Analytically depicting the calcium diffusion for Alzheimer’s affected cell

2018 ◽  
Vol 11 (07) ◽  
pp. 1850088 ◽  
Author(s):  
Devanshi D. Dave ◽  
Brajesh Kumar Jha
Keyword(s):  
Mathematical Model ◽  
Calcium Ions ◽  
Complex Structure ◽  
Calcium Signalling ◽  
Cytosolic Calcium ◽  
Free Calcium ◽  
Calcium Diffusion ◽  
The Impact ◽  
The Brain ◽  
Very High

Brain is the most complex structure of the human body. The processes going inside the brain and the mechanisms behind it have been unrevealed up to certain extent only. Out of the various physiological phenomena carried out by the brain, calcium signalling can be considered as one of the most important. Calcium being a second messenger plays an important role in transformation of various information. In view of above, an attempt has been made here to study calcium signalling in presence of buffers, i.e. one kind of proteins and endoplasmic reticulum (ER), which is also known as store house of the cell. Being the store house of the cell, it has very high amount of calcium, whereas buffers decrease the level of free calcium ions by binding calcium ions to it. A two-dimensional mathematical model has been developed to see the impact of these parameters on cytosolic calcium concentration. This mathematical model is solved analytically using Laplace transforms and similarity transforms. The simulations are carried out using MATLAB. It is observed that the impact of buffer and ER is significant on calcium signalling. The obtained results are interpreted with the Alzheimeric condition of the nerve cells.

Investigation of Stress Wave Propagation in Brain Tissues Through the Use of Finite Element Method

2010 ◽  
Author(s):  
Biaobiao Zhang ◽  
W. Steve Shepard ◽  
Candace L. Floyd
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Brain Injury ◽  
Stress Wave ◽  
Brain Research ◽  
Complex Structure ◽  
Stress Wave Propagation ◽  
Wave Loads ◽  
The Impact ◽  
The Brain

Because axons serve as the conduit for signal transmission within the brain, research related to axon damage during brain injury has received much attention in recent years. Although myelinated axons appear as a uniform white matter, the complex structure of axons has not been thoroughly considered in the study of fundamental structural injury mechanisms. Most axons are surrounded by an insulating sheath of myelin. Furthermore, hollow tube-like microtubules provide a form of structural support as well as a means for transport within the axon. In this work, the effects of microtubule and its surrounding protein mediums inside the axon structure are considered in order to obtain a better understanding of wave propagation within the axon in an attempt to make progress in this area of brain injury modeling. By examining axial wave propagation using a simplified finite element model to represent microtubule and its surrounding proteins assembly, the impact caused by stress wave loads within the brain axon structure can be better understood. Through conducting a transient analysis as the wave propagates, some important characteristics relative to brain tissue injuries are studied.

An Analytical Viscoelastic Model of the Head in Blunt Impacts

2008 ◽  
Author(s):  
Shahab Baghaei ◽  
Ali Sadegh ◽  
Mohamad Rajaai
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Spherical Shell ◽  
Head Injuries ◽  
Head Impacts ◽  
Closed Head Injuries ◽  
Brain Motion ◽  
Closed Head ◽  
The Impact ◽  
The Brain

The relative motion between the brain and skull and an increase in contact and shear stresses in the meningeal region could cause traumatic closed head injuries due to vehicular collisions, sport accidents and falls. There are many finite element studies of the brain/head models, but limited analytical models. The goal of this paper is to mathematically model subarachnoid space and the meningeal layers and to investigate the motion of the brain relative to the skull during blunt head impacts. The model consists of an elastic spherical shell representing the skull containing a visco-elastic solid material as the brain and a visco-elastic interface, which models the meningeal layers between the brain and the skull. In this study, the shell (the head) is moved toward a barrier and comes in contact with the barrier. Consequently, the skull deforms elastically and the brain is excited to come in contact with the skull. The viscoelastic characteristics of the interface (consisting of springs and dampers) are determined using experimental results of Hardy et al. [5]. Hertzian contact theory and Newtonian method are employed to acquire time dependant equations for the problem. The governing nonlinear integro-differential equations are formed and are solved using 4th order Runge Kutta method and elastic deformation of spherical shell, brain motion during the impact, and contact conditions between the brain and the skull are evaluated. Furthermore, some important mechanical parameters such as acceleration, impact force, and the impact time duration are also specified. The results of the analytical method are validated by performing an explicit finite element analysis. Acceptable agreement between these two methods is observed. The results of the analytical investigation give the contact threshold of the skull/brain, and represent the relevant velocity of this event. Furthermore, the impact analysis in different velocities is performed in order to compare the transmitted forces and the impact durations in different cases. It is concluded that the proposed mathematical model can predict head impacts in accidents and is capable in determining the relative brain motion of the skull and the brain. The mathematical model could be employed by other investigators to parametrically study the traumatic closed head injuries and hence to propose new head injury criteria.

scholarly journals Spiking in cytosolic calcium concentration in single fibrinogen-bound fura-2-loaded human platelets

1992 ◽  
Vol 283 (2) ◽  
pp. 379-383 ◽  
Author(s):  
J W Heemskerk ◽  
J Hoyland ◽  
W T Mason ◽  
S O Sage
Keyword(s):  
Calcium Concentration ◽  
Calcium Signalling ◽  
Peak Frequency ◽  
Cytosolic Calcium ◽  
Light Level ◽  
Optical Probe ◽  
Human Platelets ◽  
Free Calcium ◽  
Fura 2 ◽  
Subsequent Activation

Fura-2-loaded human platelets were immobilized on a fibrinogen-coated surface and the cytosolic free calcium concentration ([Ca2+]i) was measured in single platelets by low-light-level video-ratio image-processing of the optical probe signal. Some fibrinogen-bound platelets showed repetitive spiking in [Ca2+]i with a mean frequency of about 2/min, which increased to 5/min in the presence of ADP. Other cells showed no activity until the addition of agonist. When immobilized in the presence of prostaglandin I2 and the fibrinogen antagonist Arg-Gly-Asp-Ser, the platelets adhered less firmly to fibrinogen, and in many [Ca2+]i remained low and constant. Subsequent activation of such platelets with ADP evoked oscillations in [Ca2+]i with a peak frequency of about 5/min and which persisted for at least 5 min. These results indicate that human platelets, like many other non-excitable cells, have an elaborate system of calcium signalling involving spiking.

A mathematical model of cytosolic calcium dynamics in human umbilical vein endothelial cells

1996 ◽  
Vol 270 (5) ◽  
pp. C1556-C1569 ◽  
Author(s):  
T. F. Wiesner ◽  
B. C. Berk ◽  
R. M. Nerem
Keyword(s):  
Mathematical Model ◽  
Endothelial Cells ◽  
Calcium Release ◽  
Umbilical Vein ◽  
Kinetic Equations ◽  
Cytosolic Calcium ◽  
Receptor Activation ◽  
Free Calcium ◽  
Human Umbilical Vein ◽  
Umbilical Vein Endothelial Cells

Important among the responses of endothelial cells are cytosolic free calcium transients. These transients are mediated by several factors, including blood-borne agonists, extracellular calcium, and fluid-imposed shear forces. The transients are characterized by a rapid rise followed by a plateau phase. A base mathematical model is presented that reasonably reproduces the measured calcium transient in cultured human umbilical vein endothelial cells responding to thrombin. Kinetic equations for receptor activation and calcium mobilization comprise the model. A graded response of intracellular free calcium to increasing concentrations of agonist is predicted. Also predicted is the elevation of the peak value and the plateau level by steady nonspecific leak of calcium across the plasma membrane. The influences of capacitative calcium entry, calcium-induced calcium release, and buffering by cytosolic proteins are investigated parametrically. The model predicts significant depletion of cellular calcium in response to agonist stimulation.

scholarly journals Mathematical model shows how sleep may affect amyloid β fibrillization

2019 ◽  
Author(s):  
Masoud Hoore ◽  
Sahamoddin Khailaie ◽  
Ghazal Montaseri ◽  
Tanmay Mitra ◽  
Michael Meyer-Hermann
Keyword(s):  
Mathematical Model ◽  
Production Rate ◽  
Amyloid Β ◽  
Cellular Level ◽  
Long Time ◽  
Diseased State ◽  
Aβ Fibers ◽  
The Impact ◽  
The Brain ◽  
Good Sleep

AbstractDeposition of amyloid β (Aβ) fibers in extra-cellular matrix of the brain is a ubiquitous feature associated with several neurodegenerative disorders, especially Alzheimer’s disease (AD). While many of the biological aspects that contribute to the formation of Aβ plaques are well addressed at the intra- and inter-cellular level in short timescales, an understanding of how Aβ fibrillization usually starts to dominate at a longer timescale in spite of the presence of mechanisms dedicated to Aβ clearance, is still lacking. Furthermore, no existing mathematical model integrates the impact of diurnal neural activity as emanated from circadian regulation to predict disease progression due to a disruption in sleep-wake cycle. In this study, we develop a minimal model of Aβ fibrillization to investigate the onset of AD over a long time-scale. Our results suggest that the diseased state is a manifestation of a phase change of the system from soluble Aβ (sAβ) to fibrillar Aβ (fAβ) domination upon surpassing a threshold in the production rate of soluble Aβ. By incorporating the circadian rhythm into our model, we reveal that fAβ accumulation is crucially dependent on the regulation of sleep-wake cycle, thereby indicating the importance of a good sleep hygiene in averting AD onset. We also discuss potential intervention schemes to reduce fAβ accumulation in the brain by modification of the critical sAβ production rate.

scholarly journals DORN1/P2K1 and purino-calcium signalling in plants: making waves with extracellular ATP

2019 ◽  
Vol 124 (7) ◽  
pp. 1227-1242 ◽  
Author(s):  
Elsa Matthus ◽  
Jian Sun ◽  
Limin Wang ◽  
Madhura G Bhat ◽  
Amirah B Mohammad-Sidik ◽  
...  
Keyword(s):  
Fluorescent Protein ◽  
Calcium Signalling ◽  
Cytosolic Calcium ◽  
Extracellular Atp ◽  
Calcium Wave ◽  
Free Calcium ◽  
Wild Type ◽  
Root Responses ◽  
Leaves And Roots ◽  
Green Fluorescent

Abstract Background and Aims Extracellular ATP governs a range of plant functions, including cell viability, adaptation and cross-kingdom interactions. Key functions of extracellular ATP in leaves and roots may involve an increase in cytosolic free calcium as a second messenger (‘calcium signature’). The main aim here was to determine to what extent leaf and root calcium responses require the DORN1/P2K1 extracellular ATP receptor in Arabidopsis thaliana. The second aim was to test whether extracellular ATP can generate a calcium wave in the root. Methods Leaf and root responses to extracellular ATP were reviewed for their possible links to calcium signalling and DORN1/P2K1. Leaves and roots of wild type and dorn1 plants were tested for cytosolic calcium increase in response to ATP, using aequorin. The spatial abundance of DORN1/P2K1 in the root was estimated using green fluorescent protein. Wild type roots expressing GCaMP3 were used to determine the spatial variation of cytosolic calcium increase in response to extracellular ATP. Key Results Leaf and root ATP-induced calcium signatures differed markedly. The leaf signature was only partially dependent on DORN1/P2K1, while the root signature was fully dependent. The distribution of DORN1/P2K1 in the root supports a key role in the generation of the apical calcium signature. Root apical and sub-apical calcium signatures may operate independently of each other but an apical calcium increase can drive a sub-apical increase, consistent with a calcium wave. Conclusion DORN1 could underpin several calcium-related responses but it may not be the only receptor for extracellular ATP in Arabidopsis. The root has the capacity for a calcium wave, triggered by extracellular ATP at the apex.

scholarly journals The Brain Drain Potential of Students in the African Health and Nonhealth Sectors

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jonathan Crush ◽  
Wade Pendleton
Keyword(s):  
Brain Drain ◽  
Health Professionals ◽  
Health Sector ◽  
African Countries ◽  
Policy Makers ◽  
Public Health Systems ◽  
African Health ◽  
The Impact ◽  
The Brain ◽  
Very High

The departure of health professionals to Europe and North America is placing an intolerable burden on public health systems in many African countries. Various retention, recall, and replacement policies to ameliorate the impact of this brain drain have been suggested, none of which have been particularly successful to date. The key question for the future is whether the brain drain of health sector skills is likely to continue and whether the investment of African countries in training health professionals will continue to be lost through emigration. This paper examines the emigration intentions of trainee health professionals in six Southern African countries. The data was collected by the Southern African Migration Program (SAMP) in a survey of final-year students across the region which included 651 students training for the health professions. The data also allows for the comparison of health sector with other students. The analysis presented in this paper shows very high emigration potential amongst all final-year students. Health sector students do show a slightly higher inclination to leave than those training to work in other sectors. These findings present a considerable challenge for policy makers seeking to encourage students to stay at home and work after graduation.

scholarly journals Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans

2019 ◽  
Author(s):  
Yi Ming Lai ◽  
Stephen Coombes ◽  
Rüdiger Thul
Keyword(s):  
Membrane Potential ◽  
Sarcoplasmic Reticulum ◽  
Calcium Channels ◽  
Calcium Release ◽  
Computational Study ◽  
Calcium Signalling ◽  
Severe Condition ◽  
Calcium Diffusion ◽  
Calcium Buffers ◽  
The Impact

AbstractIn cardiac myocytes, calcium cycling links the dynamics of the membrane potential to the activation of the contractile filaments. Perturbations of the calcium signalling toolkit have been demonstrated to disrupt this connection and lead to numerous pathologies including cardiac alternans. This rhythm disturbance is characterised by alternations in the membrane potential and the intracellular calcium concentration, which in turn can lead to sudden cardiac death. In the present computational study, we make further inroads into understanding this severe condition by investigating the impact of calcium buffers and L-type calcium channels on the formation of subcellular calcium alternans when calcium diffusion in the sarcoplasmic reticulum is strong. Through numerical simulations of a two dimensional network of calcium release units, we show that increasing calcium entry is proarrhythmogenic and that this is modulated by the calcium-dependent inactivation of the L-type calcium channel. We also find that while calcium buffers can exert a stabilising force and abolish subcellular Ca2+alternans, they can significantly shape the spatial patterning of subcellular calcium alternans. Taken together, our results demonstrate that subcellular calcium alternans can emerge via various routes and that calcium diffusion in the sarcoplasmic reticulum critically determines their spatial patterns.

Mitochondrial matrix calcium ions regulate energy production in myocardium: A cytochemical study

1990 ◽  
Vol 48 (2) ◽  
pp. 166-167
Author(s):  
W.A. Jacob ◽  
R. Hertsens ◽  
A. Van Bogaert ◽  
M. De Smet
Keyword(s):  
Energy Metabolism ◽  
Calcium Ions ◽  
Energy Production ◽  
Regulation Of Respiration ◽  
Free Calcium ◽  
Mitochondrial Matrix ◽  
Cytochemical Study ◽  
Nmr Techniques

In the past most studies of the control of energy metabolism focus on the role of the phosphorylation potential ATP/ADP.Pi on the regulation of respiration. Studies using NMR techniques have demonstrated that the concentrations of these compounds for oxidation phosphorylation do not change appreciably throughout the cardiac cycle and during increases in cardiac work. Hence regulation of energy production by calcium ions, present in the mitochondrial matrix, has been the object of a number of recent studies.Three exclusively intramitochondnal dehydrogenases are key enzymes for the regulation of oxidative metabolism. They are activated by calcium ions in the low micromolar range. Since, however, earlier estimates of the intramitochondnal calcium, based on equilibrium thermodynamic considerations, were in the millimolar range, a physiological correlation was not evident. The introduction of calcium-sensitive probes fura-2 and indo-1 made monitoring of free calcium during changing energy metabolism possible. These studies were performed on isolated mitochondria and extrapolation to the in vivo situation is more or less speculative.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

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