| 1. |
- Anjum, Asad Ur Rehman, et al.
(författare)
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Sensitivity Analysis of Mathematical Model to Study the Effect of T Cells Infusion in Treatment of CLL
- 2020
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Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 8:4
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we considered a mathematical model concerned with the treatment of Chronic Lymphocytic Leukemia (CLL) taking into account the effect of superficially infused T cells in this particular type of tumor. The model is described thoroughly by the system of non-linear differential equations explaining the interaction of naive, infected, cancer and immune cell population. The detailed sensitivity analysis with the application is the major part of this paper. The basic objective is to provide insight to how parameters' behavior varies model results by elaborating the results obtained from the application of sensitivity analysis. The sensitivity of the model was evaluated not only theoretically, but also with the help of a numerical approach, producing graphs providing better imminent of results. We argue that the application of the sensitivity analysis method endows an insight into how and which parameters are of primary significance in controlling the spread of leukemia.
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| 2. |
- Arslan, Muhammad, et al.
(författare)
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Impact of Varying Load Conditions and Cooling Energy Comparison of a Double-Inlet Pulse Tube Refrigerator
- 2020
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Ingår i: Processes. - : MDPI. - 2227-9717. ; 8:3
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Tidskriftsartikel (refereegranskat)abstract
- Modeling and optimization of a double-inlet pulse tube refrigerator (DIPTR) is very difficult due to its geometry and nature. The objective of this paper was to optimize-DIPTR through experiments with the cold heat exchanger (CHX) along the comparison of cooling load with experimental data using different boundary conditions. To predict its performance, a detailed two-dimensional DIPTR model was developed. A double-drop pulse pipe cooler was used for solving continuity, dynamic and power calculations. External conditions for applicable boundaries include sinusoidal pressure from an end of the tube from a user-defined function and constant temperature or limitations of thermal flux within the outer walls of exchanger walls under colder conditions. The results of the system's cooling behavior were reported, along with the connection between the mass flow rates, heat distribution along pulse tube and cold-end pressure, the cooler load's wall temp profile and cooler loads with varied boundary conditions i.e. opening of 20% double-inlet and 40-60% orifice valves, respectively. Different loading conditions of 1 and 5W were applied on the CHX. At 150 K temperature of the cold-end heat exchanger, a maximum load of 3.7 W was achieved. The results also reveal a strong correlation between computational fluid dynamics modeling results and experimental results of the DIPTR.
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| 3. |
- Chaudhry, Qasim Ali
(författare)
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Computational Modeling of Reaction and Diffusion Processes in Mammalian Cell
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- PAHs are the reactive toxic chemical compounds which are present as environmental pollutants. These reactive compounds not only diffuse through the membranes of the cell but also partition into the membranes. They react with the DNA of the cell giving rise to toxicity and may cause cancer. To understand the cellular behavior of these foreign compounds, a mathematical model including the reaction-diffusion system and partitioning phenomenon has been developed. In order to reduce the complex structure of the cytoplasm due to the presence of many thin membranes, and to make the model less computationally expensive and numerically treatable, homogenization techniques have been used. The resulting complex system of PDEs generated from the model is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. Then the model was reduced to a system of ODEs, a compartment model (CM). The quantitative analysis of the results of the CM shows that it cannot fully capture the features of metabolic system considered in general. Thus the PDE model affords a more realistic representation. In order to see the influence of cell geometry in drug diffusion, the non-spherical axi-symmetric cell geometry is considered, where we showed that the cellular geometry plays an important role in diffusion through the membranes. For further reduction of complexity of the model, another simplified model was developed. In the simplified model, we used PDEs for the extracellular domain, cytoplasm and nucleus, whereas the plasma and nuclear membranes were taken away, and replaced by the membrane flux, using Fick's Law. We further extended the framework of our previously developed model by benchmarking against the results from four different cell lines. Global optimization techniques are used for the parameters describing the diffusion and reaction to fit the measured data. Numerical results were in good agreement with the in vitro results. For the further development of the model, the process of surface bound reactions were added, thus developing a new cell model. The effective equations were derived using iterative homogenization for this model. The numerical results of some of the species were qualitatively verified against the in vitro results found in literature.
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| 4. |
- Chaudhry, Qasim Ali, et al.
(författare)
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Influence of Biological Cell Geometry on Reaction and Diffusion Simulation
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Mathematical modeling of reaction-diffusion system in a biological cellis an important and difficult task, especially when the chemical compoundsare lipophilic. The difficulty level increases, when we take into account theheterogeneity of the cell, and the variation of cellular architecture. Mathematicalmodeling of reaction-diffusion systems in spherical cell geometryhas earlier been performed by us. In the present paper, we have workedwith non-spherical cell geometry, because the cellular geometry can play animportant role for drug diffusion in the cell. Homogenization techniques,which were earlier applied in the case of a spherical cell model, have beenused for the numerical treatment of the model. This technique considerablyreduces the complexity of the model. To further reduce the complexity ofthe model, a simplified model was also developed. The key idea of this simplifiedmodel has been advocated in Virtual Cell, where PDEs are used forthe extracellular domain, cytoplasm and nucleus, whereas the plasma andnuclear membranes have been taken away, and replaced by membrane flux,using Fick’s Law of diffusion. The numerical results of the non-sphericalcell model have been compared with the results of the spherical cell model,where the numerical results of spherical cell model have already been validatedagainst in vitro cell experimental results. From the numerical results,we conclude that the plasma and nuclear membranes can be protective reservoirsof significance. The numerical results of the simplified model werecompared against the numerical results of our detailed model, revealing theimportance of detailed modeling of membranes in our model.
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| 5. |
- Chaudhry, Qasim Ali, et al.
(författare)
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Mathematical Modeling of Reaction and Diffusion Systems in a Cell Including Surface Reactions on the Cytoplasmic Membranes
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Benzo[a]pyrene (BP) is a toxic polycyclic aromatic hydrocarbon (PAH) whichis found in our environment. These BPs are metabolized to benzo[a]pyrene diol(BPD) by enzymes bound to the cytoplasmic membranes e.g. members of thecytochrome P450 protein family and epoxide hydrolyses. BPDs are further metabolizedto two stereochemical variants of Benzo[a]pyrene diol expoxide (BPDE) bythe cytochrome P450 family of proteins. These are the two steps of metabolismcategorized as Phase I. In Phase II, BPDEs are further metabolized by soluble enzymesin the cytoplasm e.g. members of the glutathione transferase protein familyto GSH conjugates. BPDE can also diffuse into the cellular nucleus and reactwith DNA forming mutagenic DNA adducts. The formation of GSH conjugatesand DNA adducts, was earlier studied by us by developing a mathematical modeldescribing the intracellular reaction and diffusion of lipophilic PAHs taking intoaccount the partitioning phenomenon (Dreij K et al. PLoS One 6(8), 2011). In thispaper part of Phase I metabolism i.e formation of BPDE metabolites, will be addedto the model, thus enhancing the previous model. These cytochrome P450 reactionstake place on the intracellular membranes, and are modeled as a membranesurface reaction within the cytoplasm using the standard process of adsorption anddesorption. The effective equations are derived using iterative homogenization forthe numerical treatment of the cytoplasm including surface effects. The numericalresults of some of the species have been qualitatively verified against in vitroresults found in the literature.
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| 6. |
- Chaudhry, Qasim Ali, 1982-
(författare)
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Numerical Approximation of Reaction and Diffusion Systems in Complex Cell Geometry
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The mathematical modelling of the reaction and diffusion mechanism of lipophilic toxic compounds in the mammalian cell is a challenging task because of its considerable complexity and variation in the architecture of the cell. The heterogeneity of the cell regarding the enzyme distribution participating in the bio-transformation, makes the modelling even more difficult. In order to reduce the complexity of the model, and to make it less computationally expensive and numerically treatable, Homogenization techniques have been used. The resulting complex system of Partial Differential Equations (PDEs), generated from the model in 2-dimensional axi-symmetric setting is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. The model can be extended to more complex reaction systems and also to 3-dimensional space. For the reduction of complexity and computational cost, we have implemented a model of mixed PDEs and Ordinary Differential Equations (ODEs). We call this model as Non-Standard Compartment Model. Then the model is further reduced to a system of ODEs only, which is a Standard Compartment Model. The numerical results of the PDE Model have been qualitatively verified by using the Compartment Modeling approach. The quantitative analysis of the results of the Compartment Model shows that it cannot fully capture the features of metabolic system considered in general. Hence we need a more sophisticated model using PDEs for our homogenized cell model.
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| 7. |
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| 8. |
- Chaudhry, Qasim Ali, 1982-, et al.
(författare)
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On the numerical approximation of drug diffusion in complex cell geometry
- 2009
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Ingår i: Proceedings of the 6th International Conference on Frontiers of Information Technology, FIT '09. - Abbottabad : ACM. - 9781605586427
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The mathematical modeling of a mammalian cell is a very tedious work due to its very complex geometry. Especially, taking into account the spatial distribution and the inclusion of lipophilic toxic compounds greatly increases its complexity. The nonhomogeneity and the different cellular architecture of the cell certainly affect the diffusion of these compounds. The complexity of the whole system can be reduced by a homogenization technique. To see the effect of these compounds on different cell architectures, we have implemented a mathematical model. The work has been done in 2-dimensional space. The simulation results have been qualitatively verified using compartmental modeling approach. This work can be extended with a more complex reaction-diffusion system and to 3-dimensional space as well. Copyright 2009 ACM.
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