Modeling of the contrast-enhanced perfusion test in liver based on the multi-compartment flow in porous media

The paper deals with modeling the liver perfusion intended to improve quantitative analysis of the tissue scans provided by the contrast-enhanced computed tomography (CT). For this purpose, we developed a model of dynamic transport of the contrast fluid through the hierarchies of the perfusion trees. Conceptually, computed time-space distributions of the so-called tissue density can be compared with the measured data obtained from CT; such a modeling feedback can be used for model parameter identification. The blood flow is characterized at several scales for which different models are used. Flows in upper hierarchies represented by larger branching vessels are described using simple 1D models based on the Bernoulli equation extended by correction terms to respect the local pressure losses. To describe flows in smaller vessels and in the tissue parenchyma, we propose a 3D continuum model of porous medium defined in terms of hierarchically matched compartments characterized by hydraulic permeabilities. The 1D models corresponding to the portal and hepatic veins are coupled with the 3D model through point sources, or sinks. The contrast fluid saturation is governed by transport equations adapted for the 1D and 3D flow models. The complex perfusion model has been implemented using the finite element and finite volume methods. We report numerical examples computed for anatomically relevant geometries of the liver organ and of the principal vascular trees. The simulated tissue density corresponding to the CT examination output reflects a pathology modeled as a localized permeability deficiency.

[1]  Rebecca Fahrig,et al.  Deconvolution-Based CT and MR Brain Perfusion Measurement: Theoretical Model Revisited and Practical Implementation Details , 2011, Int. J. Biomed. Imaging.

[2]  Paul R Carney,et al.  Voxelized Model of Brain Infusion That Accounts for Small Feature Fissures: Comparison With Magnetic Resonance Tracer Studies. , 2016, Journal of biomechanical engineering.

[3]  J Racek,et al.  Immediately preoperative use of biological therapy does not influence liver regeneration after large resection--porcine experimental model with monoclonal antibody against epidermal growth factor. , 2012, In vivo.

[4]  P. Segers,et al.  Perfusion characteristics of the human hepatic microcirculation based on three-dimensional reconstructions and computational fluid dynamic analysis. , 2012, Journal of biomechanical engineering.

[5]  Vladimír Lukes,et al.  Numerical simulation of liver perfusion: from CT scans to FE model , 2014, ArXiv.

[6]  Robert Cimrman.  SfePy - Write Your Own FE Application , 2014, ArXiv.

[7]  Nazim Haouchine,et al.  Patient-Specific Biomechanical Modeling for Guidance During Minimally-Invasive Hepatic Surgery , 2015, Annals of Biomedical Engineering.

[8]  Ralph E. Showalter,et al.  Double-diffusion models from a highly-heterogeneous medium☆ , 2004 .

[9]  Tobias Preusser,et al.  Analysis and Algorithmic Generation of Hepatic Vascular Systems , 2012, International journal of hepatology.

[10]  Petra Kochová,et al.  Stereological quantification of microvessels using semiautomated evaluation of X-ray microtomography of hepatic vascular corrosion casts , 2016, International Journal of Computer Assisted Radiology and Surgery.

[11]  T. Sochi,et al.  A computationally efficient framework for the simulation of cardiac perfusion using a multi‐compartment Darcy porous‐media flow model , 2013, International journal for numerical methods in biomedical engineering.

[12]  A. Bonfiglio,et al.  Mathematical modeling of the circulation in the liver lobule. , 2010, Journal of biomechanical engineering.

[13]  Stanley Middleman,et al.  Flow of Viscoelastic Fluids through Porous Media , 1967 .

[14]  Jack Lee,et al.  Parameterisation of multi-scale continuum perfusion models from discrete vascular networks , 2012, Medical & Biological Engineering & Computing.

[15]  J M Huyghe,et al.  Mechanical blood-tissue interaction in contracting muscles: a model study. , 1998, Journal of biomechanics.

[16]  Salah Naili,et al.  Multiscale modeling of a fluid saturated medium with double porosity: Relevance to the compact bone , 2012 .

[17]  Richard Palek,et al.  Monoclonal antibody against transforming growth factor Beta 1 does not influence liver regeneration after resection in large animal experiments. , 2015, In vivo.

[18]  Jmrj Jacques Huyghe,et al.  Finite deformation theory of hierarchically arranged porous solids - I. Balance of mass and momentum. , 1995 .

[19]  Alfio Quarteroni,et al.  Cardiovascular mathematics : modeling and simulation of the circulatory system , 2009 .

[20]  Eduard Rohan,et al.  On modelling the parallel diffusion flow in deforming porous media , 2007, Math. Comput. Simul..

[21]  C. Dangelo,et al.  Multiscale modelling of metabolism and transport phenomena in living tissues , 2007 .

[22]  T. Ryba,et al.  An automatic liver segmentation algorithm based on grow cut and level sets , 2013, Pattern Recognition and Image Analysis.

[23]  C. Pozrikidis,et al.  Numerical simulation of blood and interstitial flow through a solid tumor , 2010, Journal of mathematical biology.

[24]  Jmrj Jacques Huyghe,et al.  Finite deformation theory of hierarchically arranged porous solids. II: Constitutive behaviour , 1995 .

[25]  Milena Králíčková,et al.  Segmental and age differences in the elastin network, collagen, and smooth muscle phenotype in the tunica media of the porcine aorta. , 2015, Annals of anatomy = Anatomischer Anzeiger : official organ of the Anatomische Gesellschaft.

[26]  Karl J. Friston,et al.  Bayesian estimation of cerebral perfusion using a physiological model of microvasculature , 2006, NeuroImage.

[27]  H. Holzhütter,et al.  Modeling function–perfusion behavior in liver lobules including tissue, blood, glucose, lactate and glycogen by use of a coupled two-scale PDE–ODE approach , 2014, Biomechanics and Modeling in Mechanobiology.

[28]  Jan Bruha,et al.  Portal vein embolisation with application of haematopoietic stem cells in patients with primarily or non-resectable colorectal liver metastases. , 2014, Anticancer research.

[29]  Roland Bammer,et al.  Revision of the theory of tracer transport and the convolution model of dynamic contrast enhanced magnetic resonance imaging , 2007, Journal of mathematical biology.

[30]  B. V. Van Beers,et al.  Non-invasive quantification of liver perfusion with dynamic computed tomography and a dual-input one-compartmental model. , 2000, Clinical science.

[31]  S. Whitaker.  Diffusion and dispersion in porous media , 1967 .

[32]  Eduard Rohan,et al.  COMPLEX HIERARCHICAL MODELING OF THE DYNAMIC PERFUSION TEST : APPLICATION TO LIVER , 2013 .

[33]  Younane N. Abousleiman,et al.  Generalized Biot's theory and Mandel's problem of multiple‐porosity and multiple‐permeability poroelasticity , 2014 .

[34]  Horst K. Hahn,et al.  Global Constructive Optimization of Vascular Systems , 2010 .

[35]  C. Ho,et al.  Mathematical model of blood and interstitial flow and lymph production in the liver , 2013, Biomechanics and Modeling in Mechanobiology.

[36]  K. Lettmann,et al.  The importance of liver microcirculation in promoting autoimmune hepatitis via maintaining an inflammatory cytokine milieu--a mathematical model study. , 2014, Journal of theoretical biology.

[37]  Jd Jan Janssen,et al.  Finite element analysis of blood flow through biological tissue , 1997 .

[38]  Manuel Dierick,et al.  Analyzing the human liver vascular architecture by combining vascular corrosion casting and micro‐CT scanning: a feasibility study , 2014, Journal of anatomy.

[39]  Ondřej Bublík,et al.  A comparative study of 1D and 3D hemodynamics in patient-specific hepatic portal vein networks , 2014 .

[40]  Rebecca J. Shipley,et al.  Multiscale Modelling of Fluid and Drug Transport in Vascular Tumours , 2010, Bulletin of mathematical biology.

[41]  Patrick Jenny,et al.  Vascular Graph Model to Simulate the Cerebral Blood Flow in Realistic Vascular Networks , 2009, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[42]  Stephane Cotin,et al.  Modeling and Real-Time Simulation of a Vascularized Liver Tissue , 2012, MICCAI.

[43]  Eduard Rohan,et al.  Two-Scale Modeling of Tissue Perfusion Problem Using Homogenization of Dual Porous Media , 2010 .

[44]  Johannes Reichold.  Cerebral blood flow modeling in realistic cortical microvascular networks , 2011 .

[45]  Marek Kretowski,et al.  Multiscale Model of Liver DCE-MRI Towards a Better Understanding of Tumor Complexity , 2010, IEEE Transactions on Medical Imaging.

[46]  Eduard Rohan,et al.  CT based identification problem for the multicompartment model of blood perfusion , 2015 .

[47]  O. Dirsch,et al.  A biphasic model for sinusoidal liver perfusion remodeling after outflow obstruction , 2010, Biomechanics and modeling in mechanobiology.

[48]  J. Hogg.  Magnetic resonance imaging. , 1994, Journal of the Royal Naval Medical Service.

[49]  Gábor Székely,et al.  Tissue metabolism driven arterial tree generation , 2012, Medical Image Anal..

[50]  W A Hollis.  Tissue Metabolism , 1921, Nature.

[51]  R. E. Showaltera,et al.  Double-diffusion models from a highly-heterogeneous medium ✩ , 2004 .

[52]  Tong San Koh,et al.  Cerebral perfusion mapping using a robust and efficient method for deconvolution analysis of dynamic contrast-enhanced images , 2006, NeuroImage.