human body drug simulation
DESCRIPTION
Human Body Drug Simulation. Nathan Liles Benjamin Munda. Presentation Outline. Objective Background Model Overview Organ and Body Theory Case Studies. Objective. Pharmacokinetics : Seeks to determine fate of substances administered externally to a living organism. - PowerPoint PPT PresentationTRANSCRIPT
Human Body Drug Simulation
Nathan LilesBenjamin Munda
Presentation Outline
Objective
Background
Model Overview
Organ and Body
Theory
Case Studies
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?
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
dosesLower costs of prescription
drugs
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
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
1 2 34
5
6a
6b
6b 7
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 liquids 2) 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) Massc)
Liberation
Concentration:
Stomach Results
0 0.5 1 1.5 2 2.5 30
100000
200000
300000
400000
500000
600000
Mass in Stomach vs. Time after consuming a 500 g drink
Time (hours)
Mass (
mg
)
Absorbtion: Small IntestineSmall Intestine Information:
1) Main site of drug absorption
2) ≈7 meters long with an average diameter of 2.5-3 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
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.
Numerical MethodsMethod of Lines
1) Discretize Space Variable Z2) System of Equations to Solve
Numerical Methods4th Order Runge-Kutta
Method of lines means we have many ordinary differential equations=4RK
Used to integrate a function:
Described by a 1st Order ODE:
Given initial values for y estimates next y in time by:
Where values for k (slope estimates) come from:
Small Intestine Results
0 2 4 6 8 10 12 14 160
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
Concentration vs. Time for Different Lengths
Entrance Mid LengthEnd
Time (hours)
Con
cen
trati
on
(m
g/m
l)
1 2 3 4 5 6 7 80
0.05
0.1
0.15
0.2
0.25
0.3
Concentration vs Dis-tance for Different Times
Early Middle End
Length (m)
Con
cen
trati
on
(m
g/m
l)
Absorbtion: Small Intestine
Amount absorbed through the gut wall for each time interval
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
1 2
3
45
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
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)
From the Heart
Return to the Heart
Organ Capillary
Organ Tissue
≈1 billion capillaries
Capillary Results
0 2 4 6 8 10 12 14 16 18 200
0.001
0.002
0.003
0.004
0.005
0.006
Concentration vs Distance for Different Times
Early Middle End
Length (10^-4 m)
Con
cen
trati
on
(m
g/m
l)
Metabolism: The Liver
Governing Equations
Macrostructure
Microstructure
Liver Information1. 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)
Hepatic Portal Vein
Return to the Heart
Sinusoid Volume
Liver Tissue Volume
`
Metabolic Elimination
Hepatic Artery
Liver Results
0 2 4 6 8 10 12 14 160
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Concentration vs Time for Different Lengths
Entrance Mid Length
Time (Hours)
Con
cen
trati
on
(m
g/m
l)
0 5 10 15 20 25 300
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.005
Concentration vs Dis-tance for Different Times
Early Mid End
Length (cm)
Con
cen
trati
on
(m
g/m
l)
Liver Results
0 2 4 6 8 10 12 140
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
Tissue Concentration vs. Time for Different
Lengths
Entrance Midlength
Time (hours)
Con
cen
trati
on
(m
g/m
l)
0 5 10 15 20 25 300
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
Tissue Concentration vs Distance for Different
Times
Early Mid
Length (cm)
Con
cen
trati
on
(m
g/m
l)
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)
From the Heart
Return to the Heart
Kidney Capillary
Kidney Tissue
`
The Bladder
GFR
Kidney Results
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.00E+00
2.00E+00
4.00E+00
6.00E+00
8.00E+00
1.00E+01
1.20E+01
Urine Concentration vs. Time for Different Lengths
Time (Hours)
Co
nce
ntr
ati
on
(m
g/m
l)
Case Studies: LimitationsModel Requires ≈200
Physiological Parameters:1) Drug Differences2) Human Differences3) Literature Limitations
Our Strategy:1) Values have data/theory behind them2) Human differences don’t matter3) Drug parameters optimized to reproduce data
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
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.000.00E+00
1.00E-04
2.00E-04
3.00E-04
4.00E-04
5.00E-04
6.00E-04 Blood Concentration of
Atenolol vs Time
Experimental Value Model PredictionCompartmental Prediction
Time (hours)
Co
nce
ntr
ati
on
(m
g/m
l)
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.
0 5 10 15 200
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0.0004
0.00045
0.0005
Concentration vs. Time for Imatinib
Experimental ModelCompartmental
Times (hours)
Co
nce
ntr
ati
on
(m
g/m
l)
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?
4) Develop a method to determine the model parameters
5) Account for differences between people6) Compare more extensively to simpler models