Theoretical modeling of fluid flow in cellular biological media: An overview

Generative models of morphogenesis in developmental biology

Understanding the mechanism by which cells coordinate their differentiation and migration is critical to our understanding of many fundamental processes such as wound healing, disease progression, and developmental biology. Mathematical models have been an essential tool for testing and developing our understanding, such as models of cells as soft spherical particles, reaction-diffusion systems that couple cell movement to environmental factors, and multi-scale multi-physics simulations that combine bottom-up rule-based models with continuum laws. However, mathematical models can often be loosely related to data or have so many parameters that model behaviour is weakly constrained. Recent methods in machine learning introduce new means by which models can be derived and deployed. In this review, we discuss examples of mathematical models of aspects of developmental biology, such as cell migration, and how these models can be combined with these recent machine learning methods.

Low-Field Nuclear Magnetic Resonance Characteristics of Biofilm Development Process

To in situ and noninvasively monitor the biofilm development process by low-field nuclear magnetic resonance (NMR), experiments should be made to determine the mechanisms responsible for the T₂ signals of biofilm growth. In this paper, biofilms were cultivated in both fluid media and saturated porous media. T₂ relaxation for each sample was measured to investigate the contribution of the related processes to T₂ relaxation signals. In addition, OD values of bacterial cell suspensions were measured to provide the relative number of bacterial cells. We also obtained SEM photos of the biofilms after vacuum freeze-drying the pure sand and the sand with biofilm formation to confirm the space within the biofilm matrix and identify the existence of biofilm formation. The T₂ relaxation distribution is strongly dependent on the density of the bacterial cells suspended in the fluid and the stage of biofilm development. The peak time and the peak percentage can be used as indicators of the biofilm growth states.

Visualizing, quantifying, and controlling local hydrodynamic effects on biofilm accumulation in complex flow paths

Complex flow paths (CFPs) are commonly applied in precision equipment to accurately supply controllable fluids with designed structures. However, the presence of biofilms in CFPs causes quite a few unwanted issues, such as bio-erosion, clogging, or even health risks. To date, visualizing and quantifying the interaction between biofilm distribution and local hydrodynamics remains difficult, and the mechanism during the process is unclear. In this paper, the remodeling simulation method (3D industrial computed tomography scanning-inverse modeling-numerical simulation) and 16S rRNA high-throughput sequencing were integrated. The results indicated that local hydrodynamic characteristics significantly affected biofilm thicknesses on CFP surfaces (relative differences of 41.3-71.2%), which inversely influenced the local turbulence intensity. The average biofilm thicknesses exhibited a significant quadratic correlation with the near-wall hydraulic shear forces (r > 0.72, p < 0.05), and the biofilm reached a maximum thickness at 0.36-0.45 Pa. On the other hand, the near-wall hydraulic shear forces not only affected microbial community characteristics of biofilms, but they also influenced the number of microorganisms involved, which determined the biofilm accumulation thereafter. The PHYLUM Firmicutes and Proteobacteria were the dominant bacteria during the process. The results obtained in this paper could provide practical conceptions for the targeted control of biofilms and put forward more efficient controlling methods in commonly applied CFP systems.

Incorporating Cellular Stochasticity in Solid-Fluid Mixture Biofilm Models

The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses, which determine the overall evolution. Incorporating stochastic cellular behavior in macroscopic models of biological media is a challenging task. Herein, we propose hybrid models for bacterial biofilm growth, which couple a two phase solid/fluid mixture description of mechanical and chemical fields with a dynamic energy budget-based cellular automata treatment of bacterial activity. Thin film and plate approximations for the relevant interfaces allow us to obtain numerical solutions exhibiting behaviors observed in experiments, such as accelerated spread due to water intake from the environment, wrinkle formation, undulated contour development, and the appearance of inhomogeneous distributions of differentiated bacteria performing varied tasks.

Effect of rotation on wave propagation through a poroelastic wet bone with cavity

Purpose

The purpose of this paper is to investigate the wave propagation of wave in an infinite poroelastic cylindrical bone. The dynamic behavior of a wet long bone that has been modeled as a piezoelectric hollow cylinder of crystal class 6 is investigated.

Design/methodology/approach

An exact closed form solution is presented by employing an analytical procedure. The frequency equation for poroelastic bone is obtained when the boundaries are stress free and is examined numerically.

Findings

The study of wave propagation over a continuous medium is of practical importance in the field of engineering, medicine and bio-engineering. Application of the poroelastic materials in medicinal fields such as orthopedics, dental and cardiovascular is well known. In orthopedics, wave propagation over bone is used in monitoring the rate of fracture healing. There are two types of osseous tissue, such as cancellous or trabecular and compact or cortical bone, which are of different materials, with respect to their mechanical behavior.

Originality/value

The frequencies are calculated for poroelastic bone for various values for different values of rotation, angular velocity and density. In wet bone little velocity dispersion was observed, in contrast to the results of earlier studies on wet bone. Large values of attenuation were observed. Such a model would in particular be useful in large-scale parametric studies of bone mechanical response.

Cardiopulmonary responses to maximal aerobic exercise in patients with cystic fibrosis

Cystic fibrosis (CF) is a debilitating chronic condition, which requires complex and expensive disease management. Exercise has now been recognised as a critical factor in improving health and quality of life in patients with CF. Hence, cardiopulmonary exercise testing (CPET) is used to determine aerobic fitness of young patients as part of the clinical management of CF. However, at present there is a lack of conclusive evidence for one limiting system of aerobic fitness for CF patients at individual patient level. Here, we perform detailed data analysis that allows us to identify important systems-level factors that affect aerobic fitness. We use patients’ data and principal component analysis to confirm the dependence of CPET performance on variables associated with ventilation and metabolic rates of oxygen consumption. We find that the time at which participants cross the gas exchange threshold (GET) is well correlated with their overall performance. Furthermore, we propose a predictive modelling framework that captures the relationship between ventilatory dynamics, lung capacity and function and performance in CPET within a group of children and adolescents with CF. Specifically, we show that using Gaussian processes (GP) we can predict GET at the individual patient level with reasonable accuracy given the small sample size of the available group of patients. We conclude by presenting an example and future perspectives for improving and extending the proposed framework. The modelling and analysis have the potential to pave the way to designing personalised exercise programmes that are tailored to specific individual needs relative to patient’s treatment therapies.

Dynamic in vitro models for tumor tissue engineering

Cancer research uses in vitro studies for controllable analysis of tumor behavior and preclinical testing of therapeutics. Shortcomings of basic cell culture systems in recreating in vivo interactions have driven the development of more efficient and biomimetic in vitro environments for cancer research. Assimilation of certain developments in tissue engineering will accelerate and improve the design of these environments. With the continual improvement of the tumor engineering field, the next step is towards macroscopic systems such as scaffold-supported, flow-perfused macroscale tumor bioreactors. Surface modifications of synthetic scaffolds allow for targeted cell adhesion and improved ECM development. Flow perfusion has emerged as means to expose cancerous tissues to critical biomechanical forces for tumor progression while simultaneously improving nutrient and waste transport. Macroscale perfusable systems allow for non-destructive real-time monitoring using biosensors capable of improving understanding of in vitro tumor development at reduced cost and waste. The combination of macroscale perfusable systems, surface-modified synthetic scaffolds, and non-destructive real-time monitoring will provide advanced platforms for in vitro modeling of tumor development, with broad applications in basic tumor research and preclinical drug development.

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling's law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.

Multiscale Modeling for Food Drying: State of the Art

Plant-based food materials are mostly porous in nature and heterogeneous in structure with huge diversity in cellular orientation. Different cellular environments of plant-based food materials, such as intercellular, intracellular, and cell wall environments, hold different proportions of water with different characteristics. Due to this structural heterogeneity, it is very difficult to understand the drying process and associated morphological changes during drying. Transport processes and morphological changes that take place during drying are mainly governed by the characteristics of and the changes in the cells. Therefore, to predict the actual heat and mass transfer process that occurs in the drying process and associated morphological changes, development of multiscale modeling is crucial. Multiscale modeling is a powerful approach with the ability to incorporate this cellular structural heterogeneity with microscale heat and mass transfer during drying. However, due to the huge complexity involved in developing such a model for plant-based food materials, the studies regarding this issue are very limited. Therefore, we aim in this article to develop a critical conceptual understanding of multiscale modeling frameworks for heterogeneous food materials through an extensive literature review. We present a critical review on the multiscale model formulation and solution techniques with their spatial and temporal coupling options. Food structure, scale definition, and the current status of multiscale modeling are also presented, along with other key factors that are critical to understanding and developing an accurate multiscale framework. We conclude by presenting the main challenges for developing an accurate multiscale modeling framework for food drying.

The Lattice Boltzmann method and computational analysis of bone dynamics-I

Bone is comprised of an enormously hierarchical construction that promotes transportation of necessary fluids and solids, guaranteeing accurate function and growth. Bone remodeling is a combined process of bone creation and destruction. A number of mathematical models have been developed for the balanced and imbalanced bone remodeling. A brief overview regarding mathematical modeling of bone remodeling is provided. The Lattice Boltzmann method (LBM) has widely been implemented in CFD simulations, and it is becoming more suitable in the application of image processing amongst several others. Mainly, the LBM simulates the communication between synthetic particles dispersed in a lattice. Canaliculi and tortuous channels that have more or less roughly circular structure link among oval bodies identified as lacunae, and are vital to the function of bone. As there is a lack of equipment to inspect flow in channels on the order of measure of canaliculi, so the use of computational methods are more advantageous to give perceptivities into the nature of the flows. In this article, the computational fluid dynamics analysis is descried, using the Lattice Boltzmann method, to examine the result of the microscopic surface roughness of the canalicular wall, which is formed by collagen fibrils, on the flow profiles in the pericellular space.

Biofilm imaging in porous media by laboratory X-Ray tomography: Combining a non-destructive contrast agent with propagation-based phase-contrast imaging tools

X-ray tomography is a powerful tool giving access to the morphology of biofilms, in 3D porous media, at the mesoscale. Due to the high water content of biofilms, the attenuation coefficient of biofilms and water are very close, hindering the distinction between biofilms and water without the use of contrast agents. Until now, the use of contrast agents such as barium sulfate, silver-coated micro-particles or 1-chloronaphtalene added to the liquid phase allowed imaging the biofilm 3D morphology. However, these contrast agents are not passive and potentially interact with the biofilm when injected into the sample. Here, we use a natural inorganic compound, namely iron sulfate, as a contrast agent progressively bounded in dilute or colloidal form into the EPS matrix during biofilm growth. By combining a very long source-to-detector distance on a X-ray laboratory source with a Lorentzian filter implemented prior to tomographic reconstruction, we substantially increase the contrast between the biofilm and the surrounding liquid, which allows revealing the 3D biofilm morphology. A comparison of this new method with the method proposed by Davit et al (Davit et al., 2011), which uses barium sulfate as a contrast agent to mark the liquid phase was performed. Quantitative evaluations between the methods revealed substantial differences for the volumetric fractions obtained from both methods. Namely, contrast agent—biofilm interactions (e.g. biofilm detachment) occurring during barium sulfate injection caused a reduction of the biofilm volumetric fraction of more than 50% and displacement of biofilm patches elsewhere in the column. Two key advantages of the newly proposed method are that passive addition of iron sulfate maintains the integrity of the biofilm prior to imaging, and that the biofilm itself is marked by the contrast agent, rather than the liquid phase as in other available methods. The iron sulfate method presented can be applied to understand biofilm development and bioclogging mechanisms in porous materials and the obtained biofilm morphology could be an ideal basis for 3D numerical calculations of hydrodynamic conditions to investigate biofilm-flow coupling.

Pruning to Increase Taylor Dispersion in Physarum polycephalum Networks

How do the topology and geometry of a tubular network affect the spread of particles within fluid flows? We investigate patterns of effective dispersion in the hierarchical, biological transport network formed by Physarum polycephalum. We demonstrate that a change in topology-pruning in the foraging state-causes a large increase in effective dispersion throughout the network. By comparison, changes in the hierarchy of tube radii result in smaller and more localized differences. Pruned networks capitalize on Taylor dispersion to increase the dispersion capability.

Hydrodynamics and convection enhanced macromolecular fluid transport in soft biological tissues: Application to solid tumor

This work addresses a theoretical framework for transvascular exchange and extravascular transport of solute macromolecules through soft interstitial space inside a solid tumor. Most of the soft biological tissues show materialistic properties similar to deformable porous material. They exhibit mechanical behavior towards the fluid motion since the solid phase of the tumor tissue gets compressed by the drag force that is associated with the extracellular fluid flow. This paper presents a general view about the transvascular and interstitial transport of solute nutrients inside a tumor in the macroscopic level. Modified Starling׳s equation is used to describe transvascular nutrient transport. On the macroscopic level, motion of extracellular fluid within the tumor interstitium is modeled with the help of biphasic mixture theory and a spherical symmetry solution is given as a simpler case. This present model describes the average interstitial fluid pressure (IFP), extracellular fluid velocity (EFV) and flow rate of extracellular fluid, as well as the deformation of the solid phase of the tumor tissue as an immediate cause of extracellular fluid flow. When the interstitial transport is diffusion dominated, an analytical treatment of advection-diffusion-reaction equation finds the overall nutrient distribution. We propose suitable criteria for the formation of necrosis within the tumor interstitium. This study introduces some parameters that represent the nutrient supply from tumor blood vessels into the tumor extracellular space. These transport parameters compete with the reversible nutrient metabolism of the tumor cells present in the interstitium. The present study also shows that the effectiveness factor corresponding to a first order nutrient metabolism may reach beyond unity if the strength of the distributive solute source assumes positive non-zero values.

Differential growth of wrinkled biofilms

Biofilms are antibiotic-resistant bacterial aggregates that grow on moist surfaces and can trigger hospital-acquired infections. They provide a classical example in biology where the dynamics of cellular communities may be observed and studied. Gene expression regulates cell division and differentiation, which affect the biofilm architecture. Mechanical and chemical processes shape the resulting structure. We gain insight into the interplay between cellular and mechanical processes during biofilm development on air-agar interfaces by means of a hybrid model. Cellular behavior is governed by stochastic rules informed by a cascade of concentration fields for nutrients, waste, and autoinducers. Cellular differentiation and death alter the structure and the mechanical properties of the biofilm, which is deformed according to Föppl-Von Kármán equations informed by cellular processes and the interaction with the substratum. Stiffness gradients due to growth and swelling produce wrinkle branching. We are able to reproduce wrinkled structures often formed by biofilms on air-agar interfaces, as well as spatial distributions of differentiated cells commonly observed with B. subtilis.

Treatment of microbial biofilms in the post-antibiotic era: prophylactic and therapeutic use of antimicrobial peptides and their design by bioinformatics tools

The treatment for biofilm infections is particularly challenging because bacteria in these conditions become refractory to antibiotic drugs. The reduced effectiveness of current therapies spurs research for the identification of novel molecules endowed with antimicrobial activities and new mechanisms of antibiofilm action. Antimicrobial peptides (AMPs) have been receiving increasing attention as potential therapeutic agents, because they represent a novel class of antibiotics with a wide spectrum of activity and a low rate in inducing bacterial resistance. Over the past decades, a large number of naturally occurring AMPs have been identified or predicted from various organisms as effector molecules of the innate immune system playing a crucial role in the first line of defense. Recent studies have shown the ability of some AMPs to act against microbial biofilms, in particular during early phases of biofilm development. Here, we provide a review of the antimicrobial peptides tested on biofilms, highlighting their advantages and disadvantages for prophylactic and therapeutic applications. In addition, we describe the strategies and methods for de novo design of potentially active AMPs and discuss how informatics and computational tools may be exploited to improve antibiofilm effectiveness.

TISSUE ENGINEERING PERFUSABLE CANCER MODELS

The effect of fluid flow on cancer progression is currently not well understood, highlighting the need for perfused tumor models to close this gap in knowledge. Enabling biological processes at the cellular level to be modeled with high spatiotemporal control, microfluidic tumor models have demonstrated applicability as platforms to study cell-cell interactions, effect of interstitial flow on tumor migration and the role of vascular barrier function. To account for the multi-scale nature of cancer growth and invasion, macroscale models are also necessary. The consideration of fluid dynamics within tumor models at both the micro- and macroscopic levels may greatly improve our ability to more fully mimic the tumor microenvironment.

Multidimensional modeling of biofilm development and fluid dynamics in a hydrogen-based, membrane biofilm reactor (MBfR)

A two-dimensional, particle-based biofilm model coupled with mass transport and computational fluid dynamics was developed to simulate autotrophic denitrification in a spiral-wound membrane biofilm reactor (MBfR), where hydrogen is supplied via hollow-fiber membrane fabric. The spiral-wound configuration consists of alternating layers of plastic spacer net and membrane fabric that create rows of flow channels, with the top and bottom walls comprised of membranes. The transversal filaments of the spacer partially obstruct the channel flow, producing complex mixing and shear patterns that require multidimensional representation. This study investigated the effect of hydrogen and nitrate concentrations, as well as spacer configuration, on biofilm development and denitrification fluxes. The model results indicate that the cavity spacer filaments, which rest on the bottom membranes, cause uneven biofilm growth. Most biofilm resided on the bottom membranes, only in the wake of the filaments where low shear zones formed. In this way, filament configuration may help achieve a desired biofilm thickness. For the conditions tested in this study, the highest nitrate fluxes were attained by minimizing the filament diameter and maximizing the filament spacing. This lowered the shear stress at the top membranes, allowing for more biofilm growth. For the scenarios studied, biomass limitation at the top membranes hindered performance more significantly than diffusion limitation in the thick biofilms at the bottom membranes. The results also highlighted the importance of two-dimensional modeling to capture uneven biofilm growth on a substratum with geometrical complexity.

Hydrodynamic dispersion within porous biofilms

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport.