Cell Volume Fraction Research Articles

Ultrasound Scattering From Cell-Pellet Biophantoms and Ex Vivo Tumors Provides Insight Into the Cellular Structure Involved in Scattering.

The histologically identifiable cellular structure(s) involved in ultrasonic scattering is(are) yet to be uniquely identified. The study quantifies six possible cellular scattering parameters, namely, cell and nucleus radii and their respective cell and nucleus volume fractions as well as a combination of cell and nucleus radii and their volume fraction. The six cellular parameters are each derived from four cell lines (4T1, JC, LMTK, and MAT) and two tissue types (cell-pellet biophantom and ex vivo tumor). Optical histology and quantitative ultrasound (QUS), both independent approaches, are used to yield these cellular parameters. QUS scatterer parameters are experimentally determined using two ultrasonic scattering models: the spherical Gaussian model (GM) and the structure factor model (SFM) to yield insight about scattering from nuclei only and cells only. GM is a classical ultrasonic scattering model to evaluate QUS parameters and is well adapted for diluted media. SFM is adapted for dense media to estimate reasonably well scatterer parameters of cellular structures from ex vivo tissue. Nucleus and cell radii and volume fractions are measured optically from histology. They were used as inputs to calculate BSC for scattering from cells, nuclei, and both cells and nuclei. The QUS-derived scatterers (radii and volume fractions) distributions were then compared to the optical histology scatterer parameters derived from these calculated BSCs. The results suggest scattering from cells only (LMTK and MAT) or both cells and nuclei (4T1 and JC) for cell-pellet biophantoms and scattering from nuclei only for tumors.

On the impact of the mesostructure on the creep response of cellular NiAl-Mo eutectics

Directionally solidified eutectics of NiAl matrix and fibrous refractory metals, like Mo, can form cellular mesostructures with significant fiber misalignment and changing fiber volume fraction, for example, when being solidified at high growth rates or when increased solidification intervals are present in the alloys. In order to reveal the deteriorating impact of the mesostructure, i.e., the volume fraction and aspect ratio of the well-aligned cells, on the creep response of such cellular eutectics, we rely on scale-bridging numerical simulations, using the level-set framework by Sonon et al. [1] for microstructure generation and FFT-based solvers for computing the creep response. Our results indicate, firstly, that the fraction of properly aligned regions in cellular NiAl composites is lower than estimated in earlier experimental studies, due to the existence of degenerated regions surrounding the well-aligned cell interiors. Secondly, studying the influence of the cell aspect ratio shows that the apparent stress exponent of the composite is very sensitive with respect to this parameter, providing a possible explanation for the large scatter of experimentally determined stress exponents in previous studies. A comparison of the numerical simulations to a linear rule of mixtures and the frequently applied analytical Kelly-Street model illustrates that both fail to accurately describe the magnitude of minimum creep rates in the investigated ranges of volume fractions and aspect ratios. The heterogeneity of the strain-rate field on the mesoscale is identified as the primary error source, demonstrating that either numerical simulations or more sophisticated analytical models are required for reliably predicting for the creep response of cellular materials.

Thin-film lubrication model for biofilm expansion under strong adhesion.

Understanding microbial biofilm growth is important to public health because biofilms are a leading cause of persistent clinical infections. In this paper, we develop a thin-film model for microbial biofilm growth on a solid substratum to which it adheres strongly. We model biofilms as two-phase viscous fluid mixtures of living cells and extracellular fluid. The model explicitly tracks the movement, depletion, and uptake of nutrients and incorporates cell proliferation via a nutrient-dependent source term. Notably, our thin-film reduction is two dimensional and includes the vertical dependence of cell volume fraction. Numerical solutions show that this vertical dependence is weak for biologically feasible parameters, reinforcing results from previous models in which this dependence was neglected. We exploit this weak dependence by writing and solving a simplified one-dimensional model that is computationally more efficient than the full model. We use both the one- and two-dimensional models to predict how model parameters affect expansion speed and biofilm thickness. This analysis reveals that expansion speed depends on cell proliferation, nutrient availability, cell-cell adhesion on the upper surface, and slip on the biofilm-substratum interface. Our numerical solutions provide a means to qualitatively distinguish between the extensional flow and lubrication regimes, and quantitative predictions that can be tested in future experiments.

The effect of rigid cells on blood viscosity: linking rheology and sickle cell anemia.

Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.

FLatt Pack: A research-focussed lattice design program

Lattice structures are an important aspect of design for additive manufacturing (DfAM). They enable significant component light-weighting and the tailoring of a wide range of physical responses; mechanical, thermal, acoustic, etc. In turn, lattice design relies on fundamental research to uncover useful structure-property relationships, such as the influence of cell geometry and volume fraction. A number of commercial computer-aided-design (CAD) programs exist that offer lattice generation, but these tend to prioritise product design. This paper describes the FLatt Pack program (or Functional Lattice Package), which was created to address the paucity of research-focussed lattice design software. It possesses a number of features with this in mind, including; (i) it is free to use for research, (ii) it is standalone software with minimal, and also free, dependencies, and (iii) it undergoes frequent and rapid development based on state of the art lattice information and modelling methods. FLatt Pack includes twenty-three lattice cell types covering a broad range of pore connectivity, structural anisotropy, and surface area; a clear GUI presenting the lattice design stages in a sequential manner; and the option to export designs in appropriate formats for AM and finite element (FE) simulation. The program also features conformal lattice generation in arbitrary shapes, arbitrary volume fraction grading, and resource-efficient computation through an adaptive spatial resolution based on the user’s design choices. The most recent version of FLatt Pack is freely available at: www.github.com/ian27ax/FLatt_Pack_dist .

Laser powder bed fusion of AISI 316L lattice structures for biomedical applications

Additive Manufacturing (AM) is a class of manufacturing technologies in which a complex part can be built directly in its final or semi-final shape through a layerwise process. These technologies enable the production of engineered materials with a high level of complexity, of which lattice structures are one of the most promising structures for several applications. On the other hand, cellular structures have been extensively studied over the last few decades, mainly owing to their unique performances in energy absorption, thermal and electrical conductivity, and acoustic. The biggest challenge in cellular solids is the replication of their cell geometries with complex shapes and often small dimensions. Therefore, AM methods that facilitate the fabrication of nature-inspired geometries devices could play a key role in developing new cellular structures for various applications. Hence, the present paper aims to manufacture and characterise AISI 316 L lattice structures produced by the laser powder bed fusion process. Two different types of structures are considered: the strut-based based on strut elements and the triply periodic minimal surfaces generated from trigonometric functions. Statistic compression tests were performed to investigate the influence of cell geometries, unit cell size, relative density, and volume fraction on mechanical properties, such as Youngs’ modulus, ultimate compressive strength, and the amount of energy absorbed.

Assessing Myocardial Microstructure With Biophysical Models of Diffusion MRI.

Biophysical models are a promising means for interpreting diffusion weighted magnetic resonance imaging (DW-MRI) data, as they can provide estimates of physiologically relevant parameters of microstructure including cell size, volume fraction, or dispersion. However, their application in cardiac microstructure mapping (CMM) has been limited. This study proposes seven new two-compartment models with combination of restricted cylinder models and a diffusion tensor to represent intra- and extracellular spaces, respectively. Three extended versions of the cylinder model are studied here: cylinder with elliptical cross section (ECS), cylinder with Gamma distributed radii (GDR), and cylinder with Bingham distributed axes (BDA). The proposed models were applied to data in two fixed mouse hearts, acquired with multiple diffusion times, q-shells and diffusion encoding directions. The cylinderGDR-pancake model provided the best performance in terms of root mean squared error (RMSE) reducing it by 25% compared to diffusion tensor imaging (DTI). The cylinderBDA-pancake model represented anatomical findings closest as it also allows for modelling dispersion. High-resolution 3D synchrotron X-ray imaging (SRI) data from the same specimen was utilized to evaluate the biophysical models. A novel tensor-based registration method is proposed to align SRI structure tensors to the MR diffusion tensors. The consistency between SRI and DW-MRI parameters demonstrates the potential of compartment models in assessing physiologically relevant parameters.

Mathematical modeling and simulation of mechano-chemical effect on two-phase avascular tumor

In this paper, we derive the mathematical model that allows chemotaxis in avascular tumor growth in a two-phase medium. The two phases are the viscous cell phase and the inviscid fluid phase. The conservation of mass–momentum is incorporated in each phase, and appropriate constitutive laws are applied to formulate the governing equations. Further, these equations are simplified into three main variables: cell volume fraction, cell velocity, and nutrient concentration. These variables generate a coupled system of nonlinear partial differential equations. A numerical scheme based on the finite volume method is applied to approximate the solution of cell volume fraction. The finite element method is applied to approximate the solutions of cell velocity and nutrient concentration. In this research paper, we investigate tumor growth when tumor cells move along a fluid containing a diffusible nutrient to which the cells are drawn. We perform some numerical simulations to show the effect of the parameters. The findings of this literature are compatible with the existing literature.

Effective interface conditions for continuum mechanical models describing the invasion of multiple cell populations through thin membranes

We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different proliferative abilities and mobility, which may vary from part to part of the tissue, as well as by different invasion potentials within the membranes. The original transmission problem, consisting of a set of mass balance equations for the volume fraction of cells of every population complemented with continuity of stresses and mass flux across the surfaces of the membranes, is then reduced to a limiting transmission problem whereby each thin membrane is replaced by an effective interface. In order to close the limiting problem, a set of biophysically-consistent transmission conditions is derived through a formal asymptotic method. Models based on such a limiting transmission problem may find fruitful application in a variety of research areas in the biological and medical sciences, including developmental biology, immunology and cancer growth and invasion.

Isolation of Plant Mitochondria Using Affinity Purification.

Mitochondria are highly dynamic organelles that are vital for eukaryotic cellular metabolism. Mitochondria account only for a small fraction of the total cell volume. As such, intact organelle isolation is a basic requirement to study mitochondrial biochemistry and physiology. However, established isolation procedures are tedious, and require a substantial amount of tissue material to start with. We addressed this matter and developed a single step purification for Arabidopsis thaliana (Arabidopsis) mitochondria. Ubiquitous expression of an 3xHA-sGFP-TOM5 fusion protein in the outer mitochondrial membrane allows affinity purification by immunocapture in a single step. We here provide a detailed step-by-step protocol for rapid immunocapture of intact and physiologically active mitochondria from Arabidopsis plants.

Morphofunctional Changes in Colon after Cold Stress in Male C57BL/6 Mice Susceptible and Tolerant to Hypoxia.

There are individual differences in the tolerance to hypoxia and stress. Stress can contribute to the development of various diseases, including inflammatory bowel disease. It was found that inflammatory bowel diseases in animals susceptible to hypoxia runs more severe course than in tolerant animals. We studied morphofunctional changes in the colon under conditions of modeled cold stress in male C57BL/6 mice susceptible and tolerant to hypoxia. The animals were daily subjected to cold stress (20 min at -20°C) for 2 weeks. Cold stress was followed by an increase in the volume fraction of goblet cells in the colon and production of mucins by these cells in mice tolerant to hypoxia and an increase in cell content in the lamina propria of the colon mucous membrane in animals susceptible to hypoxia. The number of serotoninproducing endocrine cells increased in both groups, but these changes were more pronounced in mice susceptible to hypoxia.

Study of optical properties of gold nanoparticles embedded in normal, benign, and malignant breast tissues

In this work, the complex dielectric permittivity of breast tissue is calculated for different growth rates of benign and malignant tumors using the Maxwell Garnett (MG) effective medium theory. The results show a wide variability of the dielectric properties depending on the nature and the volume fraction of the cancer cells. The benign-normal and malignant-normal heterostructures are denoted respectively x-B/N and x-M/N where x is the volume fraction of cancer cells in the breast tissue. The real and imaginary parts of dielectric permittivity increases when the growth rates of benign and malignant tumors increase and decrease when the microwave frequency increases from 0.5 to 8 GHz. In the aim to use the gold nanoparticles (GNPs) in breast cancer therapy, both for a better image diagnostic and photothermal therapy (PTT), we present here a study on the optical properties of GNPs embedded in normal, benign and malignant breast tissue in the frequency range from 0.5 GHz to 8 GHz. optical band gap energy for GNP is located in [0.5eV−1.46eV](±0.06eV), [0.72eV−1.20eV](±0.04eV) and [0.11eV−0.74eV](±0.02eV) ranges for Normal, Benign and Malignant breast tissues, respectively. We use the Finite Element Method (FEM) to evaluate the spectra of the dielectric and optical parameters of GNPs namely: complex dielectric permittivity, absorption cross section, reflectivity, dielectric loss function and conductivity, the surface plasmons resonance (SPR) properties are deduced from these spectra. The obtained results show that the SPR-peak of the GNPs is located in the Visible (Vis), near infrared (NIR) and short wavelength infrared (SWIR) bands when they are embedded respectively in the normal, benign and malignant breast tissue. For these three tissues when the microwave frequency increases from 0.5 to 8 GHz, the SPR-peak position λmax shifts towards the short wavelengths. The calculations show that in the vicinity of λmax the dielectric loss function take a maximum value and the reflectivity change strongly. These results show that the absorption and dielectric loss peaks are less wide for the high microwave frequencies and very wide for the low frequencies, which also influences the difference between the asymptotic values of the real part of permittivity and of the reflectivity. These results make it possible to identify the nature of the breast tumor using the GNPs in the sensors based on the of SPR phenomenon. The optical properties of GNPs depending on their size and on the tumor growth rate in the breast tissue are also studied and discussed. The study carried out represents a feasibility proposal for the use of GNPs for determining the degree of breast tumor progression and estimate the good performance of using the GNPs for the selective destruction of breast cancer cells.

Influence of substrate microstructure on hydroxyapatite coating and corrosion behavior of coated Mg[sbnd]Zn alloys

Abstract Hydroxyapatite (HAp) coatings were formed on as-cast and T4-treated Mg-xZn (x = 1, 5, and 7 wt%) alloys by a chemical solution deposition method. The uniformity of HAp coatings showed an enhancement with finer particle size and lower volume fraction of (α-Mg + MgZn) eutectic cells and Zn-segregated regions. The Mg1Zn sample showed a defect-free HAp coating, while the HAp coating of the Mg7Zn sample showed cracks preferentially over the eutectic cells causing micro-galvanic corrosion with the matrix. Initially, the corrosion rate of the HAp-coated alloys was governed by the uniformity of HAp coating, and eventually it was dominated by the corrosion resistance of substrate alloys after the HAp coatings irreversibly broken. Ultimately, the volume fraction and size of (α-Mg + MgZn) eutectic cells and Zn-segregated regions governed the corrosion behavior of the HAp-coated MgZn alloys. The HAp-coated Mg1Zn alloy showed 2–4 times lower corrosion rate than other alloys after 1 day and 4–10 times after 14 days of immersion. The 14-day average corrosion rate of the as-cast Mg-1, 5, and 7Zn alloys decreased by 45%, 5% and 15% with the HAp coatings, respectively. The polarization resistance (Rp) of the as-cast Mg-1, 5, and 7 Zn alloys increased by 10, 7.5 and 5 times with the HAp coatings, respectively. Consequently, the HAp coating effectively improved the corrosion resistance of MgZn alloys with low volume fraction of (α-Mg + MgZn) eutectic cells.

On a subdiffusive tumour growth model with fractional time derivative

AbstractIn this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply and chemotherapy. The subdiffusion of the system is modelled by a time fractional derivative in the equation governing the volume fraction of the tumour cells. The mass densities of the nutrients and the chemotherapeutic agents are modelled by reaction diffusion equations. We prove the existence and uniqueness of a weak solution to the model via the Faedo–Galerkin method and the application of appropriate compactness theorems. Lastly, we propose a fully discretized system and illustrate the effects of the fractional derivative and the influence of the fractional parameter in numerical examples.

Modeling of Glioma Growth With Mass Effect by Longitudinal Magnetic Resonance Imaging.

It is well-known that expanding glioblastomas typically induce significant deformations of the surrounding parenchyma (i.e., the so-called "mass effect"). In this study, we evaluate the performance of three mathematical models of tumor growth: 1) a reaction-diffusion-advection model which accounts for mass effect (RDAM), 2) a reaction-diffusion model with mass effect that is consistent only in the case of small deformations (RDM), and 3) a reaction-diffusion model that does not include the mass effect (RD). The models were calibrated with magnetic resonance imaging (MRI) data obtained during tumor development in a murine model of glioma (n = 9). We obtained T2-weighted and contrast-enhanced T1-weighted MRI at 6 time points over 10 days to determine the spatiotemporal variation in the mass effect and the volume fraction of tumor cells, respectively. We calibrated the three models using data 1) at the first four, 2) only at the first and fourth, and 3) only at the third and fourth time points. Each of these calibrations were run forward in time to predict the volume fraction of tumor cells at the conclusion of the experiment. The diffusion coefficient for the RDAM model (median of 10.65 × 10 -3 mm 2· d -1) is significantly less than those for the RD and RDM models (17.46 × 10 -3 mm 2· d -1 and 19.38 × 10 -3 mm 2· d -1, respectively). The error in the tumor volume fraction for the RD, RDM, and RDAM models have medians of 40.2%, 32.1%, and 44.7%, respectively, for the calibration using data from the first four time points. The RDM model most accurately predicts tumor growth, while the RDAM model presents the least variation in its estimates of the diffusion coefficient and proliferation rate. This study demonstrates that the mathematical models capture both tumor development and mass effect observed in experiments.

Investigations on the NiAl–Cr(Mo) eutectic alloy with optimized microstructure and improved room-temperature compressive properties

In this paper, microstructural optimization was chosen to strengthen NiAl-based alloys based on hot pressing sintering of pre-alloyed powders. The Cr(Mo) phase in the eutectic cell was refined to 200 nm successfully. Owing to the growth of the Cr(Mo) phase, the volume fraction of the eutectic cells greatly reduced. The compact sample has been obtained at a relatively lower temperature and an extended holding time to retain the eutectic cells. Each compact sample shows considerable performance both in strength and plasticity for compression test at room-temperature. The grown Cr(Mo) phase which can resist the cracks and the eutectic cells with nano-sized Cr(Mo) phase are the main reasons for toughening and strengthening. The improvement of strength and plasticity of alloy in this paper can provide basic understanding for further development of NiAl-based alloy.

Convergence analysis of a numerical scheme for a tumour growth model

Abstract A one–spatial dimensional tumour growth model Breward et al. ( 2001, 2002, 2003) that consists of three dependent variables of space and time is considered. These variables are volume fraction of tumour cells, velocity of tumour cells, and nutrient concentration. The model variables satisfy a coupled system of semilinear advection equation (hyperbolic), simplified linear Stokes equation (elliptic), and semilinear diffusion equation (parabolic) with appropriate conditions on the time–dependent boundary, which is governed by an ordinary differential equation. A reformulation of the model defined in a larger, fixed time–space domain is employed to overcome theoretical difficulties related to the time–dependent boundary. This reformulation reduces the complexity of the model by removing the need to explicitly track the time–dependent boundary. A numerical scheme that employs a finite volume method for the hyperbolic equation, a finite element method for the elliptic equation, and a backward Euler in time–mass lumped finite element in space method for the parabolic equation is developed. We establish the existence of a time interval $(0,T_{\ast })$ over which a convergent subsequence of the numerical approximations can be extracted using compactness techniques. The limit of any such convergent subsequence is proved to be a weak solution of the continuous model in an appropriate sense, which is called a threshold solution. Numerical tests and justifications that support the theoretical findings conclude the paper.

A simulation study of cell size and volume fraction mapping for tissue with two underlying cell populations using diffusion-weighted MRI.

To propose a method for voxel-wise estimation of cell radii and volume fractions of two cell populations when they coexist in the same MR voxel using the combination of diffusion-weighted MRI and microstructural modeling. Microstructure models were investigated using diffusion data simulated with the matrix method for a range of microstructures mimicking tumor tissue with two cell populations, using acquisition parameters available on preclinical scanners. The effect of noise was investigated for a subset of these microstructures. The accuracy and precision of the estimated radii and volume fractions for large and small cells were evaluated by comparing the estimates to their true values. The stability of model fitting was characterized by the percentage of accepted fits. The estimation accuracy and precision, and thus the ability to robustly distinguish the two cell populations, depended on the microstructural properties and SNR. For a SNR of 50, a minimum difference of 3 μm between the radius of the large and small cell populations was required for differentiation. Proposed modifications to the two cell population microstructure model, including constrained fits, improved the stability of fits. This proof-of-concept study proposed a diffusion MRI-based method for voxel-wise estimation of cell radii and volume fractions of two cell populations when they coexist in the same MR voxel. The ability to reliably characterize tissue with two cell populations opens exciting avenues of potential applications in both tumor diagnosis and treatment monitoring.

Microstructure-dependent Band Gaps for Elastic Wave Propagation in a Periodic Microbeam Structure

A new model for producing band gaps for flexural elastic wave propagation in a periodic microbeam structure is developed using an extended transfer matrix method and a non-classical Bernoulli–Euler beam model that incorporates the strain gradient, couple stress and velocity gradient effects. The band gaps predicted by the new model depend on the three microstructure-dependent material parameters of each constituent material, the beam thickness, the unit cell length and the volume fraction. A parametric study is conducted to quantitatively illustrate these factors. The numerical results reveal that the first band gap frequency range increases with the increases of the three microstructure-dependent material parameters, respectively. In addition, the band gap size predicted by the current model is always larger than that predicted by the classical model, and the difference is large for very thin beams. Furthermore, both the unit cell length and volume fraction have significant effects on the band gap.

Partially open cell Ti-6Al-2Co ternary alloy foams with a range of size and volume fraction of spacer particle

Partially open cell Ti-6Al-2Co alloys foams of varying cell (pore) size (0 to 500 µm) and volume fraction (40 to 70%) are made by varying the space-holder size (SHS) and volume fraction. The increase of space-holder (spacer) size increased the cell size and cell-wall thicknesses, which led to increased plateau stress, energy absorbed (Toughness), hardness and Young’s modulus. Further, increased spacer content and decrease of strain rate; reduced the strength, toughness, and modulus of Ti6Al2Co ternary alloy foams. The corrosion rate was found to be decreasing with increase of particle size of space-holder Also, the corrosion rate and weight loss percent increases with increase in cell volume fraction. Further, the Ti6Al2Co alloy foam’s mechanical properties were found to have a trend of power-law relations with relative densities.