An imaging-based stochastic model for simulation of tumour vasculature

Abstract

A mathematical model which reconstructs the structure of existing vasculature using patient-specific anatomical, functional and molecular imaging as input was developed. The vessel structure is modelled according to empirical vascular parameters, such as the mean vessel branching angle. The model is calibrated such that the resultant oxygen map modelled from the simulated microvasculature stochastically matches the input oxygen map to a high degree of accuracy (R2 ≈ 1). The calibrated model was successfully applied to preclinical imaging data. Starting from the anatomical vasculature image (obtained from contrast-enhanced computed tomography), a representative map of the complete vasculature was stochastically simulated as determined by the oxygen map (obtained from hypoxia [64Cu]Cu-ATSM positron emission tomography). The simulated microscopic vasculature and the calculated oxygenation map successfully represent the imaged hypoxia distribution (R2 = 0.94). The model elicits the parameters required to simulate vasculature consistent with imaging and provides a key mathematical relationship relating the vessel volume to the tissue oxygen tension. Apart from providing an excellent framework for visualizing the imaging gap between the microscopic and macroscopic imagings, the model has the potential to be extended as a tool to study the dynamics between the tumour and the vasculature in a patient-specific manner and has an application in the simulation of anti-angiogenic therapies.

An imaging-based computational model for simulating angiogenesis and tumour oxygenation dynamics

“…Tumour oxygenation map is derived from its hypoxia map using a functional relationship as described in earlier works (Lewis et al 1999, Titz and Jeraj 2008, Adhikarla and Jeraj 2012). A previous work (Adhikarla and Jeraj 2012) quantified the amount of vasculature present in the microenvironment based on its oxygen tension with higher vessel density reflecting higher oxygen tension (equation (1)).…”

“…A previous work (Adhikarla and Jeraj 2012) quantified the amount of vasculature present in the microenvironment based on its oxygen tension with higher vessel density reflecting higher oxygen tension (equation (1)). …”

“…The simulation of vasculature structure based on tumour oxygenation has been previously described (Titz and Jeraj 2008, Adhikarla and Jeraj 2012). Briefly, all vessels are simulated as cylindrical elements of equal lengths and diameters and are assumed to have equal oxygen concentration within them.…”

“…Briefly, all vessels are simulated as cylindrical elements of equal lengths and diameters and are assumed to have equal oxygen concentration within them. Further details regarding the simulation of vessels are provided in the supplementary materials and the previous publication (Adhikarla and Jeraj 2012). …”

“…The model uses the hypoxia PET imaging data to characterize tumour oxygenation status and proliferation PET imaging data to characterize tumour growth. We build upon a previous work where a stochastic model for the simulation of the vasculature based on a hypoxia PET scan was proposed (Adhikarla and Jeraj 2012). The current work extends the model to incorporate tumour growth and angiogenesis based on the molecular imaging as well as literature-based experimental data.…”