Acoustic waves propagation in biological tissues has been studied usually in the context of diagnostic methods, such as the elastography. In microfluidic devices, nonlinear acoustic phenomena, namely the acoustic radiation, acoustic streaming are employed to manipulate particles and actuate fluid flow. These principles have attracted much interest of the research focused on developing new tissue engineering technologies since the acoustic wave are highly biocompatible, providing a non-contact controlable handle to manipulate bioparticles, or cells.
The paper reports on development of multiscale models of the acoustic waves and related phenomena in porous fluid saturated structures representing perfused tissues, or biomaterial structures intended for fluid suspensions and particle transport due to acoustic power, taking into account nonlinear interactions between to deforming pores and particles.
We focus on modelling two important phenomena induced in porous structures by acoustic waves: the peristaltic deformation and the acoustic streaming. Both can propel the fluid and particle transport, influencing interaction between particles and pore walls. This problem is motivated by the recellularization in decellularized tissue scaffolds, an important progressive tissue engineering technology .
The fluid-structure interaction problem is imposed in elastic scaffolds. To capture both the peristaltic deformation and acoustic streaming in response to propagating acoustic wave, nonlinearities originating in the divergence of the Reynolds stress, the advection acceleration term in the Navier Stokes equation, and the nonlinearity generated deforming pore geometry must be retained. The perturbation with respect to a small parameter proportional to the inverse Strouhal number is applied. This yields the first and the second order sub-problem enabling to linearize the Navier-Stokes equations governing the barotropic viscous fluid dynamics in periodic scaffolds. Subsequent treatment by the asymptotic homogenization leads to a two scale problem where the macroscopic model of the porous medium describes the acoustic streaming. The vibro-acoustic analysis of the first order problem yields the streaming source term for the second order problem which attains the form of the Biot-type medium.
To respect the peristaltic deformation wave in the homogenized model derived in the fixed reference configuration, influence of the deforming channel geometry on the homogenized coefficients must be considered. We use the linear expansions of the permeability and other poroelastic coefficients of the homogenized model; these are based on the sensitivity analysis of the homogenized coefficients with respect to macroscopic strain and pressure which determine the deformation of local microconfigurations.
To account for the acoustic waves influence on the propulsion of cells in the tissue scaffolds, we consider microstructures with trains of inclusions flowing in pores. Using simplified assumption and additional kinematic constraints, the contact of cells with pore walls is avoided. The two-scale homogenization-based modelling provides analytical and computational tools to simulate the influence of the bulk acoustic waves on the microflow of the biological fluids in tissues. In particular, the presented research is aimed at providing a computational feedback to experimental studies of the acoustic waves impact on the tissue scaffolds recellularization. The models are implemented in our in-house developed finite element based software SfePy. Numerical illustrations are presented.

Many liver diseases display an increasing incidence, whereby hepatocellular carcinoma rank 4^th in mortality among cancers. A deep understanding of liver functioning and disease requires to study the complex orchestration of processes at many levels of organization, which favor a systems medicine approach, where experiments, clinical data acquisition and computational modeling are integrated.

The computational models are able to verify or falsify hypothesized mechanisms and already led to the identification of unrecognized mechanisms that could be used to propose new therapeutic strategies [Ghallab et. al., J. Hepat. 2016]. Along the same line of argument, a systems medicine approach recently questioned the consensus mechanism of bile transport by flow in bile canaliculi, the smallest bile conduits in the liver [Vartak et. al. Hepatology 2020], and demonstrated that novel experimental results were compatible with diffusive transport alone. The latter work focused on transport in the bile canaliculi network but did not take into account the entire pathway of bile salts from the liver entrance into the liver capillaries (sinusoids), through the hepatocytes, their excretion into the bile canaliculi and then their flux to the bile ducts from where they are transported to the gall bladder.

Here we will present the necessary modeling components for such a model at the level of liver tissue micro-architecture, from which some have recently been established, as, e.g., blood hemodynamics in sinusoids [Boissier et. al. 2021], and flux of metabolites into and out of hepatocytes [Dichamp et. al., 2023]. The works vary a number of parameters, e.g., in [Boissier et. al.] different numerical algorithms are compared with regard to accuracy and computational efficiency. For clinical relevance, such an entire circulation model shall study the effect of heterogeneity, and permit scalability.

Given the complexity, these requirements may make such models computationally inefficient or even infeasible. To overcome this, various model reduction techniques can be applied, that partially depend on the nature of available data.

We present recent research and first steps towards a proof-of concept model of fluorescent marker transport in the blood-hepatocyte-bile system at the level of liver micro-architecture displaying each individual cell. Starting from general 3D model of mixture flow and transport in each part of the system, we present a strategy for reducing the governing equations into 1D. We then follow by formulating a mathematical description of exchanges occurring at compartment interfaces. Numerical solutions of the model are presented for cases corresponding to used experimental setups. Even with the rather oversimplified assumption on the system geometry (1D) in the prototype model, we are able to capture qualitatively the zonation features that are observed experimentally in mice.

In the future, this model will be refined to explain image data on vascular and biliary networks obtained in intravital imaging. An extension towards upscaling could start from interpreting the parameters of the model at cellular resolution as effective values of their real-world counterparts and go to more complex techniques, such as homogenization (cf. Rohan et al. [2021a], Rohan et al. [2021b]).

The flexoelectricity corresponds to the couplings between the electric polarization of a solid and strain gradient. Identified in the sixties, this nanoscopic electromechanical interaction presents two main attractive features. Firstly, this phenomenon may exist in materials with centrosymmetry, contrary to the piezoelectric effect. Secondly, strain gradient effects being inversely proportional to the medium size, the scale of flexoelectricity is then rather large. Flexoelectricity still presents challenging experimental and theoretical issues [1] and offers promising avenues of research and promises as new therapies in the context of regenerative medicine [2]. Up to now, recent advances in the understanding of bone physiology point out the possible relevance of flexoelectricity effects in bone. Indeed, putting forward the seminal studies of Williams [3], Vasquez-Sancho et al. [4] experimentally showed that part of bone electricity may be due to the bone’s mineral flexoelectric property in addition to already described collagen’s piezoelectricity and stress-generated streaming potentials. This may explain the in vitro observation of osteoblasts (bone forming cells) activity near a crack in pure hydroxyapatite (HAP), without the presence of collagen (COL) [5]. Since this electrical polarization and its consequences in interstitial fluid flow within bone is a key issue in its adaptation and repair [6,7], the high potential of smart flexoelectric tailored biomaterials in the highly competitive osteo-articular tissue engineering domain has to be investigated.

In this context, this study aims at correlating the crack-induced flexoelectric effect combined to collagen piezoelectricity on the bone cell behaviour in its fluid environment. It is thus necessary to connect the microscopic phenomena in the vicinity of bone cells to bone tissue structures. Thus, a trans-scale approach (homogenization) is carried out to propagate nanoscopic electromechanical consequences at the upper scale where the bone modelling units (BMU) activity occurs. In particular, we derive from this multiscale approach the coupled phenomena governing the osteocytic sensing and cell-to-cell communication known to drive BMU. This study potentially may have in a longer term a great technological impact with the design of novel biomaterials and technological solutions to stimulate bone repair.

[1] Chae et al., ACS Appl Bio Mater, 1: 936, 2018.

[2] Wang et al., Prog Mat Sci, 106:100570, 2019.

[3] Williams & Breger, J. Biomech, 8:407, 1975.

[4] Vasquez-Sancho et al., Adv Mater, 30:1705316, 2018.

[5] Shu et al., Mater Sci Eng C, 44:191, 2014.

[6] Lemaire et al., J Mech B Biomed Mat, 4:909, 2011.

[7] Lemaire et al., Int J Num Meth Biomed Eng, 29:1223, 2013.