Fast Statistical Surrogates for Dynamical 3D Computer Models of Brain Tumors

Understanding how malignant brain tumors are formed and evolve has direct consequences on the development of efficient methods for their early detection and treatment. Adequate mathematical models for brain tumor growth and invasion can be helpful in clarifying some aspects of the mechanism responsible for the tumor. These mathematical models are typically implemented in computer models, which can be used for computer experimentation to study how changes in inputs, such as growth and diffusion parameters, affect the evolution of the virtual brain tumor. The computer model considered in this article is defined on a three-dimensional (3D) anatomically accurate digital representation of the human brain, which includes white and gray matter, and on a time interval of hundreds of days to realistically simulate the tumor development. Consequently, this computer model is very computationally intensive and only small-size computer experiments can be conducted, corresponding to a small sample of inputs. This article presents a computationally efficient multidimensional kriging method to predict the evolution of the virtual brain tumor at new inputs, conditioned on the virtual brain tumor data available from the small-size computer experiment. The analysis shows that this prediction can be more accurate than a computationally competing model.