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A Multiscale-Multiphysics Framework for Modeling Organ-scale Liver Regrowth

Adnan Ebrahem, Jannes Hohl, Etienne Jessen, Marco F. P. ten Eikelder, Dominik Schillinger

TL;DR

The paper tackles organ-scale modeling of liver regrowth after partial hepatectomy by introducing a three-component framework that couples a multiscale perfusion model (synthetic vascular trees plus a multi-compartment homogenized flow system) with a poroelastic finite-growth model and a data-driven, hyperperfusion-driven growth evolution equation. The approach enables simulation of hyperperfusion post-resection, regrowth toward a homeostatic perfusion state, and localized hypoperfusion near orphan vessels, demonstrated on a prototypical 2D problem and a full-scale patient-specific liver with a common surgical cut. Key contributions include a detailed discretization/homogenization strategy to extract permeability tensors and intercompartmental perfusion coefficients, a quasi-static poroelastic growth formulation, and a calibrated growth law tied to measured perfusion signals. The framework provides a computational tool for planning partial liver resections, predicting regrowth dynamics, and identifying risk regions for ischemia, with potential extensions to anisotropic growth, lobule-level perfusion modeling, and patient-specific validation.

Abstract

We present a framework for modeling liver regrowth on the organ scale that is based on three components: (1) a multiscale perfusion model that combines synthetic vascular tree generation with a multi-compartment homogenized flow model, including a homogenization procedure to obtain effective parameters; (2) a poroelastic finite growth model that acts on all compartments and the synthetic vascular tree structure; (3) an evolution equation for the local volumetric growth factor, driven by the homogenized flow rate into the microcirculation as a measure of local hyperperfusion and well-suited for calibration with available data. We apply our modeling framework to a prototypical benchmark and a full-scale patient-specific liver, for which we assume a common surgical cut. Our simulation results demonstrate that our model represents hyperperfusion as a consequence of partial resection and accounts for its reduction towards a homeostatic perfusion state, exhibiting overall regrowth dynamics that correspond well with clinical observations. In addition, our results show that our model also captures local hypoperfusion in the vicinity of orphan vessels, a key requirement for the prediction of ischemia or the preoperative identification of suitable cut patterns.

A Multiscale-Multiphysics Framework for Modeling Organ-scale Liver Regrowth

TL;DR

The paper tackles organ-scale modeling of liver regrowth after partial hepatectomy by introducing a three-component framework that couples a multiscale perfusion model (synthetic vascular trees plus a multi-compartment homogenized flow system) with a poroelastic finite-growth model and a data-driven, hyperperfusion-driven growth evolution equation. The approach enables simulation of hyperperfusion post-resection, regrowth toward a homeostatic perfusion state, and localized hypoperfusion near orphan vessels, demonstrated on a prototypical 2D problem and a full-scale patient-specific liver with a common surgical cut. Key contributions include a detailed discretization/homogenization strategy to extract permeability tensors and intercompartmental perfusion coefficients, a quasi-static poroelastic growth formulation, and a calibrated growth law tied to measured perfusion signals. The framework provides a computational tool for planning partial liver resections, predicting regrowth dynamics, and identifying risk regions for ischemia, with potential extensions to anisotropic growth, lobule-level perfusion modeling, and patient-specific validation.

Abstract

We present a framework for modeling liver regrowth on the organ scale that is based on three components: (1) a multiscale perfusion model that combines synthetic vascular tree generation with a multi-compartment homogenized flow model, including a homogenization procedure to obtain effective parameters; (2) a poroelastic finite growth model that acts on all compartments and the synthetic vascular tree structure; (3) an evolution equation for the local volumetric growth factor, driven by the homogenized flow rate into the microcirculation as a measure of local hyperperfusion and well-suited for calibration with available data. We apply our modeling framework to a prototypical benchmark and a full-scale patient-specific liver, for which we assume a common surgical cut. Our simulation results demonstrate that our model represents hyperperfusion as a consequence of partial resection and accounts for its reduction towards a homeostatic perfusion state, exhibiting overall regrowth dynamics that correspond well with clinical observations. In addition, our results show that our model also captures local hypoperfusion in the vicinity of orphan vessels, a key requirement for the prediction of ischemia or the preoperative identification of suitable cut patterns.

Paper Structure

This paper contains 39 sections, 53 equations, 25 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Physiological mechanisms of liver regrowth across different scales
  3. Multiscale vasculature and liver perfusion
  4. Liver regeneration and driving mechanisms at the microscale
  5. Fundamental concepts for modeling hyperperfusion-driven liver regrowth
  6. A multi-compartment perfusion model
  7. Discrete non-intersecting vascular trees for blood supply and drainage
  8. Mathematical formulation
  9. Algorithmic framework and computer implementation
  10. Homogenization of blood flow through hierarchical vascular networks
  11. Multi-compartment homogenized flow equations
  12. Estimation of permeability tensors and perfusion coefficients
  13. Compartmentalization strategy
  14. Averaging volume size and vessel radius threshold
  15. Prototypical model problem in 2D
  16. ...and 24 more sections

Figures (25)

  • Figure 1: Multiscale liver vasculature (organism- and lobule-scale pictures from RefDebbautDiss, sinusoid-scale picture from RefSinusoid).
  • Figure 2: Liver size regulation after surgical resection (picture adapted from grosse2021role).
  • Figure 3: Concept for modeling liver regrowth.
  • Figure 4: Model problem: supplying (in red) and draining (in blue) vascular trees.
  • Figure 5: Averaging volume at spatial position $\mathbf{x}$.
  • ...and 20 more figures

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3