A technique for the classification of tissues by combining mechanics based models with Bayesian inference

This paper deals with a key issue in diagnostics and classification of tissue: given a few samples of tissue which are known to belong to certain categories (such as “healthy” and “diseased”) how to categorize a new sample? This is a well known and analyzed problem and very powerful purely data driven approaches have been developed. However, in situations with limited experimental data with a large spread that is typical of biomaterials, a purely data driven approach to classifying the samples is inadequate, since it can suffer from serious bias due to scant data. Here we propose an approach that uses our understanding of the mechanics of the behavior of tissues to transform the problem from the high dimensional space of raw data to a probability distribution on a low dimensional parameter space and then use a Bayesian technique for the classification based on the parameters. A key point in the paper is that the mapping from the raw data to the parameters is not a deterministic mapping (as would be obtained from a lest squares or maximum likelihood approach) but a probabilistic one based on Bayes rule. To apply this rule, there is a need for hypothesis on the prior probability distributions of the parameters themselves and a way to systematically update the hypothesis as more data is obtained. Such a framework should be able to (1) capture prior knowledge that we have about the parameters (such as for example minimum and maximum values for the parameters, likely mean values etc.) ; (2) provide a means for incorporating the knowledge gained from experiments and (3) gradually evolve towards a purely data driven approach as large amounts of data become available.We utilize a “max-ent” approach to the prior distribution: i.e. we select a distribution that incorporates any available statistical information about the data while being maximally indifferent to all other information. this probability distribution is updated by Bayesian inference where the posterior distributions are obtained by a Markov Chain Monte Carlo (MCMC) sampling method combined with a continuum mechanics based exact solution of a boundary value problem. We illustrate this approach by considering the “soft” classification (i.e we computer the probability of belonging to a class or category) of nominally similar sheep arteries (from two different sheep) based on the probability distribution of the parameters corresponding to each class This is an alternative to a logistic regression type approach in situations where there is high uncertainty or limited data distribution.