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Computer Simulation in Gait Analysis Abstract Performing simulated experiments on a virtual human or computer model is one of the most powerful methods to elucidate relationships between physiological structure and biomechanical performance [3, 56, 82, 83, 93]. Surgical outcomes prediction, response to mechanical or therapy interventions, factors producing injury, theories of motor control and improved design of equipment are some areas that have been studied through simulation. Questions can be studied that may be difficult or even impossible, costly, and/or unethical to answer through human subject testing. The simulation framework lends itself to predicting the effect of neural, muscular, or skeletal alterations on performance. Biology, physics, and engineering relations are used to create the model or mathematical representation of the body. Because a variety of strategies can produce a single movement, similarity of model performance to reality does not ensure consistency between mathematical and natural control schemes. Assessing this consistency is a major obstacle to obtaining maximum benefit from simulation. Biomechanical simulation is a developing field; much effort goes into developing, controlling, and validating models. However, inroads to using models to answer questions relevant to rehabilitation are being made. An overview of the role of simulation, description of model development, and examples of some modeling and simulation applications in gait analysis are provided in this chapter. As the field matures, efficient control techniques, supercomputing resources, and accurate subject specific data from advanced imaging techniques are a few areas that can significantly enhance the practical utility of simulation as a clinical tool.

A Modeling and Simulation Perspective Modeling is the development of a mathematical representation of the body and simulation is the process of running experiments on the model. There are two main types of modeling frequently and widely used in biomechanics : inverse and forward dynamics (Figure 1). Inverse dynamics, the more widely used, relies on measuring the motion of a subject while walking and combining these data with a body model to calculate the forces that must have been present to produce this movement. Standard inverse dynamics, due to its dependence on measured data, is not well suited to predict outcomes. However, a few groups have utilized the simplicities of this approach to perform limited predictive simulations [37, 68]. The label inverse is a reminder that flow of calculations in this analysis is opposite to the way in which movement is actually produced in the body. In reality the neural inputs give rise to muscle forces that generate joint and ground reaction forces that together drive the movement. This order is maintained in the forward dynamics or simulation paradigm. Simulation is well suited to predict how performance (movement) is affected by pathology or intervention. Intersegmental dynamics analysis (IDA) or induced acceleration analysis is a new perspective that bridges the gap between standard inverse dynamics analysis and forward dynamics simulation. IDA has emerged from the principle that a force anywhere in the body will affect the motion in the entire body due to the mechanical coupling present [82, 92]. Uses of this methodology are discussed briefly in Applications.

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Figure 1. Simplified depiction of the sequence of events in the inverse and forward dynamics (simulation) analysis paradigms. The flowchart in the middle depicts the information and processes that coordinate to produce human movement. The upper arrow indicates the forward or natural flow of this information used in computer simulation. The lower arrow indicates the inverse flow of information used in the more common inverse dynamics analysis.

Advantages of Simulation Simulation offers significant potential in increasing our understanding and furthering our ability to improve care provided in a clinical setting (Table 1). It is a powerful tool to coordinate and facilitate the integration of many different kinds of biomechanical information. Models can be used to estimate performance under specific conditions or to assess how performance changes when specific factors are changed due to intervention such as strengthening, relearning, surgery, etc. [11, 56, 64, 68, 78, 93]. Furthermore, simulation allows exact control over the characteristics of the “test subject” (i.e. the computer model) and the test conditions [78]. The researcher can systematically change a single factor at a time [1, 47] and identify factors critical to performance. The many and interdependent factors that affect performance make it difficult to understand cause-effect relationships in human movement. Muscle strength, coordination of muscle activity, and body orientation are just a few factors that can affect performance. A change in one factor may affect other factors. For example, a change in body orientation due to contracture may change muscle length, which affects force production ability. Inevitably, multiple factors are changed due to pathology or injury. To accurately assess the effect of simultaneous changes in

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more than one factor is a daunting task.. Accommodation or compensation further complicate understanding [15, 16]. Relative freedom from ethical constraints associated with actual subject testing offers important benefits. Experiments can be repeated with out concerns of patient fatigue or discomfort. A brace may be adjusted in hundreds of different settings to try to determine the most suitable one. Variables that otherwise require invasive procedures can be measured. [1, 78]. For example muscle or joint reaction forces can be calculated instead of implanting force transducers. Muscle lengths may be estimated [10] to assess the effect of contracture or spasticity on the force generating capacity of a muscle. Such findings can assist in understanding the causes of abnormal muscle activity or resulting motion, and may be an important step in identifying a suitable treatment plan.

Table 1. Summary of major advantages and disadvantages of computer simulation Advantages Ability to predict effect or response Tight control over testing situation Ability to estimate parameters that are difficult or impossible to measure Can untangle the complex interactions involved in human movement Freedom from ethical constraints of human subject testing

Disadvantages

Model must be carefully validated Modeling process can require significant time, expertise and resources

One major obstacle to obtaining full benefit of the above advantages in simulating experiments on computer models is establishing that the computer model adequately represents the human system. Validation is the process of determining that the model accurately reflects reality to the degree necessary to answer the study questions. True “validation” may be too strong a goal and that perhaps “evaluation” is more realistic [78]. Modeling and simulation methodology selected ultimately determine model use, the quantity and quality of the “answers” obtained, to what extend results can be generalized, and how validation may be attempted. Current modeling and simulation techniques are presented to help the interested reader gain an appreciation of the science behind the process as well as to more critically evaluate published study results.

Simulation Methods Models consists of varying levels of detail in three major areas : musculoskeletal, actuator, and neural dynamics [47, 82, 87] (Table 2). The model is a mathematical representation of the relevant characteristics of the body, task, and environment using physiology, physics, and engineering relations. The task is an integral part of the system definition. A jumping simulation will likely have different task constraints than a walking simulation, though both may use the Talaty, M.

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same body model. Musculoskeletal dynamics involves mechanical properties of the body and joints and the laws of motion to which they are subjected due to the earth’s gravitational field. For a model including muscles, actuator dynamics refers to the response of the muscle to the neural control signal. Such a model may include the electrochemical delay, force-length and force-velocity properties of muscle, tendon slack lengths, muscle fiber angles, curvilinear muscle wrapping paths, etc. These give rise to differential equations relating muscle activation to the force it produces. The muscle force accelerates the body segments producing joint rotation and full-body motion. Neural dynamics refers to the generation of control signals to selectively activate the appropriate muscles or joint moments at the correct time and with the necessary strength to accurately and efficiently produce the desired smooth, coordinated performance. Neural dynamics is perhaps the most complicated part of the total model. Specific techniques in all three areas are now briefly discussed. Table 2. Examples of some of the choices in major model subsections. Neural control Tracking based optimization vs. Functional goal based optimization vs. Central pattern generator or neural networks vs. State based engineering controller

Actuator Individual muscles vs. Muscle groups (net joint moment) Viscoelastic (Hill based) vs. Crossbridge contractile elements “On/Off” vs. Continuous neuromuscular activation Straight line vs. wrapped muscle paths

Musculoskeletal Planar (2-D) vs. 3Dimensional Which body segments to include Style of joints connecting segments Single lumped rigid segments vs. Flexible and/or wobbling masses Rigid vs. Viscoelastic foot

Musculoskeletal dynamics In general, musculoskeletal dynamics encompasses factors such as selecting (i) the number and articulation of body segments to include in the model, (ii) how to allow each segment to move, (iii) mass and inertial properties to define segments, and (iv) writing equations to define their motion. Availability of flexible commercial engineering software as well as specific packages developed for biomechanical modeling [12, 43] has considerably simplified these tasks. Interaction of the body model with the environment is an area that continues to develop significantly as the increasing importance of the role the foot plays in walking become clear. The foot sub-model must accurately reproduce key features of the foot-ground interface, yet be simple enough to be integrated into a more complex, nonlinear human body model. Adverse effects of inaccuracies already present in the whole body model can be amplified by an improper representation of the foot, producing complete or partial simulation failure. Methods have progressed from treating the foot as simple rigid geometric shapes [6, 54, 57, 58] to the use of multiple elements and degrees of freedom [45] that may include the deformation characteristics of the soft tissues into the model [2, 25, 26, 43, 81]. The current standard foot model approach attempts to integrate the geometry and deformation characteristics of the foot-ground interface [76] and approximates the continuously changing articulation of the stance phase foot. Talaty, M.

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Actuator dynamics A model must be driven or actuated to perform a task, such as walking. Muscles are the only active means by which we can produce controlled movement. The net effect of a muscle force acting on the segments of a joint is to produce a torque or moment. Simulations use either muscle forces or net joint moments to produce movement. Each approach has advantages and disadvantages. Joint moment actuated The predominant advantage of using net joint moments to drive the model is simplicity. A joint moment represents the rotational force or torque produced by all the muscles and tissues that span a joint and/or contact segments of the joint. The torque produced by a muscle adequately describes the total action of that muscle on joint motion for the joint in which translation or sliding between segments is negligible. The total effect of the forces produced by all muscles and tissues (ligaments, fascia, bone, etc.) at each joint is the net joint moment. Many useful models have been developed with this approach [23, 55, 57, 64, 66]. An obvious limitation is that insight into the activity and role of individual muscles is not available. Further use of net joint moments makes it difficult to ensure that muscle forces do not became unphysiologically high during the simulation. Since the joint moment represents the net effect of agonist and antagonist groups, information regarding level of co-contraction is also not available. Finally, insight into the role of biarticular muscles is considerably reduced. Many muscles in the body span more than one joint – thus effectively producing a moment at each of these joints. It has been suggested that such muscles have roles of power transfer, stabilization, or control and efficiency [24, 79, 80]. Inherent muscle properties, that are by definition omitted in a joint moment actuated model, have been shown to benefit model stability [23]. The self-regulating relationship between muscle force and length, muscle force and shortening velocity, activation delay, etc. are examples of these properties. Muscle actuated Explicitly modeling muscle characteristics rather than just the net force output adds stability and utility but at the expense of increased development and computational time. Simulation using muscle-based body models are inherently more robust than those using joint moments only [23]. Further, it is suggested that the force-length and force-velocity relationships of muscle give rise to self-regulating properties. This allows them to produce, in a gross sense, appropriate forces in spite of imperfect neural activation signals [87]. A variety of parameters can be included in muscle models. Muscle origin, insertion and path have been extensively detailed [11, 20]. Peak isometric force, fiber length at peak force, fiber angle, slack length of the tendon, and maximum shortening velocity of the muscles and how they can be used in musculoskeletal models are well described [12]. The most widely accepted mathematical model for muscle [33] assumes a basic contractile element in parallel with a passive tissue element (Figure 2). The contractile element represents the actual muscle fibers and the parallel elastic element represents tissue such as fascia and others that surround the muscle. Together, this unit is in series with another passive tissue element, analogous to the tendon, which is mainly elastic [78]. The contractile element incorporates the basic force-length and force-velocity properties of muscle. This structure allows the mechanical aspect of muscle to be modeled by a simple nonlinear differential equation. Using

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many such muscle elements in a complex simulation model is feasible. Models that include crossbridges more accurately represents muscle physiology [34, 91], but are not feasible to implement in large scale [84], require significant computation, introduce additional uncertainty, and suffer from lack consensus [90]. These models may be important to human movement studies in the future [78].

(a)

(b) Figure 2. A basis for the muscle model commonly used in walking simulations. (a) Mechanical aspects of the physiological model. (b) A simplified version of the Hill model of skeletal muscle. This engineering model represents the physiological structures by a combination of contractile elements, springs and dampers (not shown) to represent the passive soft tissues that produce force. Springs and sometimes dampers may be in parallel and series with the actual contractile elements of muscle.

Neural Dynamics : Controlling the Model Capturing the power and flexibility of the human neural control system while keeping the resultant set of model equations manageable represents a significant challenge to producing useful and practical simulations. Control refers to the generation of the timing and amount of muscle activation or joint moments that drive the model performance. This control models the selection or development of a movement plan by brain and neural centers and the deployment of

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signals to the motor system to execute it. The challenge is created largely because of the large number of possible control solutions that can produce the same effect due to mechanical redundancy, the inherent instability of the human body, and the error propagation associated with the numerical solution of the complex equations. The number of ways in which the body can produce a complex, coordinated sub-optimal movement like walking is large due to redundancy [60]. An example of redundancy on the kinematic level is that there are multiple joint angles that can result in a desired step length. On the muscular level, there are usually several muscles that have the same anatomical orientation. Further, muscles not directly contacting a segment can also influence its motion as evidenced by a person with a transfemoral amputation using hip muscles to control knee motion. Modeling the control system involves significant simplification since we do not understand the physiology (esp. at higher levels) well enough to recreate it mathematically. There are several currently used approaches to determining the appropriate control for a walking simulation. Approaches to modeling the CNS structure and function may be classified as implicit or explicit. To date, explicit neural control of locomotion has not been used as much as the implicit due to ambiguity in identification and function of CNS structures. Function is unclear in part due to the large number of cells in the CNS, their significant and complex interconnections, and the large variability in parameters due to modulation by higher CNS centers [93]. None the less, attempts to more explicitly model neural structures for the control of locomotion have been made [30, 69, 72]. Implicit methods consist of techniques from dynamic optimization and systems control theory. Tracking algorithms are used to replicate a known performance [42, 48]. Alternatively, a performance oriented goal such as minimum energy or muscle stress may be used [1, 68]. The design of goal driven state-machine controllers has also had success [64, 65]. Details of each approach are now presented. Implicit CNS Modeling using Tracking Functions Tracking provides a direct way to replicate a known baseline performance [47, 78] which can then be perturbed to assess the effect of an intervention. Algorithms are used to systematically vary the control selection until the simulated performance matches the desired to within the preset error specification (Figure 3). The resultant controls will likely capture some of the essential features of actual walking controls of the original physiological data. For a trackingbased dynamic optimization, simulation results that closely match the measured data do not ensure that the optimization criteria selected is that used by the CNS. Different optimization criteria or performance goals can produce the same or very similar performances [93]. In the tracking paradigm, priorities used to select model control are not clear because explicit mathematical representation of the priorities were not necessarily specified. For example, did the model choose the control strategy to minimize energy expenditure or maximize stability or speed? Comparison of computer-selected muscle activation profiles to measured EMG data can be used to support that the model used a similar approach to that used by human subjects.

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gait all model cycle variables

Cost Function = ∑

∑

2

( Model value−Known value )

Figure 3. A general cost function is shown below to give an idea of the form. In a tracking application, the values compared would be some form of the model motion – such as joint angles. The double summation indicates that the function is compared for all variables (for example joint angles) and over the entire performance time (gait cycle). Consequently, the predictive capabilities of such a simulation may not be as general as one that performs without or with less a priori information of the walking pattern. Use of tracking biases the model response towards that of the baseline model. The ability to predict model response to changes in control pattern or a model parameter may be compromised to the degree that the chosen performance criteria is not exactly consistent with the body’s internal “prioritization” scheme. The character of the tracking function and other model constraints and parameters used should be carefully evaluated to determine the capacity in which the simulation can be used. If a performance perturbation can be applied in real life, similarity between the model and real performances can strengthen applicability of the simulation. A step in the direction of a more functional performance goal involves combining the basic tracking approach and simple task level feedback controllers to ensure stability. The state machine controller approach uses desired movement data to simplify the control problem in combination with control designed to achieve specific gait subtasks. This has been used to develop robust walking simulations. This is a different perspective on the standard tracking approach [64, 65]. Inverse dynamics of the desired performance is used to generate a nominal set of joint moments. Applying these in a forward simulation will produce the desired effect for a short time, but will soon fail due to errors in timing or coordination. This effect is exacerbated by the inherent instability of the upright human in walking tasks. A goal level feedback controller is used to correct for these errors. Then a task level feedback is layered on top to allow modifications to the baseline performance. Another work was reported that shared many of the conceptual elements as detailed above (it is unclear which group, if either, is responsible for development of the approach) but added a genetic algorithm to “tune” the simulation parameters [65, 66]. One performance criteria used was related to distance traveled per energy expended. Stable, smooth, efficient walking was stated to have resulted. The approach seems to hold promise in that the control is built from the judicious combination relatively simple, logical elements and yet reproduces many of the salient features of human gait. Implicit CNS Modeling using Performance Goals (non-tracking) Optimization with a more physiological goal than simply reproducing a specific movement may have more predictive capability. Similarity between simulated and actual performance may more strongly suggests that the mathematical performance goal is consistent with that used by the CNS. However, the fact that multiple criteria can likely produce the same performance [93] still prohibits certainty in this assessment. To reiterate,

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optimization is a mathematical way to select a control pattern to satisfy the specified performance criterion. What have been interchangeably labeled as cost, performance or optimization functions are often educated guesses based on intuitive, sensible, and/or wishful perceptions of human efficiency. Functions such as mechanical energy, metabolic cost, work, force, muscle fatigue, and even rate of acceleration have been used in the past. It has been empirically observed that the self-selected or comfortable walking speed is frequently that of least energy expenditure [67]. An idea based on this theory has recently been used to successfully simulate walking. A walking solution that predicted all three – (1) muscle activation, (2) body movement, and (3) ground reaction forces – based on minimizing energy expenditure per unit distance traveled was reported [1, 56]. Energy expenditure was modeled as a function of various physiological heat functions (for example, shortening heat rate of muscles) and mechanical work rate of muscles. Auxiliary criteria were used to prevent joint hyperextension and to ensure performance continuity of the start and finish of the gait cycle. The performance correlated quite well with that from which the input data were taken. However, it took over 10,000 CPU-hours to calculate one half of the gait cycle. The authors’ suggest the model has the ability to predict new movement, but feel that the applicability of the model to important clinical questions may still be in the future, owing to computational effort required. Many other high fidelity simulations involving less complicated models are performed in far less time on commercially available personal computers. Inconsistency between mathematical and natural control strategy exists in all simulations, though it may be argued to be less in models that explicitly include physiologically based functions in the goal. In the explicit CNS modeling approach, this question rephrased to : “How well do the chosen model neural structure and function compare to those actually responsible for locomotion?” Explicit CNS Modeling using Central Pattern Generators More explicit representations of neural structures, pathways, and signals exchanged within this framework have been reported to produce coordinated realistic walking [29-31, 69, 7173]. Reproduction of stable walking without specification of the basic patterns suggests a strong potential for a general control framework, as the human nervous system is known to provide. The models are admittedly simple compared to the true complexity of the human neural system, but they represent important initial steps in this direction. The basic premise is that mechanisms called central pattern generators resident in the spinal chord generate a basic rhythmic motor pattern that is a template for locomotion. This idea is supported by numerous neurophysiological studies [27]. The neural oscillators at each joint integrate sensory and motor information from the body to generate the proper control signals for walking. This rhythmic pattern is modulated by sensory feedback and the higher brain center input to adapt and accommodate the control as necessary. Taga coarsely modeled this scenario lending support that such a framework could indeed produce stable locomotion [72]. The simulation successfully reproduced the salient features of walking, was capable of multiple steps, and was robust to modest perturbation. Perhaps the most important feature of the model is that the walking pattern and control evolved out of the properties of the model. Neither a tracking nor a performance goal, per se, was used.

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Figure 4. An example of the types and connections of elements for control of a walking simulation using explicit representations of neural structures. Diagram derived from structure of previously described models [73, 30].

Summary and Importance of Control Methods It is unclear whether more complexity in controls is really necessary. In creating biomechanical models, simplicity is recommended to lessen the challenge of providing adequate control. The explicit modeling of CNS structures and the dynamic optimal control methods make a strong case for the existing level of complexity in controller design. However, the success of tracking type algorithms with simple control layered on top suggest simplicity may be adequate. The very existence of relatively complex but totally passive walking “robots” further strengthens the case for simplicity [7, 19]. These walking machines represent the basic degrees of freedom in human legs (hip, knee, ankle joints), but require only a gentle downhill slope to allow them to walk continuously and stably. Gravity and careful design of the mass properties provide dynamic stability. In powered models, each

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control approach described above has a unique combination of advantages and disadvantages. There is no single best choice. The question of how well does the chosen performance goal represent the natural prioritization scheme always exists because of the many levels of redundancy in the body. This is difficult to determine with certainty. This uncertainty warrants caution, at the very least, in applying the methods to answer “what if” style clinical questions. It is imperative that the model reflect the critical properties of the system under study. Critical is determined by study objectives. Rehabilitation clinicians frequently warn that the patient treatment goal is not necessarily to restore them to “normal”. Can a control scheme that is biased towards this adequately represent response in the presence of pathology? The immense variety in functional compensations observed in pathological gait forces us to consider carefully the control methods of our simulations. Tracking algorithms reproduce, by definition, the desired performance well. However, the underlying control premise is much less clear than in other methods. There is an inherent bias towards the tracked performance. It is unclear how this affects model response to perturbation. The tracking method layered with simple goal and task level feedback controls also produces reasonable results, and with more explicit functional goals. However, these solutions have not been reported on a muscle based model and thus have limited utility for analyses requiring muscles. It is unclear and can not be assumed that the type of controllers developed for the current models can adequately handle the control of a model involving individual muscles. Dynamic optimal control methods (other than those used for tracking) may have more predictive capability. There is a significant computational cost and still no guarantee of the desired performance. Due to how the problem is solved, the solution may not necessarily be the “best”. However to reproduce normal gait an optimal solution may not be necessary – a “workable” set of controls may suffice [87]. Until and if true validation is achieved, it is necessary to provide some level of assurance that the model behavior applies, within the constraints of the model complexity, to the human system it approximates.

A Note on Validation Validation is necessary for a model to have predictive value. It is imperative that the computer model respond in a way similar to the system (human + task) it represents [47]. Validation is difficult if not impossible to truly achieve; perhaps “evaluation” is more achievable [78]. Often times, alternate or related experiments that can (physically, ethically, etc.) be performed on human test subjects may be run to test the model and simulation. Similarity of results supports the model and technique (Figure 5), but is not a guarantee of success [85]. Due to the redundancy of the human locomotor system, a similar response may have been generated by the computer model in a different way than in the human [82]. Models including muscles can compare activation patterns to that of EMG to qualitatively assess suitability of the control selection. Generalizing results of the model from other tests depends on carefully constructed logic of these perturbation tests. Perturbations should assess the same response characteristics of the model that are being used in the desired tests. It is also important the perturbation tests assess all the different aspects of the response characteristics involved in the desired test [85]. Testing the sensitivity of the model to each parameter helps to ensure the model response does not depend too much on a few critical ones. If it does, these parameters should be as accurately defined as possible. Error estimates

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in these parameters can be helpful in determining the range of results that may be considered equal. As models continue to grow more complex, importance of the validation process grows commensurately. It becomes more difficult to determine the sensitivity of the model performance as parameters are added that are not required to answer the study objectives [77]. The mindset of the simulation expert may be changing from “create the simplest model that can address each question that arises” to “build a [single] more generally applicable, albeit more complex model to answer a variety of questions” [56]. Regardless, as simulation objectives move more into the realm of clinical practice, the models and simulation techniques must keep pace. With these important cautions and limitations in mind, examples of current simulations are now presented.

Figure 5. A simple approach to assessing model validation. In this paradigm, some data recorded from actual subjects walking may be used to develop the simulation while others from the same test session may help to evaluate the simulation.

Applications A brief review of recent work illustrates the utility and current scope of simulation in rehabilitation and gait analysis. The advantages of using inverse dynamic and intersegmental dynamics analysis models are illustrated before a few simulation examples are presented. Talaty, M.

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Simulation can be used to understanding cause-effect or structure-function relationships in human movement, perform “what if” analyses, test hypotheses on the neural control or mechanics of walking [46, 54, 72], separate the effect of many factors that act simultaneously, or calculate parameters that are difficult, impossible or unethical to measure. Understanding role of muscle in performance is central to many other goals [3, 63]. This is an important question since each muscle can directly affect body motion well beyond the segments it directly contacts [92], and because many muscles can act in a great many combinations to produce a desired movement. Predicting changes in performance due to intervention such as surgery, bracing, or therapy can have significant clinical impact [13, 47]. In a broader sense, simulation can be used to better train clinicians or coach athletes to improve athletic performance [3, 11, 47, 82]. Prototyping can result in better, safer and faster development of rehabilitation products [42, 64]. Models, the basis for simulation, offer several important capabilities in gait analysis.

Analyze Subject Data A model can be tremendously useful to visualize and quantify performance. Most commercial motion analysis packages (instrumentation and software) allows motion to be recorded and played back. The computer generated figure can be viewed from any perspective, speeded up, slowed down, or in reverse (Figure 6). Body segments of the model can be removed to better visualize movement of the segments of interest. Joint angles, footfall timing patterns, displacements of body parts, etc. can be quantified to sub-degree, millisecond and millimeter accuracy, respectively. Through the computations associated with the simulation, net bony contact and individual muscle forces, muscle lengths, energy flows, etc. can be calculated. Thus, quantities not easily measurable otherwise can be assessed. For facilities without a separate forceline visualization method [8], the line of action of the ground reaction force extending from the center of pressure under the foot can be visualized from any perspective. These are just a sample of the advantages of combining a mathematical model with a measurement system. Simulation of such a model extends and enhances these capabilities. Induced acceleration or intersegmental dynamics analysis bridges the gap between modeling or analysis of measured data and simulation or synthesis of performance.

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Figure 6. Use of motion capture software to enhance visualization and integration of information relevant to clinical decision making. Actual patient data can be animated from a variety perspectives and auxiliary data (EMG, leg loading) can be juxtaposed along with motion data. [Software used : CodaMA, Charnwood Dynamics, England]. The top panels show three channels of lower extremity EMG (left) and the ground reaction force (left in blue, right in red). The blue lines indicate the current time value corresponding to the animated stick figures below. The bottom panels show the stick figure representation of the actual movement data collected from a patient in frontal, sagittal, oblique and coronal plane sections. The purple lines on the stick panels represent the line of action and magnitude of the force acting under each foot.

Intersegmental Dynamics Analysis to Assess Body-Wide Effects of a Single Joint Moment Intersegmental dynamics analysis (IDA) has been used to explain compensatory specifics responses in pathological movement data [39], to quantify the effect of an ankle foot brace on hip and knee stability as well as forwards progression [74], to assess contribution to stiff knee gait [70], and to understand the role of joint moments [35] and individual muscles [51]in gait. IDA is useful in explaining the effect of a single joint moment on remote segments and in illustrating how the effects of joint moments combine to produce the net or observed performance. In short, IDA rearranges the equations used in inverse dynamics to objectively calculate the effect of a joint moment (or muscle force) on the entire rest of the body [35]. It is known that muscles have an effect on segments and joints they do not directly contact [15, 18, 61, 92], but a suitable framework to study this has only recently begun to receive attention and use. In similar fashion, ankle foot orthoses (AFOs) have been used to control more proximal segments but a definitive quantitative assessment of the control they provide has not been reported. A recent IDA study suggested caution in regards to generalizations used in AFO prescription [75]. For example, it was shown that an AFO locked in plantarflexion could contribute to knee and hip instability in early stance (Figure 7). An increased Talaty, M.

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dorsiflexion moment after footflat produced greater knee and hip stability, however the increased resistance to dorsiflexion in midstance did not hinder forwards progression. A decreased plantarflexion moment due to restricted pushoff in late stance was associated with increased forwards propulsion and knee extension. The IDA calculations were also used to estimate synergy in brace range of motion restrictions. IDA represents a bridge between analysis capabilities of inverse dynamics and synthesis or predictive capabilities of simulation. Some researchers use a simulation platform for IDA. But IDA does not have the predictive capabilities unique to simulation. The remainder of applications presented employ simulation.

(a)

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(b) Figure 7. Illustration of the decomposition allowed by the IDA technique. (a) The familiar ground reaction force measured under the foot during walking can be separated into components from the variety of sources that produce it. Note, the Total measured and the Sum of the [calculated] components are virtually indistinguishable supporting accuracy of the method. (b) In a similar manner to the GRF decomposition of panel (a), the acceleration of a joint can be separated into components from the various sources or factors that produce it. This plot illustrates the major sources contributing to knee stability in early stance. Note the brace, a MAFO locked in plantarflexion accelerated the knee into flexion, while the knee extensor moment due to the quadriceps extended the knee during the shown time (early stance phase).

Objectively Evaluate and Refine Rehabilitation Techniques A simulation was used to determine that backwards pedaling produced higher patellofemoral loading than did forwards pedaling [50]. Stationary cycling is used in rehabilitation of a variety of knee injuries. Backwards pedaling is sometimes prescribed to increase knee extensor strength as it produces higher knee extensor moment; the effect of this on patellofemoral reaction forces is not well known. A model of a human on an ergometer was developed using SIMM (Software for Interactive Musculoskeletal Modeling) platform [12]. SIMM is perhaps the most popular of several commercially available software tools to facilitate the development of complex biomechanical models. The model included lower extremity muscles. The muscle activation scheme was experimentally calculated using a tracking algorithm to reproduce the pedaling motion. Then model joint forces were extracted from the model. Forwards pedaling was found to create lower patellofemoral joint reaction loads, suggesting it is better for patients with patellofemoral pain symptoms. The authors were careful to note that many different muscle activation patterns could have reproduced the desired mechanics. The patellofemoral reaction force was found to be relatively insensitive to knee musculature activity. Pedaling mechanics were more important. The simulation offers a platform to estimate the joint reaction force that is otherwise difficult to obtain. Further, it allows control over factors such as knee musculature excitation that can be difficult to do in humans. Talaty, M.

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Another study suggested that vastus medialis oblique (VMO) strengthening was more effective than orthotic therapy or VMO activation timing in reducing patellofemoral loading during running [52]. The authors used a tracking algorithm to duplicate subject-specific performance for nine volunteers. Then an increase in VMO strength, an orthotic with stiffened arch, and alteration in VMO timings were implemented and the simulations rerun. Only the strength modification was found to produce a statistically significant change in peak joint reaction force, but that all interventions lowered average joint reaction force.

Clarify Factors Contributing to Abnormal Movement Simulation can help clarify and assess the importance of the many factors that contribute to abnormal movement. For example, the role of overactive knee extensors in stiff knee gait has been debated. Rectus femoris lengthening does not always improve the stiff knee gait. One simulation found that an overactive rectus femoris could contribute to stiff knee during swing phase [63]. However weak hip flexors were also found to influence the knee flexion during swing phase. Another study showed good qualitative correlation between simulated and actual changes in swing phase knee flexion due to changes in knee extension and hip flexion moments [36]. Changes in the hip moment had a much larger effect on knee flexion than changes in the knee moment. This study was interesting because individual data were used to customize the simulation for each of five study subjects. Actual changes in joint moments were produced by neuromuscular block or strengthening routines. Patients showed individual variations; the simulation for each subject reflected individual variations. This demonstrated simulation sensitivity to individual factors and that simulation may be beneficial to tailoring treatment routines for individual patients. Both studies emphasized caution in attributing factors producing stiff knee gait due to its multifactorial etiology. One of the fundamental strengths of simulation is that it integrates all the factors to determine how they might interact and allows them to be individually varied to better understand the role of each. An awareness of the strong effect of body positioning on biomechanical function is one important finding from intersegmental dynamics (induced acceleration) analysis in our lab [75]. The effect of a joint moment on the motion of remote segments in the body was found to be significantly affected by small changes in joint angles. This principle likely accounts for some of the discrepancies found in the literature regarding the causes of stiff knee gait. This factor alone is difficult to visualize and account for in patient assessment because the relationship is not simple or well documented. Simulation can combine variations in other factors that also contribute to stiff knee gait (muscle strength at the knee and other joints, range of motion, joint stiffness – to name a few). It is no surprise there are discrepancies in literature given the level of complexity involved in movement disorders.

Predict Ramifications of Muscle Transfer and Lengthening Surgeries A simulation can be used to assess the possible effects on performance due to changes of soft tissue transfers, releases, lengthenings, bony reconstruction, and arthroplasty surgeries [11, 82]. Assessing the impact of biomechanical changes due to surgery and how these changes affect the operating properties of the muscles can be difficult without a tool that integrates the factors involved. Simulations combine the relevant factors and may allow an objective estimation of the effect of the surgery before it is performed. Using this approach,

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the biomechanical contribution to performance can be more accurately estimated, but the final patient response depends on additional factors. Perhaps the most important such factor is the neural control scheme that dictates the compensatory response. This factor alone can strongly influence the outcome. None the less, the biomechanical consequences of a surgical procedure are important as they guide the overall response. For example, the effect of small amounts of tilting of the tibial component in a knee replacement was shown to strongly affect knee musculotendon tension and the joint motion [62]. It was suggested that posterior tilting of the posterior cruciate-substituting knee replacement did not benefit in the same way as tilting of the posterior cruciate-retaining knee replacement. When ankle plantarflexor contracture is present, restoring the foot to a stable position is a priority to allow or improve ambulation [17]. The associated equinovarus posture can also produce knee hyperextension, reduced stance phase forwards progression, and swing phase obstruction [16, 17]. A simulation study found that independent lengthening of gastrocnemius and soleus aponeuroses was more effective at restoring range of motion while preserving force generating capacity of the plantarflexors when contracture was present in both muscles (Figure 8) [13].

Figure 8. Simulated results of muscle lengthening surgeries can be used to study how results are affected by differing initial conditions. Reproduced with permission from Delp SL, Statler K, and Carroll NC: Preserving Plantar Flexion Strength After Surgical Treatment for Contracture of the Triceps Surae: A Computer Simulation Study. Journal of Orthopaedic Research 1:96-104, 1995. Lengthening the Achilles tendon provided increased ankle range, but weakened the ability of the muscles to produce the required stance phase plantarflexion moment. Preserving the plantarflexion moment is important to avoid potential drop off gait and instability. Simulation allowed an assessment of how factors that affect performance changed with intervention. Changes in biological structures in rerouting or transfer surgeries can alter performance biomechanics. Muscle resting length, the functional range through which a muscle is active, and the lever arm by which the muscle force creates a torque about a joint can all be affected.

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Assess Feasibility and Refine Techniques for Functional Electrical Stimulation Researchers have used simulation to investigate many aspects of FES for restoring gait in paraplegics [4, 21, 22, 47, 88, 89]. One study [89] suggested that FES could be implemented to produce “undisturbed, level gait at natural walking speeds.” A computer simulation study was used to assess sensitivity of performance to muscle fatigue and strength, and the ability to artificially develop a control pattern to produce the desired movement. Control selection and strength of available muscles were found to hinder FES as a practical tool. Control selection was found to be critical to reproducing the desired walking pattern. Using a simulation allowed for a direct and safe means to assess the effect of changing the timing and strength of stimulation patterns. Small changes in the timing and selection of muscles were found to have significant effects on the walking performance – sometimes producing instability and collapse, yet a minimum set of only seven muscles in each leg was sufficient to produce walking. Changes in the magnitude of muscle contraction were much less critical. Activity levels were broken down in to 10% increments – illustrating the level of coarseness required in contraction strength modulation. Though the control of strength was not critical, the amount available was a limiting factor. This may be a significant finding since muscles in paraplegics are often easily fatigued and relatively weak, compared to those in normals. Plantarflexor strength was found to be critical and needed to be near 80% of that found in a normal population. A simulated AFO was helpful in stabilizing the leg and body during stance phase, and could help to lessen the significant strength demands placed on the plantarflexors. This could also simplify considerably the control pattern necessary. From a technical standpoint, this study was important because it suggested that open loop and trial and error methods and thus a sub-optimal control pattern may be sufficient to reproduce walking. Further, the control pattern only needed to be updated about every 50ms or about 11 times during stance phase.

Optimize Design of Equipment for Use by Humans Computer simulation may be used to assist in the design and evaluation of a range of devices or equipment that people use [47, 64, 78]. A relatively commercial application is presented to indicate how science is being taken into the clinical world in orthotics prescription and manufacturing. Though the science behind this effort is unknown, it provides a vision of the potential that simulation may one day achieve. An entrepreneur with commercial support has designed a dynamic simulation to optimize foot orthotics by aiming to minimize the iterative process of design, trial, and modification until a reasonable result is obtained [14, 42]. Patient specific data (age, gender, weight, and various anthropometric measures) are fed into a custom gait simulation. The walking parameters are compared to that from a normal database. The software then indicates specific orthotic modification necessary to normalize the patient performance. To finish up this rather futuristic-sounding process, the manufacturing instructions are output to a milling machine where the exact design selected by the simulation software is made on a computer-controlled milling machine. Plans are also underway to incorporate subject-specific MRI scans of the foot for more accurate foot structure modeling as well as software enhancements to estimate how the body response will change over time. Scientific validation of the above process has not been found, suggesting a fair amount of caution be used in assessing software results and capabilities. Many of the concepts implicit

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in such a work have been the subject of scientific study for decades. It is likely that the results appear to have more potential for generalization than they really do. The software has been validated; the details however are unclear. More importantly, the entire product has been stated to have helped hundreds of patients already. And this is a critically important outcome measure. Systematic outcomes testing may be useful. None the less, it is important to be able to envision the big picture as is so elegantly portrayed in this example. It is difficult to estimate the value of having such a tool available for clinicians to use, collect feedback from, and modify. It has surely utilized some assumptions to develop, but by its very existence, has set into motion a process that may lead to refinement, alternate developments, and even basic scientific thinking. This may ultimately lead to a better tool, founded on a more firm scientific basis, that has undergone significant testing.

Evaluate Movement Control Hypotheses Implementations of explicit CNS modeling approaches have produced the salient features of stable locomotion. This provides evidence on the functional utility of simple neural circuits (central pattern generators) in gait [72, 73]. This platform was subsequently used to investigate the role of pre-programming vs. self-organization in neural control [71]. Performance strategies in bicycling have been studied [49]. It was found that the preferred bicycle pedaling rate of experienced cyclists coincided with minimum muscular fatigue for a given range of pedaling rates. It was suggested that the neural control system may be aware of this or related quantities. Work was done using optimal control theory to determine what performance or objective criteria the body may employ during normal and pathological gait [40, 41, 45]. Various (in total seven) criteria were used to run the simulations. The closer a model using a particular criteria comes to reproducing the originally measured performance, the more likely that criteria may be one used by the CNS. For normal gait, a criteria related to minimization of the square of the joint moments was found to be the best. Minimum rate of acceleration and minimum head motion also fared well. Minimization of joint power was the poorest performer. However, for two separate pathological gait data sets (1 neurological, 1 orthopaedic), the minimization of joint power was the best criteria. Minimization of velocity, by its inclusion in the power criteria, was preferred in the pathological conditions. That the performance criteria may change when pathology was introduced was no surprise. However objective quantification of this with such a simple criteria is helpful towards a unified understanding of how pathology changes performance.

Explore Mechanisms of Injury Simulation provides a safe and controlled environment to identify factors that may promote injury and how to treat them [44, 53, 78, 86]. The effect of ankle joint laxity on ankle inversion sprain injury and the mechanism of common treatment modalities has been studied [86]. Increased ankle flexibility and compliance both caused increased ankle supination in a simulated lateral cutting maneuver. Neither correlated to less torque, and torque is what ultimately produces injury. However, ankle torque and supination was more sensitive to changes in flexibility than in stiffness. It was believed that for treatment both limited flexibility as well as a stiffened joint would assist in reducing injury of this mode. Flexibility was more a range of motion measure where as the stiffness was used to describe the torque-angle ratio. It is noted that a tracking strategy was employed to develop the

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baseline model. Comparison between model and subject kinematics and ground reaction forces was used to support use of the model and subsequent simulations. A similar study to study the effects of shoe design properties on ankle eversion injury has been undertaken, but results have not been reported yet [42].

Future Work The impact of computer simulation on clinical practice will continue to grow significantly in the decades ahead. As the field matures, less emphasis will need to be directed towards developing “working” simulations, and more can be channeled towards highly accurate subject-specific models. Advances in imaging techniques [9, 38, 59] can give researchers more accurate and subject-specific body parameter estimates. Reassessing basic modeling assumptions and improving approaches [28, 44], especially in musculoskeletal parameters, critically affect model performance and may provide valuable gains [5, 32]. The improved models may have a more direct involvement in patient care.

Acknowledgments Ton van den Bogert provided a very helpful review of the chapter for which I am deeply grateful. Cenk Guler and Necip Berme provided instrumental discussion in assessing the importance and role of foot models. I sincerely thank Barbara Hirai for her help reviewing the manuscript. I appreciate the suggestions for improving the clarity and flow and the base version of figure 4 provided by Mausam Patel and Tom Coulter. Many thanks are due to Jennifer Talaty for creating and enhancing several of the figures.

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