D8 Computational Modeling

Topic

Computational modeling integrates the physical equations of all the subsystems described so far into simulation environments that allow for predicting biomechanical behavior, optimizing designs, and testing hypotheses that would be impossible to verify experimentally. These models range from direct simulation—which numerically integrates the system's equations of motion—to machine learning, which, rather than starting from those equations, extracts patterns directly from large experimental datasets.

Based on these equations of motion, musculoskeletal biomechanical simulations solve the problem of calculating the movement produced by specific muscle forces—or, conversely, the muscle forces producing a specific movement—by treating the body as a system of rigid, interconnected segments and representing each muscle as a combination of an actively contracting element and purely elastic elements arranged in series and parallel with it. Since the body possesses more muscles than degrees of freedom of movement, there are infinite combinations of muscle activation capable of producing the same movement; this redundancy problem is resolved by identifying, among all possible combinations, the one that minimizes a specific cost metric—such as metabolic expenditure, muscle stress, or a weighted combination of individual muscle activation levels. Advancing these equations over time requires numerical methods that automatically adjust the time-step size, as different parts of the system change at vastly different rates; only a time step adapted to the fastest-changing component ensures that the calculation maintains accuracy throughout the simulation. In addition to musculoskeletal simulations that model whole-body movement, computational modeling is also used to simulate how bone or tissue deforms under load: the bone or tissue is divided into many small volumetric elements, and the equations relating applied force to resulting deformation are solved element by element—whether in a simple proportional form or a more comprehensive form that captures non-proportional behaviors. This element-by-element analysis yields the full stress and strain fields within the bone or tissue under applied physiological loads.

The machine learning mentioned earlier—specifically its supervised variant—trains networks that process information through successive layers and are particularly adept at recognizing spatial patterns. These networks have proven capable of predicting biomechanical variables, such as joint moments or muscle forces, with accuracy comparable to calculations derived from inverse dynamics based on measured forces; however, they achieve this using signals that are far less costly to obtain, such as video footage of the moving animal or electrical muscle signals recorded from the skin.

When multiple competing objectives coexist—rather than a single cost function to minimize, as in the muscle redundancy problem (e.g., maximizing movement speed while simultaneously minimizing metabolic cost)—optimization yields not a single optimal solution but a set of equally valid solutions. In this set, improving performance on one objective inevitably worsens it on the other; algorithms inspired by natural selection explore the space of possible solutions to identify this complete set.

The expected performance of these models—including the computational modeling described at the beginning—is that they reproduce kinematic and ground reaction force patterns with errors of less than 5% to 10% when compared against actual measurements taken during normal gait. That error increases, however, in extreme or pathological situations, precisely because many of these models simplify the body's behavior by assuming proportional relationships that cease to hold true when the system moves away from the conditions for which the model was calibrated.

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