MOTIVATION: Systems biology aims to better understand living systems through mathematical modelling of experimental and clinical data. A pervasive challenge in quantitative dynamical modelling is the integration of time series measurements, which often have high variability and low sampling resolution. Approaches are required to utilize such information while consistently handling uncertainties. RESULTS: We present BayModTS (Bayesian modelling of time series data), a new FAIR (findable, accessible, interoperable, and reusable) workflow for processing and analysing sparse and highly variable time series data. BayModTS consistently transfers uncertainties from data to model predictions, including process knowledge via parameterized models. Further, credible differences in the dynamics of different conditions can be identified by filtering noise. To demonstrate the power and versatility of BayModTS, we applied it to three hepatic datasets gathered from three different species and with different measurement techniques: (i) blood perfusion measurements by magnetic resonance imaging in rat livers after portal vein ligation, (ii) pharmacokinetic time series of different drugs in normal and steatotic mice, and (iii) CT-based volumetric assessment of human liver remnants after clinical liver resection. AVAILABILITY AND IMPLEMENTATION: The BayModTS codebase is available on GitHub at https://github.com/Systems-Theory-in-Systems-Biology/BayModTS. The repository contains a Python script for the executable BayModTS workflow and a widely applicable SBML (systems biology markup language) model for retarded transient functions. In addition, all examples from the paper are included in the repository. Data and code of the application examples are stored on DaRUS: https://doi.org/10.18419/darus-3876. The raw MRI ROI voxel data were uploaded to DaRUS: https://doi.org/10.18419/darus-3878. The steatosis metabolite data are published on FairdomHub: 10.15490/fairdomhub.1.study.1070.1.

A large variety of severe medical conditions involve alterations in microvascular circulation. Hence, measurements or simulation of circulation and perfusion has considerable clinical value and can be used for diagnostics, evaluation of treatment efficacy, and for surgical planning. However, the accuracy of traditional tracer kinetic one-compartment models is limited due to scale dependency. As a remedy, we propose a scale invariant mathematical framework for simulating whole brain perfusion. The suggested framework is based on a segmentation of anatomical geometry down to imaging voxel resolution. Large vessels in the arterial and venous network are identified from time-of-flight (ToF) and quantitative susceptibility mapping (QSM). Macro-scale flow in the large-vessel-network is accurately modelled using the Hagen-Poiseuille equation, whereas capillary flow is treated as two-compartment porous media flow. Macro-scale flow is coupled with micro-scale flow by a spatially distributing support function in the terminal endings. Perfusion is defined as the transition of fluid from the arterial to the venous compartment. We demonstrate a whole brain simulation of tracer propagation on a realistic geometric model of the human brain, where the model comprises distinct areas of grey and white matter, as well as large vessels in the arterial and venous vascular network. Our proposed framework is an accurate and viable alternative to traditional compartment models, with high relevance for simulation of brain perfusion and also for restoration of field parameters in clinical brain perfusion applications.

An algorithm is developed for automated modeling of tubular blood vessel segments, based on their noisy 3D raster image. The approach is based on continuous-function approximation of binary skeleton lines extracted from thresholded multiscale vesselness images. The continuous centerline functions allow robust computation of tangent vectors, to define normal planes and 3D image cross-sections on those planes. A vessel intensity profile model is next least-squares fitted to the image cross-section along straight lines segments - anchored at centerline and extended toward vessel walls, at a number of directions covering the full angle. Vessel parameters, such as local radius for circular vessels, distances between the centerline and edges for non-circular shapes or intensity profile corresponding to blood velocity distribution, are estimated through the model fitting. Subvoxel accuracy vessel representation, robustness to noise and image inhomogeneity are of primary concern. The algorithm is applied to 3D synthetic and real-life magnetic resonance images. It is demonstrated that the proposed method facilitates automated extraction of geometric vessel-tree models from images and outperforms the well-known Hessian vector approach in terms of accurate estimation of the centerline local direction in noisy images.

The human vision system can discriminate regions which differ up to the second-order statistics only. We present an algorithm designed to reveal "hidden" boundaries in gray level images, by computing gradients in higher order statistics of the data. We demonstrate it by applying it to the identification of possible "hidden" boundaries of glioblastomas as manifest themselves in three-dimensional (3-D) MRI scans, using a model driven approach. We also demonstrate the method using a nonmodel driven approach where we have no prior information about the location of possible boundaries. In this case, we use 3-D MRI data concerning schizophrenic patients and normal controls.