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.

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.

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.

scholarly journals The Mathematical Model for Total Pubertal Growth in Idiopathic Growth Hormone (GH) Deficiency Suggests a Moderate Role of GH Dose

2003 ◽  
Vol 88 (10) ◽  
pp. 4748-4753 ◽  
Author(s):  
Michael B. Ranke ◽  
Anders Lindberg ◽  
David D. Martin ◽  
Bert Bakker ◽  
Patrick Wilton ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Growth Hormone ◽  
Gh Deficiency ◽  
Pubertal Growth ◽  
The Mathematical Model

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.

Biomechanics of Soft Tissues: The Role of the Mathematical Model on Material Behavior

2019 ◽  
pp. 301-311
Author(s):  
Carlos Bustamante-Orellana ◽  
Robinson Guachi ◽  
Lorena Guachi-Guachi ◽  
Simone Novelli ◽  
Francesca Campana ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Soft Tissues ◽  
Material Behavior ◽  
The Mathematical Model

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.

KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

2021 ◽  
pp. 43-54
Author(s):  
A. N. Krutov ◽  
◽  
S. Ya. Shkol’nikov ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Method ◽  
Wave Equations ◽  
Simple Wave ◽  
Kinematic Wave ◽  
Calculation Results ◽  
Self Similar ◽  
Similar Solutions ◽  
The Mathematical Model ◽  
Good Agreement

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

A Differential Equation of the First Law of Thermodynamics for Modeling the Indicator Process of a Diesel Engine

1997 ◽  
Author(s):  
Stanislav N. Danov
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
High Pressure And Temperature ◽  
First Law Of Thermodynamics ◽  
Ideal Gases ◽  
Working Medium ◽  
Engine Cylinder ◽  
Computing Procedure ◽  
The Mathematical Model ◽  
Good Agreement

Abstract Several improvements to the mathematical model of the indicator process taking place at a diesel engine cylinder are proposed. The thermodynamic behavior of working medium is described by the equation of state, valid for real gases. Mathematical dependencies between thermal parameters (P, T, v) and caloric parameters (u, h, cv, cp) have been obtained. An improved mathematical model, based on the first law of thermodynamics, has been developed, taking into account working medium imperfections. The numerical solution of the simultaneous differential equations is made by a method of Runge-Kutta type. The computing procedure is iterative. Calculations in respect to the caloric parameters (u, h, cv and cp) for various gases under pressure up to 25 MPa and temperature up to 3000°C have been carried out. The results show, that there are significant differences between the values, calculated by equations for ideal gases, and the proposed equations for real gases under high pressure and temperature. Actual applied problems for two-stroke turbocharged engines Sulzer-RLB66 and 8DKRN 74/160 have been solved. The comparison between the experimental data and numerical results show very good agreement. The numerical experiments show that if the pressure is above 8–9 MPa, the working medium imperfections must be taken into consideration.

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