Compartment models are mathematical representations of the transport of a chemical substance in the human body, assuming uniform concentration within each compartment, which corresponds to a distinct body part. Widely used in pharmaceutical and medical imaging through pharmacokinetic and tracer kinetic (TK) models, they are formulated as systems of time-dependent ordinary differential equations. However, these models do not account for the spatial dependence of physiological processes within individual compartments. This work aims to explore the physical interpretation of these models through mathematical derivation and to analyze their limitations. Three TK models are derived from more complex models regarding the physiological processes represented. The derivation introduces the hypotheses relevant to these processes. The most notable is the well-mixed hypothesis, resembling concentration homogeneity in the region of interest. The hypotheses are numerically tested by simulating the more complex model and evaluating the reduced models' residuals. For a given tracer molecule, the validity of TK models is found to decrease as voxel size increases. This work proposes an algorithm to compute the maximum voxel size, above which the reduced models' residuals exceed a chosen error threshold. For a 3 % error, voxel sizes larger than 250 $\upmu $ m are found critical for highly permeable vessels, while sizes smaller than 4 mm induce less than 3 % error in non-permeable vessels. Tested on literature-derived datasets, these findings identify diffusion as the underlying phenomenon leading to well-mixed compartments, and highlight the need for high spatial resolution imaging to improve TK parameters ground truth estimation.

MOTIVATION: Over the last decades, image processing and analysis have become one of the key technologies in systems biology and medicine. The quantification of anatomical structures and dynamic processes in living systems is essential for understanding the complex underlying mechanisms and allows, i.e. the construction of spatio-temporal models that illuminate the interplay between architecture and function. Recently, deep learning significantly improved the performance of traditional image analysis in cases where imaging techniques provide large amounts of data. However, if only a few images are available or qualified annotations are expensive to produce, the applicability of deep learning is still limited. RESULTS: We present a novel approach that combines machine learning-based interactive image segmentation using supervoxels with a clustering method for the automated identification of similarly colored images in large image sets which enables a guided reuse of interactively trained classifiers. Our approach solves the problem of deteriorated segmentation and quantification accuracy when reusing trained classifiers which is due to significant color variability prevalent and often unavoidable in biological and medical images. This increase in efficiency improves the suitability of interactive segmentation for larger image sets, enabling efficient quantification or the rapid generation of training data for deep learning with minimal effort. The presented methods are applicable for almost any image type and represent a useful tool for image analysis tasks in general. AVAILABILITY AND IMPLEMENTATION: The presented methods are implemented in our image processing software TiQuant which is freely available at tiquant.hoehme.com. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Biliary ducts collect bile from liver lobules, the smallest functional and anatomical units of liver, and carry it to the gallbladder. Disruptions in this process caused by defective embryonic development, or through ductal reaction in liver disease have a major impact on life quality and survival of patients. A deep understanding of the processes underlying bile duct lumen formation is crucial to identify intervention points to avoid or treat the appearance of defective bile ducts. Several hypotheses have been proposed to characterize the biophysical mechanisms driving initial bile duct lumen formation during embryogenesis. Here, guided by the quantification of morphological features and expression of genes in bile ducts from embryonic mouse liver, we sharpened these hypotheses and collected data to develop a high resolution individual cell-based computational model that enables to test alternative hypotheses in silico. This model permits realistic simulations of tissue and cell mechanics at sub-cellular scale. Our simulations suggest that successful bile duct lumen formation requires a simultaneous contribution of directed cell division of cholangiocytes, local osmotic effects generated by salt excretion in the lumen, and temporally-controlled differentiation of hepatoblasts to cholangiocytes, with apical constriction of cholangiocytes only moderately affecting luminal size.

Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite experimental response curves look largely different. We develop a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics from the growth kinetics in absence of external stress. Our model simulation results suggest a generic, even quantitatively same, growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function.

Diffusion-weighted magnetic resonance imaging (DWI) is a key non-invasive imaging technique for cancer diagnosis and tumor treatment assessment, reflecting Brownian movement of water molecules in tissues. Since densely packed cells restrict molecule mobility, tumor tissues produce usually higher signal (a.k.a. less attenuated signal) on isotropic maps compared with normal tissues. However, no general quantitative relation between DWI data and the cell density has been established. In order to link low-resolution clinical cross-sectional data with high-resolution histological information, we developed an image processing and analysis chain, which was used to study the correlation between the diffusion coefficient (D value) estimated from DWI and tumor cellularity from serial histological slides of a resected non-small cell lung cancer tumor. Color deconvolution followed by cell nuclei segmentation was performed on digitized histological images to determine local and cell-type specific 2d (two-dimensional) densities. From these, the 3d cell density was inferred by a model-based sampling technique, which is necessary for the calculation of local and global 3d tumor cell count. Next, DWI sequence information was overlaid with high-resolution CT data and the resected histology using prominent anatomical hallmarks for co-registration of histology tissue blocks and non-invasive imaging modalities' data. The integration of cell numbers information and DWI data derived from different tumor areas revealed a clear negative correlation between cell density and D value. Importantly, spatial tumor cell density can be calculated based on DWI data. In summary, our results demonstrate that tumor cell count and heterogeneity can be predicted from DWI data, which may open new opportunities for personalized diagnosis and therapy optimization.

We develop a quantitative single cell-based mathematical model for multi-cellular tumor spheroids (MCTS) of SK-MES-1 cells, a non-small cell lung cancer (NSCLC) cell line, growing under various nutrient conditions: we confront the simulations performed with this model with data on the growth kinetics and spatial labeling patterns for cell proliferation, extracellular matrix (ECM), cell distribution and cell death. We start with a simple model capturing part of the experimental observations. We then show, by performing a sensitivity analysis at each development stage of the model that its complexity needs to be stepwise increased to account for further experimental growth conditions. We thus ultimately arrive at a model that mimics the MCTS growth under multiple conditions to a great extent. Interestingly, the final model, is a minimal model capable of explaining all data simultaneously in the sense, that the number of mechanisms it contains is sufficient to explain the data and missing out any of its mechanisms did not permit fit between all data and the model within physiological parameter ranges. Nevertheless, compared to earlier models it is quite complex i.e., it includes a wide range of mechanisms discussed in biological literature. In this model, the cells lacking oxygen switch from aerobe to anaerobe glycolysis and produce lactate. Too high concentrations of lactate or too low concentrations of ATP promote cell death. Only if the extracellular matrix density overcomes a certain threshold, cells are able to enter the cell cycle. Dying cells produce a diffusive growth inhibitor. Missing out the spatial information would not permit to infer the mechanisms at work. Our findings suggest that this iterative data integration together with intermediate model sensitivity analysis at each model development stage, provide a promising strategy to infer predictive yet minimal (in the above sense) quantitative models of tumor growth, as prospectively of other tissue organization processes. Importantly, calibrating the model with two nutriment-rich growth conditions, the outcome for two nutriment-poor growth conditions could be predicted. As the final model is however quite complex, incorporating many mechanisms, space, time, and stochastic processes, parameter identification is a challenge. This calls for more efficient strategies of imaging and image analysis, as well as of parameter identification in stochastic agent-based simulations.

MOTIVATION: TiQuant is a modular software tool for efficient quantification of biological tissues based on volume data obtained by biomedical image modalities. It includes a number of versatile image and volume processing chains tailored to the analysis of different tissue types which have been experimentally verified. TiQuant implements a novel method for the reconstruction of three-dimensional surfaces of biological systems, data that often cannot be obtained experimentally but which is of utmost importance for tissue modelling in systems biology. AVAILABILITY AND IMPLEMENTATION: TiQuant is freely available for non-commercial use at msysbio.com/tiquant. Windows, OSX and Linux are supported. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Isogenic cells sensing identical external signals can take markedly different decisions. Such decisions often correlate with pre-existing cell-to-cell differences in protein levels. When not neglected in signal transduction models, these differences are accounted for in a static manner, by assuming randomly distributed initial protein levels. However, this approach ignores the a priori non-trivial interplay between signal transduction and the source of this cell-to-cell variability: temporal fluctuations of protein levels in individual cells, driven by noisy synthesis and degradation. Thus, modeling protein fluctuations, rather than their consequences on the initial population heterogeneity, would set the quantitative analysis of signal transduction on firmer grounds. Adopting this dynamical view on cell-to-cell differences amounts to recast extrinsic variability into intrinsic noise. Here, we propose a generic approach to merge, in a systematic and principled manner, signal transduction models with stochastic protein turnover models. When applied to an established kinetic model of TRAIL-induced apoptosis, our approach markedly increased model prediction capabilities. One obtains a mechanistic explanation of yet-unexplained observations on fractional killing and non-trivial robust predictions of the temporal evolution of cell resistance to TRAIL in HeLa cells. Our results provide an alternative explanation to survival via induction of survival pathways since no TRAIL-induced regulations are needed and suggest that short-lived anti-apoptotic protein Mcl1 exhibit large and rare fluctuations. More generally, our results highlight the importance of accounting for stochastic protein turnover to quantitatively understand signal transduction over extended durations, and imply that fluctuations of short-lived proteins deserve particular attention.

UNLABELLED: CellSys is a modular software tool for efficient off-lattice simulation of growth and organization processes in multi-cellular systems in 2D and 3D. It implements an agent-based model that approximates cells as isotropic, elastic and adhesive objects. Cell migration is modeled by an equation of motion for each cell. The software includes many modules specifically tailored to support the simulation and analysis of virtual tissues including real-time 3D visualization and VRML 2.0 support. All cell and environment parameters can be independently varied which facilitates species specific simulations and allows for detailed analyses of growth dynamics and links between cellular and multi-cellular phenotypes. AVAILABILITY: CellSys is freely available for non-commercial use at http://msysbio.com/software/cellsys. The current version of CellSys permits the simulation of growing monolayer cultures and avascular tumor spheroids in liquid environment. Further functionality will be made available ongoing with published papers. CONTACT: [email protected]; [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The topology and function of gene regulation networks are commonly inferred from time series of gene expression levels in cell populations. This strategy is usually invalid if the gene expression in different cells of the population is not synchronous. A promising, though technically more demanding alternative is therefore to measure the gene expression levels in single cells individually. The inference of a gene regulation network requires knowledge of the gene expression levels at successive time points, at least before and after a network transition. However, owing to experimental limitations a complete determination of the precursor state is not possible. RESULTS: We investigate a strategy for the inference of gene regulatory networks from incomplete expression data based on dynamic Bayesian networks. This permits prediction of the number of experiments necessary for network inference depending on parameters including noise in the data, prior knowledge and limited attainability of initial states. Our strategy combines a gradual 'Partial Learning' approach based solely on true experimental observations for the network topology with expectation maximization for the network parameters. We illustrate our strategy by extensive computer simulations in a high-dimensional parameter space in a simulated single-cell-based example of hematopoietic stem cell commitment and in random networks of different sizes. We find that the feasibility of network inferences increases significantly with the experimental ability to force the system into different initial network states, with prior knowledge and with noise reduction. AVAILABILITY: Source code is available under: www.izbi.uni-leipzig.de/services/NetwPartLearn.html SUPPLEMENTARY INFORMATION: Supplementary Data are available at Bioinformatics online.