This page is about the somewhat unusual way that biomechanics research with detailed musculoskeletal models is done. Note, these are my own views and not necessarily those of my lab or colleagues. I wrote this page because I wanted to (1) reconcile with myself what the advantages and disadvantages are of the way we do research in biomechanics with detailed models, (2) to have this page available for others to understand the rationale and challenges of doing research with detailed models, and (3) to promote mutual respect and collaboration between the different communities of biomechanics researchers.
The goal of biomechanics is to understand the movement of humans and other animals. In particular, we want to understand how humans' brains and nerves control their muscles to produce movement, how their muscles, bones, tendons, and ligaments interact during movement, and how pathologies (like cerebral palsy) affect human movement, and how changes to the human body (like surgeries) affect human movement.
To investigate these questions, traditionally biomechanists have experimented directly with humans, human cadavers, animals, and even robot models of humans or animals. Researchers would set up experiments, measure quantities of interest to them, and then analyze those measurements and come up with a story about some aspect of human or animal movement.
However, in living humans, there is only so much we can measure without damaging the human. For example, measuring the force applied by a muscle or the activation of muscle fibers inside a muscle require fairly elaborate and/or painful methods, and even then there can be measurement errors that lead to somewhat inaccurate results. Understanding the behavior of the human body as a whole, which is a highly complex system, is difficult to do with measurements alone.
Mathematical models of human and animal movement have become powerful tools for investigating movement when measurements alone give incomplete answers. For example, gait analysis1, in which a model of a human consisting of a system of rigid links is used to estimate the torques at the joints of a human as they perform a movement, is now a standard practice in clinical labs that study and treat patients with movement disorders. Although the positions of a human's body segments can be measured with cameras and other equipment, it is easiest to compute the joint angles and joint torques of a human using a mathematical model rather than trying to measure these quantities directly. Simple models of walking have revealed many interesting insights into the dynamics and control of walking as well.2,3,4
For questions about human movement that require understanding the behavior of individual muscles, since measurements of muscle force are difficult or impossible to make, complex models of the human body including a large number of important muscles are helpful. For example, to understand why children with cerebral palsy walk with a stiff knee or a crouched posture, and to evaluate existing theories on what muscles are abnormally functioning to cause these abnormal movements, since measurements of surface muscle excitations alone do not tell the whole story of how muscles apply forces to cause abnormal movements, it can be helpful to build a detailed model of a human's musculoskeletal system that enable us to estimate the forces applied by muscles in a real human subject as they walk abnormally.
Accurate, detailed models have the potential to, for the first time ever, estimate the activations and forces exerted by a large number of muscles in order to coordinate a walking movement. Simulations (estimations of muscle excitations, activations, and forces) modeling how muscles coordinate a particular movement have suggested many new dynamically plausible stories about how muscles coordinate human movement--stories that simple visual reasoning and measurements of some muscles' excitations alone did not reveal previously. For example, patients with stiff-knee gait were originally thought to have overactivity of the rectus femoris muscle (a quadriceps muscle) during the swing phase of walking, which created the knee to extend more than normal, thus inhibiting knee flexion during the swing phase. So, a common surgery done for stiff-knee patients was to detach the rectus femoris muscle from its tendon at the knee, and re-attach it behind the knee, to make the overactive rectus femoris muscle cause knee flexion5. However, not all patients benefit from this surgery, suggesting that other factors may play a role in causing stiff-knee gait. Simulations made with detailed musculoskeletal models suggested that knee flexion in swing can be increased by an increase in hip flexion moment during swing6, and that knee flexion during swing can be decreased by an increase in knee extension moment or by a decrease in hip flexion moment, with the rectus femoris accelerating the knee into extension during swing, and the hip flexors, ankle dorsiflexors (ankle flexors), and lateral hamstrings accelerating the knee into flexion7. These kinds of conclusions, while conditional on the numerous assumptions made in developing these complex models, would be practically impossible to arrive at from experimental measurements or even simple models alone. A technique called induced acceleration analysis (IAA) has been used to estimate the contributions of individual muscles to the motions of different segments and the center of mass of the whole body from a simulation. IAA-like methods have been used to study the roles of individual muscles in supporting the body, propelling the body forward, and swinging the legs during walking8,9,10.
However, conclusions drawn from complex models are conditional on a large number of assumptions, many of which are subject to criticism. For example, the detailed Delp lower extremity model11, used extensively in computational biomechanics, has muscle properties chosen from experiments whose measurements disagree substantially. Physiologic cross-sectional areas (PCSAs) were taken from Friedrich et al.12, who made measurements on a young cadaver and reported the ``specific tension" (maximum force divided by PCSA) of muscles to be 25 N/cm2. However, moments measured on young subjects tended to be much higher than what a specific tension of 25 N/cm2 could produce, so the specific tension for the Delp lower extremity model was chosen from Wickiewicz et al.13, who made measurements on elderly cadavers and reported the specific tension to be 61 N/cm2, even though another study14 reported the specific tension to be 23 N/cm2. Optimal fiber lengths and muscle pennation angles in the model were taken from Wickiewicz et al.13, but for muscles not reported by Wickiewicz et al., these parameters were taken from Friedrich et al.12. Thus it is well known that there may be large uncertainties in the experimental data on which the model is based, and it is not well understood how sensitive the model is to changes or inaccuracies in these parameters. There is agreement though that significant improvements can be made to simulations based on more accurate model parameters. In addition, the model does not include models of compensatory strategies that the human body often uses to adapt to altered environments, but may have significant effects on conclusions drawn about movement control. This is a major challenge that those of us working with complex models may not be able to accurately attack for a while.
Induced acceleration analysis (IAA) itself has been subject to criticism. It has been shown that varying the number of degrees of freedom in a model can have dramatic effects on the results drawn from induced acceleration analyses15,16. There have also been criticisms of a basic assumption of induced acceleration analyses: that the way a model responds to small perturbations in muscle forces is the same as the way a real human's body would respond to the same small perturbations in muscle forces. How the human body responds to such perturbations is a question of interest to some experimentalists and computational biomechanists, but no definitive answers to this question have been obtained so far. The real interest of those who use induced acceleration analyses is to study the relative contributions of muscles and other force generators to the movement of individual body segments. Although telling a story about the relative contributions (rather than the actual numerical contributions) of muscles to body movements is less strong than teling a story about the specific numerical contributions, no convincing argument has been presented, to my knowledge, as to whether the relative contributions reported in the literature are correct or incorrect. However, an even less strong conclusion may be more believable: that the signs of the contributions (e.g., that a muscle that extends the knee pushes the center of mass of the body backward rather than forward in a certain configuration, while it may propel the body forward rather than backward in another configuration) are useful to study.
While the simulations and induced acceleration analyses published to date do not represent 100%, definitive conclusions about how muscles coordinate human movement, these tools may still be a useful way to gather evidence to infer the roles of individual muscles in movement control, and help guide experimental studies that could try to test and support or reject the results of these conclusions drawn from computational methods. The way this process plays out tends to be that experimentalists conduct studies and publish their results, even if their conclusions were based on many incorrect assumptions about the dynamics of the human body. At the same time, computational researchers create models and simulations and analyze their models and simulations to draw conclusions about their models, which in turn suggest that similar conclusions may hold for actual humans, and these studies are also published even though they, too, are conditional on many assumptions whose accuracy is greatly uncertain. Those who work with simple computational models have a much more complete understanding of their models, but there is much uncertainty about how well their assumptions hold for real humans. And in many studies dealing with simple or complex models, many factors that could cause great differences in results, such as whether a model is representing an adult or a child, a male or a female, an elderly person or a young adult, a person with impaired or unimpaired movement control or anatomy, or a person who has or has not undergone an anatomical surgery, are often not modeled.
In fact, human movement control is a very complex control problem dealing with a very complex system (the human body), with the added constraint that we want to study the human body without destroying it (as pointed out to me by a fellow student). Many areas of science do allow invasive, destructive ways of investigating questions, such as splitting atoms apart or killing mice. Fortunately, this is not allowed with the human body. The seemingly strange but still seemingly effective approach that the field of biomechanics takes, is to have experimentalists continue to develop new ways to investigate questions, while computational researchers continue to develop better models to draw their own guesses about how movement is controlled, and then have the two communities work together to support, refute, and refine each others' conclusions. I believe that continual investigation of all of these questions with both experimental and computational approaches will gradually support the ideas that are consistently true, while refining or disproving the ideas that are not true. I think the key is to keep investigating these questions from all fronts, since these are questions that we need to answer if we are to continue understanding human movement, improving human movement, and treating human movement problems.
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