A new two-component approach in modeling red blood cells

Luca Meacci; Gustavo C. Buscaglia; Fernando Mut; Roberto F. Ausas; Mario Primicerio

doi:10.1515/caim-2020-0004

A new two-component approach in modeling red blood cells

Communications in Applied and Industrial Mathematics ◽

10.2478/caim-2020-0004 ◽

2020 ◽

Vol 11 (1) ◽

pp. 55-71

Author(s):

Luca Meacci ◽

Gustavo C. Buscaglia ◽

Fernando Mut ◽

Roberto F. Ausas ◽

Mario Primicerio

Keyword(s):

Red Blood Cells ◽

Blood Cells ◽

Computational Modelling ◽

Small Time ◽

Discrete Models ◽

Continuous Treatment ◽

Particle Methods ◽

Adhesion Forces ◽

Component Approach ◽

External Forces

Abstract This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 nm) is much smaller than the overall size (≃ 8000 nm). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.

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Simulation of Red Blood Cell Mechanical Behavior in Optical Tweezers Experiment Based on a Particle Method

Volume 2: Biomedical and Biotechnology Engineering ◽

10.1115/imece2010-38164 ◽

2010 ◽

Cited By ~ 1

Author(s):

M. T. Ahmadian ◽

K. Firoozbakhsh ◽

M. Hasanian

Keyword(s):

Mechanical Behavior ◽

Red Blood Cells ◽

Optical Tweezers ◽

Blood Cells ◽

Experimental Studies ◽

Particle Method ◽

Living Cells ◽

Discrete Models ◽

Particle Methods ◽

External Forces

Optical tweezers provide an accurate measurement technique for evaluating mechanical properties of the living cells and many experimental studies have been done to understand the behavior of cells due to external forces. Numerical studies such as finite element methods have been used in order to simulate mechanical behavior of the Red Blood Cells (RBCs). Recent studies have shown that the particle methods are useful tools to simulate the mechanical behavior of living cells. Since in microscopic scales, using discrete models are preferred than continuum methods, a particle-based method is used to simulate the deformation of RBC which is stretched by optical tweezers. The cytoplasm of RBC is modeled as a fluid and cell membrane is replaced by a set of discrete particles connected by springs. The results are comparable with previous observations of RBC optical tweezers experiments. It was observed that RBC viscoelastic characteristics are mainly associated with the cytoplasm fluidic properties. In order to understand the behavior and function of living red blood cells, this significant developed model could be implemented to RBC interaction within micocapillaries and constricted zones in blood flow.

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Modeling biomembranes and red blood cells by coarse-grained particle methods

Applied Mathematics and Mechanics ◽

10.1007/s10483-018-2252-6 ◽

2017 ◽

Vol 39 (1) ◽

pp. 3-20 ◽

Cited By ~ 7

Author(s):

H. Li ◽

H. Y. Chang ◽

J. Yang ◽

L. Lu ◽

Y. H. Tang ◽

...

Keyword(s):

Red Blood Cells ◽

Blood Cells ◽

Coarse Grained ◽

Particle Methods

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Up-down biphasic volume response of human red blood cells to PIEZO1 activation during capillary transits

PLoS Computational Biology ◽

10.1371/journal.pcbi.1008706 ◽

2021 ◽

Vol 17 (3) ◽

pp. e1008706 ◽

Cited By ~ 2

Author(s):

Simon Rogers ◽

Virgilio L. Lew

Keyword(s):

Red Blood Cells ◽

Blood Cells ◽

Time Course ◽

Capillary Flow ◽

Cell Model ◽

Recovery Period ◽

Large Body ◽

Computational Modelling ◽

Companion Paper ◽

Human Red Blood Cells

In this paper we apply a novel JAVA version of a model on the homeostasis of human red blood cells (RBCs) to investigate the changes RBCs experience during single capillary transits. In the companion paper we apply a model extension to investigate the changes in RBC homeostasis over the approximately 200000 capillary transits during the ~120 days lifespan of the cells. These are topics inaccessible to direct experimentation but rendered mature for a computational modelling approach by the large body of recent and early experimental results which robustly constrain the range of parameter values and model outcomes, offering a unique opportunity for an in depth study of the mechanisms involved. Capillary transit times vary between 0.5 and 1.5s during which the red blood cells squeeze and deform in the capillary stream transiently opening stress-gated PIEZO1 channels allowing ion gradient dissipation and creating minuscule quantal changes in RBC ion contents and volume. Widely accepted views, based on the effects of experimental shear stress on human RBCs, suggested that quantal changes generated during capillary transits add up over time to develop the documented changes in RBC density and composition during their long circulatory lifespan, the quantal hypothesis. Applying the new red cell model (RCM) we investigated here the changes in homeostatic variables that may be expected during single capillary transits resulting from transient PIEZO1 channel activation. The predicted quantal volume changes were infinitesimal in magnitude, biphasic in nature, and essentially irreversible within inter-transit periods. A sub-second transient PIEZO1 activation triggered a sharp swelling peak followed by a much slower recovery period towards lower-than-baseline volumes. The peak response was caused by net CaCl2 and fluid gain via PIEZO1 channels driven by the steep electrochemical inward Ca2+ gradient. The ensuing dehydration followed a complex time-course with sequential, but partially overlapping contributions by KCl loss via Ca2+-activated Gardos channels, restorative Ca2+ extrusion by the plasma membrane calcium pump, and chloride efflux by the Jacobs-Steward mechanism. The change in relative cell volume predicted for single capillary transits was around 10−5, an infinitesimal volume change incompatible with a functional role in capillary flow. The biphasic response predicted by the RCM appears to conform to the quantal hypothesis, but whether its cumulative effects could account for the documented changes in density during RBC senescence required an investigation of the effects of myriad transits over the full four months circulatory lifespan of the cells, the subject of the next paper.

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Hemoglobin crystals of the red blood cells in the human renal cortex: electron microscopic observations of the renal lithiasis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100083266 ◽

1978 ◽

Vol 36 (2) ◽

pp. 480-481

Author(s):

Kosuke Ueda ◽

Hiroto Washida ◽

Nakazo Watari

Keyword(s):

Red Blood Cells ◽

Blood Cells ◽

Renal Cortex ◽

Uranyl Acetate ◽

Osmic Acid ◽

Renal Lithiasis ◽

Electron Microscopic ◽

Hemoglobin C ◽

First Case ◽

Ultrathin Sections

IntroductionHemoglobin crystals in the red blood cells were electronmicroscopically reported by Fawcett in the cat myocardium. In the human, Lessin revealed crystal-containing cells in the periphral blood of hemoglobin C disease patients. We found the hemoglobin crystals and its agglutination in the erythrocytes in the renal cortex of the human renal lithiasis, and these patients had no hematological abnormalities or other diseases out of the renal lithiasis. Hemoglobin crystals in the human erythrocytes were confirmed to be the first case in the kidney.Material and MethodsTen cases of the human renal biopsies were performed on the operations of the seven pyelolithotomies and three ureterolithotomies. The each specimens were primarily fixed in cacodylate buffered 3. 0% glutaraldehyde and post fixed in osmic acid, dehydrated in graded concentrations of ethanol, and then embedded in Epon 812. Ultrathin sections, cut on LKB microtome, were doubly stained with uranyl acetate and lead citrate.

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Densitometric Identification of Primitive Erythroblasts After Reaction With Diaminobenzidine

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100072083 ◽

1973 ◽

Vol 31 ◽

pp. 328-329

Author(s):

John A. Trotter

Keyword(s):

Red Blood Cells ◽

Analytical Method ◽

Blood Cells ◽

Guinea Pigs ◽

Specific Protein ◽

Visual Examination ◽

Hemoglobin Synthesis ◽

Peroxidatic Activity ◽

Small Density

Hemoglobin is the specific protein of red blood cells. Those cells in which hemoglobin synthesis is initiated are the earliest cells that can presently be considered to be committed to erythropoiesis. In order to identify such early cells electron microscopically, we have made use of the peroxidatic activity of hemoglobin by reacting the marrow of erythropoietically stimulated guinea pigs with diaminobenzidine (DAB). The reaction product appeared as a diffuse and amorphous electron opacity throughout the cytoplasm of reactive cells. The detection of small density increases of such a diffuse nature required an analytical method more sensitive and reliable than the visual examination of micrographs. A procedure was therefore devised for the evaluation of micrographs (negatives) with a densitometer (Weston Photographic Analyzer).

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Scanning electron microscopy of erythrophagocytosis by Entamoeba histolytica trophozoites

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010012480x ◽

1992 ◽

Vol 50 (1) ◽

pp. 880-881

Author(s):

Victor Tsutsumi ◽

Adolfo Martinez-Palomo ◽

Kyuichi Tanikawa

Keyword(s):

Electron Microscopy ◽

Scanning Electron Microscopy ◽

Red Blood Cells ◽

Entamoeba Histolytica ◽

Causative Agent ◽

Blood Cells ◽

Protozoan Parasite ◽

Complex Phenomenon ◽

Great Capacity ◽

Scanning Electron

The protozoan parasite Entamoeba histolytica is the causative agent of amebiasis in man. The trophozoite or motile form is a highly dynamic and pleomorphic cell with a great capacity to destroy tissues. Moreover, the parasite has the singular ability to phagocytize a variety of different live or death cells. Phagocytosis of red blood cells by E. histolytica trophozoites is a complex phenomenon related with amebic pathogenicity and nutrition.

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Ultrastructural observations on the in vitro cytoadherence of Plasmodium falciparum infected red blood cells

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100162132 ◽

1990 ◽

Vol 48 (3) ◽

pp. 914-915

Author(s):

D.J.P. Ferguson ◽

A.R. Berendt ◽

J. Tansey ◽

K. Marsh ◽

C.I. Newbold

Keyword(s):

Plasmodium Falciparum ◽

Red Blood Cells ◽

Blood Cells ◽

Umbilical Vein ◽

Cell Types ◽

Amelanotic Melanoma ◽

Cytoplasmic Process ◽

Umbilical Vein Endothelial Cells

In human malaria, the most serious clinical manifestation is cerebral malaria (CM) due to infection with Plasmodium falciparum. The pathology of CM is thought to relate to the fact that red blood cells containing mature forms of the parasite (PRBC) cytoadhere or sequester to post capillary venules of various tissues including the brain. This in vivo phenomenon has been studied in vitro by examining the cytoadherence of PRBCs to various cell types and purified proteins. To date, three Ijiost receptor molecules have been identified; CD36, ICAM-1 and thrombospondin. The specific changes in the PRBC membrane which mediate cytoadherence are less well understood, but they include the sub-membranous deposition of electron-dense material resulting in surface deformations called knobs. Knobs were thought to be essential for cytoadherence, lput recent work has shown that certain knob-negative (K-) lines can cytoadhere. In the present study, we have used electron microscopy to re-examine the interactions between K+ PRBCs and both C32 amelanotic melanoma cells and human umbilical vein endothelial cells (HUVEC).We confirm previous data demonstrating that C32 cells possess numerous microvilli which adhere to the PRBC, mainly via the knobs (Fig. 1). In contrast, the HUVEC were relatively smooth and the PRBCs appeared partially flattened onto the cell surface (Fig. 2). Furthermore, many of the PRBCs exhibited an invagination of the limiting membrane in the attachment zone, often containing a cytoplasmic process from the endothelial cell (Fig. 2).

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