Theoretical Considerations for Patient-Specific Modeling Based on Observable State Variables

Abstract In this study, we address fundamental theoretical considerations that should guide biomedical engineers in the assessment of patient-specific risk of tissue failure, or the assesment of other material properties needed for patient-specific computational modeling, based on non-invasive imaging modalities. Upon reviewing theoretical concepts of mechanics, the primary conclusion is that patient-specific material properties, such as measures of tissue failure, cannot be observed directly, because material properties are dependent on non-observable functions of state. However, since functions of state may be formulated to depend on observable state variables, and since non-invasive imaging may be used to assess such variables, it behooves investigators to find strong correlations in vitro between the material property of interest and relevant observable state variables, such as measures of tissue morphology, transport characteristics, and composition. Once such univariate or multivariate correlations have been established experimentally in vitro, the next challenge is to relate imaging-based observable measures, acquired non-invasively (e.g., in vivo), to relevant material properties such as failure criteria. The uncertainty associated with these observation-derived material properties is, at best, equal to the uncertainty of the in vitro correlation.