROPERTIES OF A HAlERIAL ASSOCIATED VIrH rrs ELASTIC RESPONSE, SUCH AS MODULUS OF ELASTICITY EH6 ELECTROHYOGRAPHY - THE TECHN[QUE OF HONIlORIN6 ElECTRICAL ACTIVITIES OF MUSCLES EQUIL EQUILBRIUH EXT EXTREMITY OR EXTENSION fEH OR FE FrNITE ElEHENT METHODS OR FINITE ElEHENT FLEX FLEXION FUNC SP UNIT FUNCTIONAL SPINAL UNl INDET INDETERMINATE lNDIV INDIVIDUAL INIT INITIAL INV DYN PROB INYERSE DYNAMIC PROBLEM 6RD REACT 6ROUND REACTION M-A-I MODEL OF A HUMAN BODY 1N ~HICH THE HEAD, ARHS AND CONSIDERED AS A SIN6LE HASS TORSO

38 IHPED IMPEDANCE INCOHP INCOMPRESSIBLE [NEXT. JTS THE JOINTS BET9EEN BODY SEGMENTS ARE ASSUMED ro BE INEXTENSIBlE. BODY SE6HENTS CAN ONlY ROTATE HrrH REsPEcr ro EACH OTHER Jr JO[NT KElYIN MODEL A VTSCOElASTIC HODEl ~HICH HAS A HORE SOlID-LIKE BEHAVIOR ~ IN ~ INEHAT lCS LAT lATERAl LIG lI6AHENT OR lIGAHENTOUS LIN LINEAR LINEAR ELASTIC THE MODEL ASSUMES rHE BIOL06ICAL HATERIAl ro BEHAVE IN A LINEARLY ELASTIC MANNER LINEAR PR06 SOLN SOLUTION ro A SET OF lINEAR AL6EBRAIC EQUATION' LINEARlY ORTHOTROPIC LOC ION LUH HAX HAXlEll MODEL HCP HECH HIN HOD HOH HUSC NON-LIN OBJ FCN PARAH PHYSIOL X-SECT PlANE STRAIN PROB PRON PROPS PROX REDUNDANT MODEL RESONANT FREQUENCY RESP RH£0l RIGID BODY NHICH ARE REDUNDANT, USIN6 THE lINEAR PR06RA8HIN6 METHOD A HATERIAl ~HICH HAS A lINEAR RESPONSE ro srREs~ BUT HAS ~ ro 12 MATERIAL CONSTANTS LOCATION lOdER lUHBAR HAXIHUH A VISCOElASTIC MODEL dHICH HAS A hORE flUID-LI`E BEHAYIOR HETACARPAl HECHANICAl HEDIAl HINIHUH HODEl HOHENT MUSCLE OR MUSCULAR NON-LINEAR OBJECTIVE FUNCTION USED IN OPTIHI2ATION TECHNIQUES PARAMETER PHYSIOL06ICAl CROSS-SECTION A 2-DIHENSIONAl STRAIN ASSUHPlION IN kHICH THE PARTIClES DEFORM IN ONE PlANE AND REMAIN THAI PlANE PROBLEM PRONATAION PROPERTIES PROXIMAL A HAlHEHATICAL MODEL WHICH HAS HORE UNKNOlNS [HAN EQUATIONS TO SOlVE FOR THESE UNKNOINS rHE FREtUENCY AT dHICH A SYSrEH RESONATES OR HAS LAR6E AMPLITUDES OR DISPlACEHENTS RESPONSE RHEOL06ICAl AN ASSUMPTION IS HADE THAT THE BODY SE8HEN! [S RI6ID OR NON-DEFORHABlE

39 Rae s SEE SIR star STAT EOUIL STRUCT OPT TECH SUP SUPP SYN [END THOR r-~ TRAB TRANSVERSELY ISOTROPIC OR TRANS ISOf VAR VERT VERIEB ~1 RO [Al ION STATIC SEGhENT SIMULATION STATIC OR STATICALLY PRINCIPLES OF STATIC EQUILIBRIUM HERE USED TO fORHUlATE THE MODEL STRUCTURAL OPTIHIlATION TECHNIQUES SUPINATION SUPPORT SYHHEIRIC OR SYHHEIRY TENDON THORAX OR [HORACIC TEN PORAL -HAND I B AL AR TRABECULAR - fORH Of ANISOTROPY FOR CHICK 5 JO 6 DIFFERENT MATERIAL CONSTANTS ARE NEEDED JO DESCRIBE THE RESPONSE OF THE MATERIAL VARIATION VERTICAL VERTEBRAL WITH

40 a universal mode} that is applicable in a variety of situations. This mode! should accurately predict the loading on the body caused by both internal and external forces and should be capable of evaluating "wear and tear" of the body under realistic (static as well as dynamic three-dimensional) conditions. Such a mode} should be adaptable to a variety of situations. The same mode} should be able to simulate gait and weight lifting and perform a variety of human tasks. To achieve such a goal, several areas of mode! improvement and development are needed. More data are needed to describe the material and functional properties of body tissues. These findings should be incorporated into analyses that investigate the aging as wed as the time- and frequency-dependent repetitive loading effects of loads exerted on the body. The properties of bone must also be incorporated into models that are used for ergonomic purposes. More specifically, for spinal models, investigation of the load-bearing role of the articular facets ~ needed to understand low back pain etiology. For bone stress analysis, the most promising mode} is finite- element analysis, which can mode} the irregular geometry and the composite nature of bone. Validation against experimental data continues to present problems. Roh~xnann et al. (1982), Hunker et al. (1981) and Hakim and King (1979), however, have attempted such a validation. There continues to be a lack of data on ma- terial properties and a large variation in such properties for bi- ological materials. The problem is made more complex because of anisotropy, inhomogeneity, and nonlinearity. Experimental re- search and clinical application of the models are needed to further advance the modeling effort. One area for further research is that of developing a capability for a variation of mode} geometry w~th- out a complete respecification of nodal coordinates. I.ewis et al. (1980) proposed such a scaling method for femoral models. The analogy of the rigid beam link should be investigated. Instead of viewing the body as a set of rigid links, perhaps a semiflexible spinal column can provide snore accurate assessments of the lifting of loads on the body. The modeling of joints and human locomotion (single and multiple joints) is aimed primarily at predicting forces In mum cles, ligaments, and bone contact. This can serve a variety of needs, such as prosthesis design, treatment and diagnosis of mus- culoskeletal diseases, rehabilitation, and quantification of normal

41 function. There Is very little evidence, however, that current mod- els are able to calculate these forces accurately. The measurement of these forces in viva is extremely difficult, and therefore, the need exists to develop experimental techniques and transducers to verify the analytical results. Inferences from time domain cor- relations of muscle forces with EMG activity are at best a crude indication of validity. One of the major problems with this area of research Is the choice of appropriate objective functions to solve a redundant problem. It does not fad within the deterministic realm of mechanics and requires physiological data that are, as yet, unavailable. The hypothesis that an objective function indeed exists needs to be proven before further advances can be made. A secondary problem concerns the use of linear optimization tech- niques. The limitations of a linear analysis are implicit in their use and should be recognized. Whole-body models can now incorporate three-dimensional activity as well as motion. The development of these modem over the years has progressed from those based on pure Newtonian mechanics to optimization theory to control theory. The control theory mode} by Hatze (1977) appears to simulate the rate and re- cruitment coding of the muscles during the performance of a task. Unfortunately, when the predictive power of the models increases, the complexity of the mode} also increases dramatically. Hence, a trade-off must occur between mode} complexity and the degree of accuracy that is needed to model a situation for ergonomic purposes. An area which remains untouched by biomechanical model- ers is that of modeling the cognitive link. People, as information processors, possess the ability to modify the interaction with the musculoskeletal system. Under circumstances of great stress or during life-threatening situations, people can shor~circuit inter- nal protective mechanisms and are capable of exhibiting nearly "superhumans traits. There ~ also an awareness that the "psycho- logical factors can become dominant In times of illness, as shown by treatment with a placebo. Additional experimental research is needed on these issues so that the cognitive control process can be evaluated and eventually included in biomechanical modem. Pope et al. (1980) have begun to explore such a link between personality traits and biomechanical behavior. It is clear that much research is needed to achieve the goal of producing a universal biomechanical model. Progress has been

42 slow over the years. Basically, it appears that progress in the area of biomechanical modeling ~ now limited by a basic understand- ing of the body rather than by computational ability. The current state of modeling will advance when advances in basic understand- ing are achieved and better validation methods are developed. In addition, many of the limitations in existing biomechanical models are related to incomplete or unrealistic data inputs into the model. The problems include nonrigid or nonuniform links, effects of dynamic action, internal loading including antagonistic muscle action, comparison data for cumulative trauma limits, and cognitive links. furthermore, modem based on motion kinetics alone provide an inadequate description of a person who is operating equipment in a real-world environment. The human operator's need and ability to adapt the dynamic behavior of the limbs ~ not included in current models. A model of the biomechanical system that uses single values for its dynamic parameters such as muscle stiffness or viscosity is unrealistic. A fixed-parameter mode} cannot be applied reliably in situations other than those for which it was calibrated. Deterrn~nation of the difference between the net reaction forces at a given body joint and the actual internal loads (e.g., those generated by the antagonistic muscle groups that are involved) ~ essential to a complete biomechanical analysis of a strain that has an impact on the system. Predictions of internal loads usually incorporate simplistic optimizing assumptions, for example, that minnnal antagonistic muscle activity ~ used in performing a task. If the performance is not governed by the assumptions, the actual internal loads can be much higher than the predicted values. Finally, existing biomechanical models do not address the problem of repeated activities over a period of tune, and hence, physiological aspects such as fatigue are not considered.