Title
"A Bayesian Approach to Biomechanical Modeling: A Treatise on the Human Thumb", A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy, Veronica Jade Santos, May 2007
Abstract
The functionality of the human thumb is owed to the ability to attain postures that oppose the other fingers and produce well-directed forces in 3D. A realistic biomechanical thumb model would be instrumental to understanding the functional consequences of orthopedic and neurological diseases, and objectively evaluating their treatment outcomes. Our approach is to establish a model for the passive mechanical structure of the thumb that accounts for anatomical variability (overlooked by models based on mean values) and parameter uncertainty (present whenever characterizing internal structures of complex, intact biomechanical systems).
First, we use Monte Carlo simulations to simulate parameter variability in an anatomy-based kinematic thumb model. Four types of kinematic models naturally emerged from reported anatomical data (Hollister et al., 1992, 1995). We found a third alternative to the debate of the "one size fits all" versus the "subject-specific" model: that the thumb kinematic structure of a population may be described by a finite number of functionally-relevant, statistically distinct categories. We also present the Denavit-Hartenberg parameterization of the anatomy-based "virtual five-link model" (Giurintano et al., 1995) for use in robotics-based biomechanics analyses and biomimetic robotic hand development.
Next, we describe our collection of functional in vivo data from unimpaired thumbs, together with the most complete set of anthropometric hand measurement data to date which point to key anatomical differences between female and male hands. While previous studies focused on thumb motion or force production alone, we gathered functional data for both regimes from all subjects.
Finally, we apply a Bayesian, Markov chain Monte Carlo approach to our studies as a logical means to assess the sensitivity of a model structure to parameter variability/uncertainty, handle multimodal, high-dimensional model parameter spaces, and incorporate experimental data. We demonstrate a proof-of-concept for our Metropolis-Hastings sampling algorithm for a complex 36D model parameter space. We can now begin to address the appropriateness of a robotics-based model structure while accounting for subject-specific features. Once established, a validated kinematic model of the human thumb can be used as a computational testbed for motor control theories and the design of prostheses, orthoses, and surgical and rehabilitation techniques.