Lars Ole Schwen

Spatio-temporal simulation of first pass drug perfusion in the liver.

The liver is the central organ for detoxification of xenobiotics in the body. In pharmacokinetic modeling, hepatic metabolization capacity is typically quantified as hepatic clearance computed as degradation in well-stirred compartments. This is an accurate mechanistic description once a quasi-equilibrium between blood and surrounding tissue is established. However, this model structure cannot be used to simulate spatio-temporal distribution during the first instants after drug injection. In this paper, we introduce a new spatially resolved model to simulate first pass perfusion of compounds within the naive liver. The model is based on vascular structures obtained from computed tomography as well as physiologically based mass transfer descriptions obtained from pharmacokinetic modeling. The physiological architecture of hepatic tissue in our model is governed by both vascular geometry and the composition of the connecting hepatic tissue. In particular, we here consider locally distributed mass flow in liver tissue instead of considering well-stirred compartments. Experimentally, the model structure corresponds to an isolated perfused liver and provides an ideal platform to address first pass effects and questions of hepatic heterogeneity. The model was evaluated for three exemplary compounds covering key aspects of perfusion, distribution and metabolization within the liver. As pathophysiological states we considered the influence of steatosis and carbon tetrachloride-induced liver necrosis on total hepatic distribution and metabolic capacity. Notably, we found that our computational predictions are in qualitative agreement with previously published experimental data. The simulation results provide an unprecedented level of detail in compound concentration profiles during first pass perfusion, both spatio-temporally in liver tissue itself and temporally in the outflowing blood. We expect our model to be the foundation of further spatially resolved models of the liver in the future.

GPU-Accelerated Sparse Matrix-Matrix Multiplication by Iterative Row Merging

We present an algorithm for general sparse matrix-matrix multiplication (SpGEMM) on many-core architectures, such as GPUs. SpGEMM is implemented by iterative row merging, similar to merge sort, exc...

Analysis and Algorithmic Generation of Hepatic Vascular Systems

A proper geometric model of the vascular systems in the liver is crucial for modeling blood flow, the connection between the organ and the rest of the organism. In vivo imaging does not provide sufficient details, so an algorithmic concept for extending measured vascular tree data is needed such that geometrically realistic structures can be generated. We develop a quantification of similarity in terms of different geometric features. This involves topological Strahler ordering of the vascular trees, statistical testing, and averaging. Invariant features are identified in human clinical in vivo CT scans. Results of the existing “Constrained Constructive Optimization” algorithm are compared to real vascular tree data. To improve bifurcation angles in the algorithmic results, we implement a postprocessing step calibrated to the measured features. This framework is finally applied to generate realistic additional details in a patient-specific hepatic vascular tree data set.

Representative Sinusoids for Hepatic Four-Scale Pharmacokinetics Simulations

The mammalian liver plays a key role for metabolism and detoxification of xenobiotics in the body. The corresponding biochemical processes are typically subject to spatial variations at different length scales. Zonal enzyme expression along sinusoids leads to zonated metabolization already in the healthy state. Pathological states of the liver may involve liver cells affected in a zonated manner or heterogeneously across the whole organ. This spatial heterogeneity, however, cannot be described by most computational models which usually consider the liver as a homogeneous, well-stirred organ. The goal of this article is to present a methodology to extend whole-body pharmacokinetics models by a detailed liver model, combining different modeling approaches from the literature. This approach results in an integrated four-scale model, from single cells via sinusoids and the organ to the whole organism, capable of mechanistically representing metabolization inhomogeneity in livers at different spatial scales. Moreover, the model shows circulatory mixing effects due to a delayed recirculation through the surrounding organism. To show that this approach is generally applicable for different physiological processes, we show three applications as proofs of concept, covering a range of species, compounds, and diseased states: clearance of midazolam in steatotic human livers, clearance of caffeine in mouse livers regenerating from necrosis, and a parameter study on the impact of different cell entities on insulin uptake in mouse livers. The examples illustrate how variations only discernible at the local scale influence substance distribution in the plasma at the whole-body level. In particular, our results show that simultaneously considering variations at all relevant spatial scales may be necessary to understand their impact on observations at the organism scale.

Zonated quantification of steatosis in an entire mouse liver

Many physiological processes and pathological conditions in livers are spatially heterogeneous, forming patterns at the lobular length scale or varying across the organ. Steatosis, a common liver disease characterized by lipids accumulating in hepatocytes, exhibits heterogeneity at both these spatial scales. The main goal of the present study was to provide a method for zonated quantification of the steatosis patterns found in an entire mouse liver. As an example application, the results were employed in a pharmacokinetics simulation. For the analysis, an automatic detection of the lipid vacuoles was used in multiple slides of histological serial sections covering an entire mouse liver. Lobuli were determined semi-automatically and zones were defined within the lobuli. Subsequently, the lipid content of each zone was computed. The steatosis patterns were found to be predominantly periportal, with a notable organ-scale heterogeneity. The analysis provides a quantitative description of the extent of steatosis in unprecedented detail. The resulting steatosis patterns were successfully used as a perturbation to the liver as part of an exemplary whole-body pharmacokinetics simulation for the antitussive drug dextromethorphan. The zonated quantification is also applicable to other pathological conditions that can be detected in histological images. Besides being a descriptive research tool, this quantification could perspectively complement diagnosis based on visual assessment of histological images.

Physiologically-based modelling in mice suggests an aggravated loss of clearance capacity after toxic liver damage

Diseases and toxins may lead to death of active liver tissue, resulting in a loss of total clearance capacity at the whole-body level. However, it remains difficult to study, whether the loss of metabolizing tissue is sufficient to explain loss of metabolic capacity of the liver or whether the surviving tissue undergoes an adaptive response to compensate the loss. To understand the cellular impact of toxic liver damage in an in vivo situation, we here used physiologically-based pharmacokinetic modelling to investigate pharmacokinetics of a specifically designed drug cocktail at three different sampling sites of the body in healthy mice and mice treated with carbon tetrachloride (CCl4). Liver zonation was explicitly quantified in the models through immunostaining of cytochrome P450s enzymes. Comparative analyses between the simulated decrease in clearance capacity and the experimentally measured loss in tissue volume indicated that CCl4-induced impairment of metabolic functions goes beyond the mere loss of metabolically active tissue. The here established integrative modelling strategy hence provides mechanistic insights into functional consequences of toxic liver damage in an in vivo situation, which would not have been accessible by conventional methods.

Algorithmically generated rodent hepatic vascular trees in arbitrary detail

Physiologically realistic geometric models of the vasculature in the liver are indispensable for modelling hepatic blood flow, the main connection between the liver and the organism. Current in vivo imaging techniques do not provide sufficiently detailed vascular trees for many simulation applications, so it is necessary to use algorithmic refinement methods. The method of Constrained Constructive Optimization (CCO) (Schreiner et al., 2006) is well suited for this purpose. Its results after calibration have been previously compared to experimentally acquired human vascular trees (Schwen and Preusser, 2012). The goal of this paper is to extend this calibration to the case of rodents (mice and rats), the most commonly used animal models in liver research. Based on in vivo and ex vivo micro-CT scans of rodent livers and their vasculature, we performed an analysis of various geometric features of the vascular trees. Starting from pruned versions of the original vascular trees, we applied the CCO procedure and compared these algorithmic results to the original vascular trees using a suitable similarity measure. The calibration of the postprocessing improved the algorithmic results compared to those obtained using standard CCO. In terms of angular features, the average similarity increased from 0.27 to 0.61, improving the total similarity from 0.28 to 0.40. Finally, we applied the calibrated algorithm to refine measured vascular trees to the (higher) level of detail desired for specific applications. Having successfully adapted the CCO algorithm to the rodent model organism, the resulting individual-specific refined hepatic vascular trees can now be used for advanced modeling involving, e.g., detailed blood flow simulations.

Statistical osteoporosis models using composite finite elements: A parameter study

Osteoporosis is a widely spread disease with severe consequences for patients and high costs for health care systems. The disease is characterised by a loss of bone mass which induces a loss of mechanical performance and structural integrity. It was found that transverse trabeculae are thinned and perforated while vertical trabeculae stay intact. For understanding these phenomena and the mechanisms leading to fractures of trabecular bone due to osteoporosis, numerous researchers employ micro-finite element models. To avoid disadvantages in setting up classical finite element models, composite finite elements (CFE) can be used. The aim of the study is to test the potential of CFE. For that, a parameter study on numerical lattice samples with statistically simulated, simplified osteoporosis is performed. These samples are subjected to compression and shear loading. Results show that the biggest drop of compressive stiffness is reached for transverse isotropic structures losing 32% of the trabeculae (minus 89.8% stiffness). The biggest drop in shear stiffness is found for an isotropic structure also losing 32% of the trabeculae (minus 67.3% stiffness). The study indicates that losing trabeculae leads to a worse drop of macroscopic stiffness than thinning of trabeculae. The results further demonstrate the advantages of CFEs for simulating micro-structured samples.

Intrahepatic Vascular Anatomy in Rats and Mice—Variations and Surgical Implications

Introduction The intra-hepatic vascular anatomy in rodents, its variations and corresponding supplying and draining territories in respect to the lobar structure of the liver have not been described. We performed a detailed anatomical imaging study in rats and mice to allow for further refinement of experimental surgical approaches. Methods LEWIS-Rats and C57Bl/6N-Mice were subjected to ex-vivo imaging using μCT. The image data were used for semi-automated segmentation to extract the hepatic vascular tree as prerequisite for 3D visualization. The underlying vascular anatomy was reconstructed, analysed and used for determining hepatic vascular territories. Results The four major liver lobes have their own lobar portal supply and hepatic drainage territories. In contrast, the paracaval liver is supplied by various small branches from right and caudate portal veins and drains directly into the vena cava. Variations in hepatic vascular anatomy were observed in terms of branching pattern and distance of branches to each other. The portal vein anatomy is more variable than the hepatic vein anatomy. Surgically relevant variations were primarily observed in portal venous supply. Conclusions For the first time the key variations of intrahepatic vascular anatomy in mice and rats and their surgical implications were described. We showed that lobar borders of the liver do not always match vascular territorial borders. These findings are of importance for the design of new surgical procedures and for understanding eventual complications following hepatic surgery.

Validation of composite finite elements efficiently simulating elasticity of trabecular bone

Patient-specific analyses of the mechanical properties of bones become increasingly important for the management of patients with osteoporosis. The potential of composite finite elements (CFEs), a novel FE technique, to assess the apparent stiffness of vertebral trabecular bone is investigated in this study. Segmented volumes of cylindrical specimens of trabecular bone are compared to measured volumes. Elasticity under uniaxial loading conditions is simulated; apparent stiffnesses are compared to experimentally determined values. Computational efficiency is assessed and recommendations for simulation parameters are given. Validating apparent uniaxial stiffnesses results in concordance correlation coefficients 0.69 ≤ r𝒸 ≤ 0.92 for resolutions finer than 168 μm, and an average error of 5.8% between experimental and numerical results at 24 μm resolution. As an application, the code was used to compute local, macroscopic stiffness tensors for the trabecular structure of a lumbar vertebra. The presented technique allows for computing stiffness using smooth FE meshes at resolutions that are well achievable in peripheral high resolution quantitative CT. Therefore, CFEs could be a valuable tool for the patient-specific assessment of bone stiffness.