Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness

In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain. We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes

A framework for modelling the biomechanical behaviour of the human liver during breathing in real time using machine learning

Progress in biomechanical modelling of human soft tissue is the basis for the development of new clinical applications capable of improving the diagnosis and treatment of some diseases (e.g. cancer), as well as the surgical planning and guidance of some interventions. The finite element method (FEM) is one of the most popular techniques used to predict the deformation of the human soft tissue due to its high accuracy. However, FEM has an associated high computational cost, which makes it difficult its integration in real-time computer-aided surgery systems. An alternative for simulating the mechanical behaviour of human organs in real time comes from the use of machine learning (ML) techniques, which are much faster than FEM. This paper assesses the feasibility of ML methods for modelling the biomechanical behaviour of the human liver during the breathing process, which is crucial for guiding surgeons during interventions where it is critical to track this deformation (e.g. some specific kind of biopsies) or for the accurate application of radiotherapy dose to liver tumours. For this purpose, different ML regression models were investigated, including three tree-based methods (decision trees, random forests and extremely randomised trees) and other two simpler regression techniques (dummy model and linear regression). In order to build and validate the ML models, a labelled data set was constructed from modelling the deformation of eight ex-vivo human livers using FEM. The best prediction performance was obtained using extremely randomised trees, with a mean error of 0.07 mm and all the samples with an error under 1 mm. The achieved results lay the foundation for the future development of some real-time software capable of simulating the human liver deformation during the breathing process during clinical interventions.This work has been funded by the Spanish Ministry of Economy and Competitiveness (MINECO) through research projects TIN2014-52033-R and DPI2013-40859-R, both also supported by European FEDER funds. The authors acknowledge the kind collaboration of the personnel from the hospital involved in the research.Lorente, D.; Martínez-Martínez, F.; Rupérez Moreno, MJ.; Lago, MA.; Martínez-Sober, M.; Escandell-Montero, P.; Martínez-Martínez, JM.... (2017). A framework for modelling the biomechanical behaviour of the human liver during breathing in real time using machine learning. Expert Systems with Applications. 71:342-357. doi:10.1016/j.eswa.2016.11.037S3423577

Gaussian Mixture Modeling with Gaussian Process Latent Variable Models

Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent Variable Model (GPLVM) has successfully been used to find low dimensional manifolds in a variety of complex data. The GPLVM consists of a set of points in a low dimensional latent space, and a stochastic map to the observed space. We show how it can be interpreted as a density model in the observed space. However, the GPLVM is not trained as a density model and therefore yields bad density estimates. We propose a new training strategy and obtain improved generalisation performance and better density estimates in comparative evaluations on several benchmark data sets.Comment: 11 pages, 2 figures, 3 table