An Experimental Study of Package Cushioning for the Human Head

1976 ◽  
Vol 43 (3) ◽  
pp. 469-474
Author(s):  
Y. King Liu ◽  
K. B. Chandran
Keyword(s):  
Mathematical Model ◽  
Animal Experiments ◽  
Human Head ◽  
Head Impacts ◽  
Closed Head ◽  
The Mathematical Model ◽  
Experimental Pressure ◽  
The Brain ◽  
Good Agreement

An experiment was performed to determine the container acceleration and pressure distribution in a Plexiglass cylinder, filled either with water or 3 percent set-gelatin, and impacted against a wall. This experiment serves to quantitatively validate a theoretical model simulating an one-dimensional closed-head impact given earlier. The experiments showed important differences between the theoretical and experimental pressure measurements. When the medium contained within the cylinder was water the coup pressure as found by experiment, was higher than the mathematical model prediction while the contrecoup pressure was in good agreement. When the container was filled with a set gel, the coup pressure was in agreement with the mathematical model but the contrecoup pressure is considerably lower than the calculated result. Since the brain is neither water nor gel, in vivo animal experiments are needed to obtain meaningful tolerance limits for injury due to cavitation at the contrecoup region in closed-head impacts.

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 In vivo imaging of the kinetics of microglial self-renewal and maturation in the adult visual cortex

2020 ◽  
Author(s):  
Monique S. Mendes ◽  
Jason Atlas ◽  
Zachary Brehm ◽  
Antonio Ladron-de-Guevara ◽  
Matthew N. McCall ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Visual Cortex ◽  
Adult Brain ◽  
Self Renewal ◽  
Two Photon ◽  
And Migration ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
The Brain

AbstractMicroglia are the resident immune cells in the brain with the capacity to autonomously self-renew. Under basal conditions, microglial self-renewal appears to be slow and stochastic, although microglia have the ability to proliferate very rapidly following depletion or in response to injury. Because microglial self-renewal has largely been studied using static tools, the mechanisms and kinetics by which microglia renew and acquire mature characteristics in the adult brain are not well understood. Using chronic in vivo two-photon imaging in awake mice and PLX5622 (Colony stimulating factor 1 receptor (CSF1R) inhibitor) to deplete microglia, we set out to understand the dynamic self-organization and maturation of microglia following depletion in the visual cortex. We confirm that under basal conditions, cortical microglia show limited turnover and migration. Following depletion, however, microglial repopulation is remarkably rapid and is sustained by the dynamic division of the remaining microglia in a manner that is largely independent of signaling through the P2Y12 receptor. Mathematical modeling of microglial division demonstrates that the observed division rates can account for the rapid repopulation observed in vivo. Additionally, newly-born microglia resemble mature microglia, in terms of their morphology, dynamics and ability to respond to injury, within days of repopulation. Our work suggests that microglia rapidly self-renew locally, without the involvement of a special progenitor cell, and that newly born microglia do not recapitulate a slow developmental maturation but instead quickly take on mature roles in the nervous system.Graphical Abstract(a) Microglial dynamics during control condition. Cartoon depiction of the heterogenous microglia in the visual cortex equally spaced. (b) During the early stages of repopulation, microglia are irregularly spaced and sparse. (c) During the later stages of repopulation, the number of microglia and the spatial distribution return to baseline. (d-f) We then created and ran a mathematical model that sampled the number of microglia, (d) the persistent doublets, (e) the rapid divisions of microglia and (f) the secondary divisions of microglia during the peak of repopulation day 2-day 3. The mathematical model suggested that residual microglia can account for the rapid repopulation we observed in vivo.

scholarly journals A Mathematical Model of Immune-System-Melanoma Competition

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Marzio Pennisi
Keyword(s):  
Mathematical Model ◽  
Specific Immunotherapy ◽  
Melanoma Tumor ◽  
Injection Point ◽  
Combined Administration ◽  
Delay Differential ◽  
The Mathematical Model ◽  
Good Agreement

We present a mathematical model developed to reproduce the immune response entitled with the combined administration of activated OT1 cytotoxic T lymphocytes (CTLs) and Anti-CD137 monoclonal antibodies. The treatment is directed against melanoma in B16 OVA mouse models exposed to a specific immunotherapy strategy. We model two compartments: the injection point compartment where the treatment is administered and the skin compartment where melanoma tumor cells proliferate. To model the migration of OT1 CTLs and antibodies from the injection to the skin compartment, we use delay differential equations (DDEs). The outcomes of the mathematical model are in good agreement with the in vivo results. Moreover, sensitivity analysis of the mathematical model underlines the key role of OT1 CTLs and suggests that a possible reduction of the number of injected antibodies should not affect substantially the treatment efficacy.

Pressure Changes Induced by Whole Body Acceleration Shocks

1991 ◽  
Vol 113 (1) ◽  
pp. 27-29 ◽  
Author(s):  
E. Belardinelli ◽  
M. Ursino ◽  
G. Fabbri ◽  
A. Cevese ◽  
F. Schena
Keyword(s):  
Mathematical Model ◽  
Carotid Artery ◽  
Normal Pressure ◽  
Compressed Air ◽  
Whole Body ◽  
Body Acceleration ◽  
Vascular Bed ◽  
Pressure Changes ◽  
The Mathematical Model

In the present paper pressure changes induced by sudden body acceleration are studied “in vivo” on the dog and compared to the results obtainable with a recently developed mathematical model. A dog was fixed to a movable table, which was accelerated by a compressed air piston for less than 1 s. Acceleration was varied by changing the air pressure in the piston. Pressure was measured during the experiment at different points along the vascular bed. However, only data obtained in the carotid artery and abdominal aorta are presented here. The results demonstrated that impulse body accelerations cause significant pressure peaks in the vessel examined (about + 25 mmHg in the carotid artery with body acceleration of g/2). Moreover, pressure changes are rapidly damped, with a time constant of about 0.1s. From the present results it may be concluded that, according to the prediction of the mathematical model, body accelerations such as those occurring in normal life can induce pressure changes well beyond the normal pressure value.

Effects of CSF Properties on Brain Response Under Impact Loading

2009 ◽  
Author(s):  
M. S. Chafi ◽  
V. Dirisala ◽  
G. Karami ◽  
M. Ziejewski
Keyword(s):  
Human Head ◽  
Brain Response ◽  
Pia Mater ◽  
Mechanical Shocks ◽  
The Central Nervous System ◽  
Simultaneous Loading ◽  
The Impact ◽  
Impact Experiments ◽  
The Brain

In the central nervous system, the subarachnoid space is the interval between the arachnoid membrane and the pia mater. It is filled with a clear, watery liquid called cerebrospinal fluid (CSF). The CSF buffers the brain against mechanical shocks and creates buoyancy to protect it from the forces of gravity. The relative motion of the brain due to a simultaneous loading is caused because the skull and brain have different densities and the CSF surrounds the brain. The impact experiments are usually carried out on cadavers with no CSF included because of the autolysis. Even in the cadaveric head impact experiments by Hardy et al. [1], where the specimens are repressurized using artificial CSF, this is not known how far this can replicate the real functionality of CSF. With such motivation, a special interest lies on how to model this feature in a finite element (FE) modeling of the human head because it is questionable if one uses in vivo CSF properties (i.e. bulk modulus of 2.19 GPa) to validate a FE human head against cadaveric experimental data.

scholarly journals Change of photosensitizer fluorescence at its diffusion in viscous liquid flow

2016 ◽  
Vol 09 (02) ◽  
pp. 1650005 ◽  
Author(s):  
Valeriya S. Maryakhina ◽  
Vyacheslav V. Gun’kov
Keyword(s):  
Mathematical Model ◽  
Viscous Liquid ◽  
Liquid Flow ◽  
Fluorescence Spectra ◽  
Inflection Point ◽  
Biological Tissues ◽  
Transparency Window ◽  
Biological Liquid ◽  
The Mathematical Model

In this paper, the mathematical model of distribution of the injected compound in biological liquid flow has been described. It is considered that biological liquid contains a few phases such as water, peptides and cells. The injected compound (for example, photosensitizer) can interact with peptides and cells. At the time, viscosity of the biological liquid depends on pathology present in organism. The obtained distribution of the compound connects on changes of its fluorescence spectra which are registered during fluorescent diagnostics of tumors. It is obtained that the curves do not have monotonic nature. There is a sharp curves decline in the first few seconds after injection. Intensivity of curves rises after decreasing. It is especially pronounced for wavelength 590[Formula: see text]nm and 580[Formula: see text]nm (near the “transparency window” of biological tissues). Time of inflection point shifts from 8.4[Formula: see text]s to 6.9[Formula: see text]s for longer wavelength. However, difference between curves is little for different viscosity means of the biological liquid. Thus, additional pathology present in organism does not impact to the results of in vivo biomedical investigations.

scholarly journals Computer Simulation of the King's Cross Fire: Effect of Radiative Heat Transfer on Fire Spread

1991 ◽  
Vol 205 (3) ◽  
pp. 201-208 ◽  
Author(s):  
W M G Malalasekera ◽  
F Lockwood
Keyword(s):  
Mathematical Model ◽  
Radiative Heat ◽  
Health And Safety ◽  
Fire Spread ◽  
Future Research ◽  
Full Description ◽  
Department Of Health ◽  
Underground Fire ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model has been applied to simulate model experiments of the 1987 King's Cross underground fire by the Department of Health and Safety Executive. The predicted growth of the fire is compared with the experimental data and in particular the predicted and measured times to ‘flashover’ are compared. The comparisons show exceptional agreement which, in part, may be fortuitous due to the need to facilitate the prediction of the early stages of the growth with the aid of an experimentally estimated fire strength. The good agreement nonetheless is also due to the full description of the radiation transfer which is a feature of the mathematical model. It is concluded that the flashover phenomenon that occurred at King's Cross was thermal radiation driven and that future research should be devoted to modelling the details of fire spread across a combustible surface.

scholarly journals Developing Brain-Strain-Based Scaling to Inform the Clinical Relevance of Mouse Models of Concussion Induced by Rotation

2021 ◽  
Author(s):  
Xingyu Liu ◽  
Lihong Lu ◽  
Kewei Bian ◽  
Arthur Brown ◽  
Haojie Mao
Keyword(s):  
Brain Injury ◽  
Real World ◽  
Clinical Relevance ◽  
Neuronal Damage ◽  
Animal Experiments ◽  
Human Head ◽  
Axial Rotation ◽  
Head Impacts ◽  
Flexion Extension ◽  
Human And Mouse

Abstract Background Laboratory animal experiments are an invaluable tool for studying mild traumatic brain injury (mTBI)/concussion. Among them, rodent neurotrauma experiments have been most widely used, as transgenic and gene targeting technologies in mice allow us to test the roles of different genes in recovery from brain injury. Furthermore, the clinical relevance of rodent concussion studies can be improved by using these technologies to study concussions in animals that carry the human versions of genes known to play a role in neurological disease. However, delivering concussion injuries to the mice that are relevant to real-world human head impacts is challenging, as the mouse and human heads are dramatically different in shape and size. In the vast majority of mouse concussion experiments, the pathological and behavioral consequences of the injuries are evaluated without considering whether the injury model produces brain stretches (maximum principal strains) of the same magnitude as those experienced by human brains undergoing similar impacts. Methods We conducted a total of 201 computational simulations to understand both human and mouse brain strains that are directly linked to neuronal damage during closed-head concussive impacts. To represent real-world human head impacts we simulated mouse head impacts with durations of 1.5 ms (Type 1 scaling), followed by simulations with durations between 1 and 2 ms (Type 2), and finally, simulations with durations from 0.75 to 4.5 ms (Type 3) to develop scaling between human and mouse, as well as to reveal the predicted effects of small and large changes in impact durations on brain strain. Results Guided by these simulations we calculated that peak rotational velocities in mice could be achieved by scaling human peak rotational velocities with factors of 5.8, 4.6, and 6.8, for flexion/extension, lateral bending, and axial rotation, respectively, to reach equal brain strains between human and mouse. The effects of impact durations on scaling were also calculated and longer-duration mouse head impacts needed larger scaling factors to reach equal strain. Conclusions The scaling method will help us to create brain injury in the mouse with brain strain loading equivalent to those experienced in real-world human head impacts.

The Onset of Tear Propagation at Slits in Stressed Uncoated Plain Weave Fabrics

1999 ◽  
Vol 66 (4) ◽  
pp. 926-933 ◽  
Author(s):  
T. A. Godfrey ◽  
J. N. Rossettos
Keyword(s):  
Mathematical Model ◽  
Micromechanical Model ◽  
Crucial Aspect ◽  
Damage Site ◽  
Plain Weave ◽  
Actual Configuration ◽  
Tear Propagation ◽  
The Mathematical Model ◽  
Frictional Slip ◽  
Good Agreement

A simple micromechanical model is developed to predict the onset of tear propagation at slit-like damage sites (i.e., a series of consecutive aligned yarn breaks) in biaxially stressed plain weave fabrics under increasing loading. A crucial aspect of the model is the treatment of the frictional slip of yarns near the damage site. Although the actual configuration of slipping regions is complex, the onset of tear propagation in large slits (i.e., more than, say, 35 breaks) is dominated by slip occurring on the first few intact yarns adjacent to the breaks. The assumptions in the mathematical model were motivated by both experimental observations and calculations for key configurations. Analytical results obtained for this simple model exhibit good agreement with experimental results, which are presented for a variety of fabrics with initial slits of 35 and 45 breaks.

An enhanced composting process with bioaugmentation: Mathematical modelling and process optimization

2021 ◽  
pp. 0734242X2110337
Author(s):  
Tea Sokač ◽  
Anita Šalić ◽  
Dajana Kučić Grgić ◽  
Monika Šabić Runjavec ◽  
Marijana Vidaković ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Simulation ◽  
Process Conditions ◽  
Air Flow Rate ◽  
Optimal Process ◽  
Composting Process ◽  
Different Types ◽  
Adiabatic Reactor ◽  
The Mathematical Model ◽  
Good Agreement

In this paper, two different types of biowaste composting processes were carried out – composting without and with bioaugmentation. All experiments were performed in an adiabatic reactor for 14 days. Composting enhanced with bioaugmentation was the better choice because the thermophilic phase was achieved earlier, making the composting time shorter. Additionally, a higher conversion of substrate (amount of substrate consumed) was also noticed in the process enhanced by bioaugmentation. A mathematical model was developed and process parameters were estimated in order to optimize the composting process. Based on good agreement between experimental data and the mathematical model simulation results, a three-level-four-factor Box-Behnken experimental design was employed to define the optimal process conditions for further studies. It was found that the air flow rate and the mass fraction of the substrate have the most significant effect on the composting process. An improvement of the composting process was achieved after altering the mentioned variables, resulting in shorter composting time and higher conversion of the substrate.

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