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Human Body Drug Simulation Nathan Liles Benjamin Munda

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Presentation Outline Objective Background Model Overview Organ and Body Theory Case Studies

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Objective Pharmacokinetics : Seeks to determine fate of substances administered externally to a living organism Our focus, Oral Administration a) most common, practical b) model can be expanded Our project focuses on the first objective above: creating an overall PBPK model that is accurate, physiologically correct, and innovative 1) Overall PBPK ADME model a) How to divide the body and describe movement? b) How to make mathematical model consistent with physiology/anatomy of the human body 2) Specific Component of a PBPK model a) How does a drug’s structure and charge affect its movement in capillaries? b) How does an enzyme within the liver interact with a drug? Are any intermediates created?

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Background: Potential Applications On Pharmaceuticals every year: a)Companies R&D ≈ $70 billion b) Consumers spend≈ $200 billion A Mathematical Body Model Could: a)For Companies: Accelerate R&D b)For consumers: Help doctors optimize doses Lower costs of prescription drugs

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Background: What Has Been Done Previous Work: Our Work ≈1,100 Simultaneous ODEs ≈200 constants ≈100,000 steps 1)Began with current models of key organs 2)23 Tissues included, avoided well-mixed assumption 3)Incorporated the tissues into a circulatory system with mass transfer on the capillary level 1)Compartment models 2)Well-mixed regions 3)Few parameters <15 4)Few equations < 25

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Overview of Our Proposed Model Path of drug 1)Enters stomach 2)Moves through small intestine 3)Enters the blood, first pass through the liver 4)Liver to the heart 5)Heart to the entire body 6)Interacts with the body a) Reacts at intended site b) Eliminated in liver, kidney 7)Returns to the Heart a 6b 7

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Absorption: Stomach Stomach information : 1) “Churning” creates a well mixed volume 2) Exit flow rate of mass depends on the mass inside the stomach 3) Little absorption of the drug into the bloodstream occurs in the stomach Governing Equations: 1) For liquids2) For solids Flow rate: 1)Dose (mg) enters stomach, which has some mass inside 2)The drug exits with a semi- constant concentration and a flow rate that varies with : a) L or S? b) Mass c) Liberation Concentration:

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Stomach Results

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Absorbtion: Small Intestine Small Intestine Information: 1)Main site of drug absorption 2)≈7 meters long with an average diameter of cm 3) Modeled as a PFR Governing Equation Assumptions a) Radial variations are unimportant b) Diffusive flux term is negligible Final Form: c) Superficial velocity is a variable

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Absorbtion: Small Intestine A LaPlace transform was performed in the z-dimension. The equation became a linear homogenous ODE in the time dimension. This integral cannot be solved analytically, thus the inverse Laplace transform cannot be solved.

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Numerical Methods Method of Lines 1) Discretize Space Variable Z 2) System of Equations to Solve

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Numerical Methods 4 th Order Runge-Kutta Method of lines means we have many ordinary differential equations=4RK Used to integrate a function: Described by a 1 st Order ODE: Given initial values for y estimates next y in time by: Where values for k (slope estimates) come from:

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Small Intestine Results

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Absorbtion: Small Intestine Amount absorbed through the gut wall for each time interval

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Distribution Estimations used in distribution : 1) Time from SI to liver negligible 2) Time from Inferior vena cava to heart negligible. 3) 8 seconds to get from the right heart to the left heart 4) 3 Seconds to get to the extremities. 5) 3 seconds back to the heart

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Distribution: Blood Concentration Governing Equations 1) 2) 1)Blood concentration is the ‘heart’ of our model 2)Heart chosen as site to track Heart Information : 1)Well mixed tank 2)Receives influx from entire body and outputs to the entire body

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Distribution: Capillaries Governing Equations Capillary Information : 1)Literature ≈ 40 billion capillaries Calculated (A, d, l) ≈ 20 billion capillaries 2) Number of capillaries in an organ estimated by percent of total body blood flow Example: Brain and kidney are small, but receive a large (≈30-35%) amount of blood, requires dense capillaries 1) 2)

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Capillary Results

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Metabolism: The Liver Governing Equations Macrostructure Microstructure Liver Information 1.Modeled as PFR Simultaneous with tissue 2.Blood Mixing produces convection 3.Movement slow enough for Dispersion to matter 4.Mass transfer between vascular and tissue compartments 1) 2)

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Liver Results

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Excretion: The Kidney Governing Equations Kidney Information: 1)Blood enters kidney vascular system 2)Some flow rate transferred to bladder by GFR 3)Rest passes through capillaries where it can interact with tissue 4)From tissue moves to bladder, where excreted 1) 2) 3)

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Kidney Results

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Case Studies: Limitations Model Requires ≈200 Physiological Parameters: 1) Drug Differences 2) Human Differences 3) Literature Limitations Our Strategy: 1) Values have data/theory behind them 2) Human differences don’t matter 3) Drug parameters optimized to reproduce data

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Case Study: Atenolol Important Information 1)Acts to treat hypertension 2)Acts in the brain 3)11.1% of the dose was absorbed into the brain 4)The compartmental model does not predict the double peak

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Case Study: Imatinib Mesylate Important Information 1)Common anti-cancer drug 2)Acts within tissue where tumors located 3)18.9% was absorbed into the esophagus and stomach 4)The compartmental model and our model predict similar results for the blood concentration, however, the compartmental model would be unable to predict tissue concentrations.

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Conclusion: What did we accomplish? 1)A mathematical model that can accurately describe the way a drug moves through the body 2)Integrated all organs at the capillary level - A novel approach 3)Includes spatial variations in all body tissues What should be done in the future? 1)Develop a method to determine the model parameters 2)Account for differences between people 3)Compare more extensively to simpler models

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