A Mathematical Model of Stochastic Engraftment by Non-Interacting Single Umbilical Cord Blood (UCB) Grafts Predicts Accelerated Engraftment Using Multiple UCB Grafts.

Blood ◽  
2007 ◽  
Vol 110 (11) ◽  
pp. 2034-2034 ◽  
Author(s):  
Anthony F. Waller ◽  
Fengrong Wang ◽  
Ned Waller
Keyword(s):  
Mathematical Model ◽  
Median Time ◽  
Weighted Average ◽  
Hematopoietic Progenitor Cell ◽  
Normal Distributions ◽  
Average Percentage ◽  
Calculated Curve ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
Multiple Units

Abstract Background: The use of UCB transplants is limited by the difficulty of finding units with sufficient cells to provide reliable engraftment, and the slower kinetics of hematopoietic engraftment compared to other hematopoietic progenitor cell grafts. Grafts consisting of two unrelated UCB result in accelerated engraftment compared to single unit UCB transplants, but the mechanism for enhanced engraftment is unknown. Methods: We extracted data from published studies on myeloid engraftment following transplantation of single (9 studies, 1542 engrafted patients) or double (4 studies, 94 engrafted patients) UCB units (Table). A weighted average of median days (and estimated SD) to engraft for single and double UCB transplants was calculated. The cumulative incidence of myeloid engraftment for single or double UCB transplants was modeled based the assumption that the time to engraft was described by a normal distribution. For double and triple UCB transplants, the probability of myeloid engraftment at any time post-transplant was calculated as 1 minus the probability of non-engraftment for a single UCB unit squared or cubed, respectively. Results: The weighted average percentage for myeloid engraftment following single UCB transplants was 89%, with a median day of engraftment of 26.4 days. The weighted average for the rate of myeloid engraftment following double UCB transplants was 96%, with a median day of engraftment of 22 days. The calculated median days to engraft from single or double UCB transplants, using the assumption of normal distributions, were 22 and 26 days, respectively. Applying the mathematical model, the predicted cumulative engraftment for a double UCB graft is 99%, with a the curve for cumulative engraftment kinetics quite similar to the observed engraftment in Barker 2005 and the calculated curve for double UCB transplants based upon analysis of extracted data (Figure). Conclusion: UCB units do not appear to facilitate engraftment in grafts containing multiple units. A stochastic statistical model, in which different UCB grafts engraft independently, appears to account for the observed 4-day decrease in the median time to achieve myeloid engraftment following a double versus single UCB transplant. The use of a triple UCB graft is predicted to shorten the median time to achieve neutrophil engraftment to a median of 20 days. Published experiences describing myeloid engraftment following single and double UCB transplants Single UCB Transplant N, % engrafted Median day to engraft Double UCB Transplants N, % engrafted Median day to engraft Laughlin NEJM 2001 N=61, 90% 27 Barker Blood 2005 N=50, 100% 23 Hamza BJH 2004 N=28, 86% 29 Yoo ASH 2005 N=12, 100% 23 Barker Blood 2001 N=31, 88% 26 Kai ASH 2004 N=11, 82% 21 Thomson Blood 2000 N=30, 81% 25 Ballen ASH 2005 N=21, 90% 20 Sanz Blood 2001 N=22, 100% 22 Terakura BBMT 2007 N=148, 81% 22 Wagner Blood 2002 N=102, 86% 22 Migliaccio Blood 2000 N=200, 91% 28 Stevens Blood 2002 N=1111, 90% 27 Figure Figure

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

scholarly journals Drying kinetics of Chinese garlic (Allium tuberosum) and its effect on color

2020 ◽  
Vol 42 ◽  
pp. e8
Author(s):  
Paula De Almeida Rios ◽  
Ednilton Tavares De Andrade ◽  
Kátia Soares Moreira ◽  
Filipe Da Silva De Oliveira ◽  
Bárbara Lemes Outeiro Araújo
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Air Temperature ◽  
Linear Regression Analysis ◽  
Drying Kinetics ◽  
Allium Tuberosum ◽  
Thin Slices ◽  
The Mathematical Model ◽  
Quasi Newton ◽  
Kinetics Of

Dehydrated garlic is an important component both for culinary and medicinal purposes. However, there is a scarcity of studies that characterizes its drying kinetics. Thus, the objective of this work was to study the drying kinetics of Chinese garlic (Allium tuberosum), as well as to analyze the color effect resulting from each treatment. The garlic bulbs were cut into thin slices with a width of 2 and 3 mm, subjected to the drying air temperature of 35, 45, 55 and 70 °C in a mechanical dryer of a fixed layer with forced convection. Was performed a non-linear regression analysis by the Quasi-Newton method, for adjustment to 11 mathematical models to the experimental data of drying. The Midilli equation was the mathematical model that best characterized all the drying temperatures, for the experimental data. The diffusion coefficient presented values between 1.46 x 10-11 and 7.32 x 10-11 m2.s-1. The increase of the drying air temperature caused the dimming of the samples with a reduction of the L* coordinate and reduction of the yellow of the samples according to the coordinate results h*. The temperature of 70 °C was detrimental to the maintenance of the Chinese garlic coloration. 

scholarly journals МАТЕМАТИЧЕСКАЯ МОДЕЛЬ И МЕТОД РАСЧЕТА ДИНАМИКИ СУШКИ И ТЕРМОДЕСТРУКЦИИ БИОМАССЫ

2018 ◽  
Vol 82 (1) ◽  
Author(s):  
Наталья Николаевна Сороковая ◽  
Дмитрий Николаевич Коринчук
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Thermal Decomposition ◽  
Numerical Method ◽  
Heat And Mass Transfer ◽  
The Body ◽  
Physical Factors ◽  
Deformation Equation ◽  
The Mathematical Model ◽  
Kinetics Of

Разработана математическая модель и численный метод расчета динамики тепломассопереноса, фазовых превращений и усадки при сушке коллоидных капиллярно-пористых тел цилиндрической формы в условиях равномерного обдува теплоносителем. Математическая модель строилась на базе дифференциального уравнения переноса субстанции (энергии, массы, импульса) в деформируемых системах. Проведены экспериментальные исследования кинетики обезвоживания частиц энергетической вербы в потоке воздуха с целью верификации математической модели. Обоснована возможность ее использования для расчета совместных процессов сушки и начального этапа термического разложения биомассы. С использованием ранее полученных данных по значениям энергии активации Аэф(Т) для различных видов биомассы проведено математическое моделирование динамики и кинетики высокотемпературной сушки в потоке дымовых газов энергетической вербы, которая сопровождается термодеструкцией гемиоцеллюлозы. Результаты численных экспериментов свидетельствуют об адекватности предложенного подхода, эффективности математической модели и метода ее реализации. На их основе возможно проводить исследование динамики тепломассопереноса при сушке частиц различных видов измельченной биомассы; определение температуры начала и окончания первой стадии термического разложения; момента достижения равновесного влагосодержания в зависимости от свойств материала и сушильного агента. Эти данные позволяют выбирать оптимальные с точки зрения сохранения энергии и качества высушиваемого продукта  режимные параметры процесса.         A mathematical model and a numerical method for calculating the dynamics of heat and mass transfer, phase transformations and shrinkage during the drying of colloidal capillary-porous cylindrical bodies under conditions of equitable winding by a coolant are developed. The mathematical model was based on the differential equation of substance (energy, mass, impulse) transfer in deformable systems. It includes the equations diffusion-filtration transfer of energy for the system as a whole, and the mass transfer of the liquid, vapor and air phases in the pores of the body. Expressions for the intensity of evaporation of a liquid, capillary pressure, and the diffusion coefficients are presented. The relative volume strain was found by means of an analytical solution of the thermoconcentration deformation equation. Based on the explicit three-layer counting difference scheme and the procedure splitting of algorithm  by physical factors, a numerical method for realizing this mathematical model is developed.Experimental studies of the kinetics of dehydration of energy willow particles in the airflow were carried out to verify the mathematical model. Its applicability for calculating combined processes of drying and of the initial stage of thermal decomposition of biomass is substantiated. Using the previously obtained data on the activation energy values for various types of biomass, a mathematical simulation of the dynamics and kinetics of high-temperature drying in the flue gas flow of energy willow was carried out, which is accompanied by thermal destruction of hemiocellulose. The results of numerical experiments indicate the adequacy of the proposed approach, the effectiveness of the mathematical model and the method of its implementation. On their basis, it is possible to study the dynamics of heat and mass transfer when drying particles of different types of ground biomass; determination of the temperature of the beginning and ending of the first stage of thermal decomposition; the moment when the equilibrium moisture content is reached, depending on the properties of the material and the drying agent. These data allow choosing the process parameters that are optimal in terms of energy saving and quality of the dried product.

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.

Effect of Global Ventilation to Perfusion Ratio, for Normal Lungs, on Desflurane and Sevoflurane Elimination Kinetics

2021 ◽  
Author(s):  
James E. Baumgardner ◽  
Moritz Kretzschmar ◽  
Alf Kozian ◽  
Thomas Hachenberg ◽  
Thomas Schilling ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Time Constant ◽  
Practical Importance ◽  
Elimination Kinetics ◽  
Retention Equation ◽  
Pressure Part ◽  
Inhaled Anesthetic ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
Normal Lungs

Background Kinetics of the uptake of inhaled anesthetics have been well studied, but the kinetics of elimination might be of more practical importance. The objective of the authors’ study was to assess the effect of the overall ventilation/perfusion ratio ( .VA/.Q  ), for normal lungs, on elimination kinetics of desflurane and sevoflurane. Methods The authors developed a mathematical model of inhaled anesthetic elimination that explicitly relates the terminal washout time constant to the global lung  .VA/.Q   ratio. Assumptions and results of the model were tested with experimental data from a recent study, where desflurane and sevoflurane elimination were observed for three different  .VA/.Q   conditions: normal, low, and high. Results The mathematical model predicts that the global  .VA/.Q   ratio, for normal lungs, modifies the time constant for tissue anesthetic washout throughout the entire elimination. For all three  .VA/.Q   conditions, the ratio of arterial to mixed venous anesthetic partial pressure Part/Pmv reached a constant value after 5 min of elimination, as predicted by the retention equation. The time constant corrected for incomplete lung clearance was a better predictor of late-stage kinetics than the intrinsic tissue time constant. Conclusions In addition to the well-known role of the lungs in the early phases of inhaled anesthetic washout, the lungs play a long-overlooked role in modulating the kinetics of tissue washout during the later stages of inhaled anesthetic elimination. The  .VA/.Q  ratio influences the kinetics of desflurane and sevoflurane elimination throughout the entire elimination, with more pronounced slowing of tissue washout at lower  .VA/.Q   ratios. Editor’s Perspective What We Already Know about This Topic What This Article Tells Us That Is New

Modelling the Wear Process of Inhomogeneous Bodies

2005 ◽  
Author(s):  
I. G. Goryacheva
Keyword(s):  
Mathematical Model ◽  
Phase Composition ◽  
Contact Mechanics ◽  
Two Phase ◽  
Wear Process ◽  
Substrate Interface ◽  
Inhomogeneous Bodies ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
Local Hardening

The approaches of contact mechanics are used to evaluate the evolution of the contact characteristics in wear process of inhomogeneous bodies (coated bodies, two-phase composition, bodies with inclusions, etc.). The mathematical model is formulated and used to study the kinetics of the wear process depending on the parameters of inhomogeneity such as size and density of inclusions, waviness at the coating-substrate interface, local hardening parameters, etc.

Mathematical modeling of aluminum degassing by the impeller injector technique validated by a physical modeling

2014 ◽  
Vol 1611 ◽  
pp. 49-54 ◽  
Author(s):  
M. Hernández-Hernández ◽  
W. F. Cruz-Mendez ◽  
C. Gonzalez-Rivera ◽  
M. A. Ramírez-Argáez
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Gas Flow ◽  
Process Analysis ◽  
Liquid Aluminum ◽  
Bubble Diameter ◽  
Operating Parameter ◽  
Gas Flow Rate ◽  
The Mathematical Model ◽  
Kinetics Of

ABSTRACTA mathematical model is developed to describe deoxidation of water in a physical model of a batch aluminum degassing reactor equipped with the rotor-injector technique, assuming that deoxidation kinetics of water is similar to dehydrogenization of liquid aluminum. Degassing kinetics is described by using mass transport and mass balance principles by assuming that degassing kinetics can be characterized by a mass transfer coefficient, which depends on the process variables. The transport coefficient and the average bubble diameter are estimated with correlations reported in the literature for similar gas-injection systems. The water physical model helped to validate the mathematical model and to perform a process analysis by varying: 1) Gas flow rate (20 and 40 l/min); and 2) Impeller’s angular velocity (290 and 573 rpm). Results from the model agree well with measurements of deoxidation kinetics at low impeller rotating speeds. At high rotating speeds the model is still valid but less reliable because it does not take into account the formation of the vortex at the free surface. Nevertheless, the model provides predictions of the influence of every operating parameter and it can be used as a good approximation for real systems.

scholarly journals Extraction Process of Intracellular Substance

2010 ◽  
Vol 4 (2) ◽  
pp. 163-166
Author(s):  
Vasil Dyachok ◽  
Keyword(s):  
Mathematical Model ◽  
Plant Material ◽  
Extraction Process ◽  
Anatomical Structure ◽  
Process Conditions ◽  
Intercellular Spaces ◽  
Process Implementation ◽  
Kinetic Coefficients ◽  
The Mathematical Model ◽  
Kinetics Of

In this study the mathematical model of the extraction process from plant material is developed, taking into account the anatomical structure of plant material, namely the presence of cellular and intercellular spaces. The solution of the model enables to determine its kinetic coefficients Dc, Dt, process conditions, and predict the kinetics of the extraction process implementation in practice.

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