A kernel-based learning approach for mechanical characterization of soft tissue

In recent years, elastography has emerged as a viable technique for non-invasive assessment of mechanical properties of tissue. Elastography techniques rely on imaging modalities, such as ultrasound imaging, to quantitatively assess changes in the elasticity of soft tissue in various pathologies, which is useful for diagnostic purposes. However, these techniques require solving an inverse problem to identify the mechanical properties of soft tissue while under external load, which is computationally expensive particularly for tissues that exhibit nonlinear mechanical characteristics under finite deformation. We propose a kernel-based machine learning approach for rapid assessment of mechanical properties of soft tissue based on a training dataset for which the deformation map represents the cause and the corresponding spatial distribution of material parameter, or elasticity map, is the response to be predicted. A nonlinear kernel-based partial least square (KPLS) regression model is employed to learn the relationship between the deformation map and corresponding elasticity map. KPLS is a chemometric tool that is particularly useful in situations where the number of cause variables exceeds the number of observations, which is often the case with clinical patient specific dataset. Hence, KPLS is chosen to directly address this problem of small  elastography datasets. A Gaussian kernel is used to construct the nonlinear mapping for the KPLS model. The parameters of KPLS model, i.e. the latent variable sets and Gaussian kernel parameter, are obtained by n-fold cross-validation to guarantee an independent assessment of the model. The prediction error of the KPLS regression model is estimated by n-fold cross validation on a synthetic dataset.