scholarly journals Development and Validation of a Mathematical Model to Describe Anti-Cancer Prodrug Activation by Antibody-Enzyme Conjugates

2000 ◽  
Vol 2 (2) ◽  
pp. 93-111 ◽  
Author(s):  
Trachette L. Jackson ◽  
Peter D. Senter ◽  
James D. Murray
Keyword(s):  
Mathematical Model ◽  
Cancer Chemotherapy ◽  
Critical Parameters ◽  
Treatment Protocols ◽  
Drug Permeability ◽  
Drug Levels ◽  
Anti Cancer ◽  
Model Predictions ◽  
Development And Validation ◽  
Systemic Drug

A mathematical model has been developed for a two-step approach to cancer chemotherapy involving the use of targeted monoclonal antibody-enzyme conjugates for the selective activation of anti-cancer prodrugs. Theoretical analysis and numerical simulation are used to characterize critical parameters for intratumoral and systemic drug generation. The model suggests that the most important pharmacokinetic and clinical parameters for increased drug production in the tumor are the rate of prodrug clearance from the blood and the initial injected dose of prodrug. The physiological parameters with the most influence are the prodrug and drug permeability. The ratio of tumor to blood drug generation can best be improved by increasing the conjugate clearance from the blood and decreasing the rate at which prodrug is converted to active drug. Predictions from this model concerning intratumoral prodrug and drug levels are validated by comparison with experimental data. Finally, the effects of certain barriers to chemotherapeutic treatments including vascular heterogeneity and radially outward convection are studied. If vascular heterogeneity alone is considered, the model predicts that the highest drug levels will occur in the most poorly vascularized sections of the tumor. However, when the effects of convection directed radially outward is considered, the highest drug levels are seen in the semi-well vascularized regions. This implies that the rapidly growing periphery of the tumor and the semi-necrotic tumor interior will receive the least amount of drug. These mathematical model predictions can lead to improved treatment protocols for this two step approach to cancer chemotherapy.

Cyclodextrin polymers decorated with RGD peptide as delivery systems for targeted anti-cancer chemotherapy

2018 ◽  
Vol 37 (4) ◽  
pp. 771-778 ◽  
Author(s):  
Maurizio Viale ◽  
Rita Tosto ◽  
Valentina Giglio ◽  
Giuseppe Pappalardo ◽  
Valentina Oliveri ◽  
...  
Keyword(s):  
Cancer Chemotherapy ◽  
Delivery Systems ◽  
Rgd Peptide ◽  
Anti Cancer ◽  
Cyclodextrin Polymers

CH4 Direct Reduction of In-Flight Fe3O4 Concentrate Particles

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Bahador Abolpour ◽  
M. Mehdi Afsahi ◽  
Ataallah Soltani Goharrizi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fine Particles ◽  
Direct Reduction ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Dynamic Motion ◽  
Magnetite Ore ◽  
Model Predictions ◽  
Kinetics Of

Abstract In this study, reduction of in-flight fine particles of magnetite ore concentrate by methane at a constant heat flux has been investigated both experimentally and numerically. A 3D turbulent mathematical model was developed to simulate the dynamic motion of these particles in a methane content reactor and experiments were conducted to evaluate the model. The kinetics of the reaction were obtained using an optimizing method as: [-Ln(1-X)]1/2.91 = 1.02 × 10−2dP−2.07CCH40.16exp(−1.78 × 105/RT)t. The model predictions were compared with the experimental data and the data had an excellent agreement.

A mathematical model of rat collecting duct II. Effect of buffer delivery on urinary acidification

2002 ◽  
Vol 283 (6) ◽  
pp. F1252-F1266 ◽  
Author(s):  
Alan M. Weinstein
Keyword(s):  
Mathematical Model ◽  
Carbonic Anhydrase ◽  
Collecting Duct ◽  
Phosphate Concentration ◽  
Rate Coefficients ◽  
Urinary Flow ◽  
Urinary Acidification ◽  
Model Predictions ◽  
Disequilibrium Ph ◽  
Urinary Acid

A mathematical model of the rat collecting duct (CD) is used to examine the effect of delivered load of bicarbonate and nonbicarbonate buffer on urinary acidification. Increasing the delivered load of HCO[Formula: see text] produces bicarbonaturia, and, with luminal carbonic anhydrase absent, induces a disequilibrium luminal pH and a postequilibration increase in urinary Pco 2. At baseline flows, this disequilibrium disappears when luminal carbonic anhydrase rate coefficients reach 1% of full catalysis. The magnitude of the equilibration Pco 2 depends on the product of urinary acid phosphate concentration and the disequilibrium pH. Thus, although increasing phosphate delivery to the CD decreases the disequilibrium pH, the increase in urinary phosphate concentration yields an overall increase in postequilibration Pco 2. In simulations of experimental HCO[Formula: see text] loading in the rat, model predictions of urinary Pco 2 exceed the measured Pco 2 of bladder urine. In part, the higher model predictions for urinary Pco 2 may reflect higher urinary flow rates and lower urinary phosphate concentrations in the experimental preparations. However, when simulation of CD function during HCO[Formula: see text] loading acknowledges the high ambient renal medullary Pco 2 (5), the predicted urinary Pco 2 of the model CD is yet that much greater. This discrepancy cannot be resolved within the model but requires additional experimental data, namely, concomitant determination of urinary buffer concentrations within the tubule fluid sampled for Pco 2 and pH. This model should provide a means for simulating formal testing of urinary acidification and thus for examining hypotheses regarding transport defects underlying distal renal tubular acidosis.

scholarly journals Modelling Macrophage Infiltration into Avascular Tumours

2002 ◽  
Vol 4 (1) ◽  
pp. 21-38 ◽  
Author(s):  
C. E. Kelly ◽  
R. D. Leek ◽  
H. M. Byrne ◽  
S. M. Cox ◽  
A. L. Harris ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Spatial Structure ◽  
Random Motion ◽  
Numerical Results ◽  
Macrophage Infiltration ◽  
Numerical Techniques ◽  
Model Predictions ◽  
Independent Experimental Data

In this paper a mathematical model that describes macrophage infiltration into avascular tumours is presented. The qualitative accuracy of the model is assessed by comparing numerical results with independent experimental data that describe the infiltration of macrophages into two types of spheroids: chemoattractant-producing (hepa-1) and chemoattractant-deficient (or C4) spheroids. A combination of analytical and numerical techniques are used to show how the infiltration pattern depends on the motility mechanisms involved (i.e. random motion and chemotaxis) and to explain the observed differences in macrophage infiltration into the hepa-1 and C4 spheroids. Model predictions are generated to show how the spheroid's size and spatial structure and the ability of its constituent cells influence macrophage infiltration. For example, chemoattractant-producing spheroids are shown to recruit larger numbers of macrophages than chemoattractant-deficient spheroids of the same size and spatial structure. The biological implications of these results are also discussed briefly.

scholarly journals Mathematical model and simulations of MERS outbreak: Predictions and implications for control measures

BIOMATH ◽  
2017 ◽  
Vol 5 (2) ◽  
pp. 1612141 ◽  
Author(s):  
Nofe Al-Asuoad ◽  
Libin Rong ◽  
Sadoof Alaswad ◽  
Meir Shillor
Keyword(s):  
Mathematical Model ◽  
Middle East ◽  
Coupled System ◽  
Control Measures ◽  
Nonlinear Ordinary Differential Equations ◽  
Contact Rate ◽  
Isolation Rate ◽  
Model Predictions ◽  
The World ◽  
The City

The Middle East Respiratory Syndrome (MERS) has been identified in 2012 and since then outbreaks have been reported in various localities in the Middle East and in other parts of the world. To help predict the possible dynamics of MERS, as well as ways to contain it, this paper develops a mathematical model for the disease. It has a compartmental structure similar to SARS models and is in the form of a coupled system of nonlinear ordinary differential equations (ODEs). The model predictions are fitted to data from the outbreaks in Riyadh (Saudi Arabia) during 2013-2016. The results reveal that MERS will eventually be contained in the city. However, the containment time and the severity of the outbreaks depend crucially on the contact coefficients and the isolation rate constant. When randomness is added to the model coefficients, the simulations show that the model is sensitive to the scaled contact rate among people and to the isolation rate. The model is analyzed using stability theory for ODEs and indicates that when using only isolation, the endemic steady state is locally stable and attracting. Numerical simulations with parameters estimated from the city of Riyadh illustrate the analytical results and the model behavior, which may have important implications for the disease containment in the city. Indeed, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. The model is general and may be used to analyze outbreaks in other parts of the Middle East and other areas.

Experimental and Theoretical Investigation of Performance of a Solar Chimney Model Part II: Model Development and Validation

2021 ◽  
Vol 5 (2) ◽  
Author(s):  
Ibrahim A Abuashe ◽  
Bashir H Arebi ◽  
Essaied M Shuia
Keyword(s):  
Mathematical Model ◽  
Power Output ◽  
Model Development ◽  
Geometrical Parameters ◽  
Balance Equations ◽  
Solar Chimney ◽  
And Performance ◽  
Development And Validation ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model based on the momentum, continuity and energy balance equations was developed to simulate the behavior of the air flow inside the solar chimney system. The model can estimate the power output and performance of solar chimney systems. The developed mathematical model is validated by the experimental data that were collected from small pilot solar chimney; (experiment was presented in part I). Good agreement was obtained between the experimental results and that from the mathematical model. The model can be used to analyze the solar chimney systems and to determine the effect of geometrical parameters such as chimney height and collector diameter on the power output and the efficiency of the system

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