Physiology for Engineers Michael Chappell & Stephen Payne www.physiologyforengineers.org

Not a classic course in physiology. We want to be quantitative: Overview We are interested in: Structure - how it is built. Function - how it works. Not a classic course in physiology. We want to be quantitative: Describe with mathematical models. Take measurements. We ultimately want to see what physiological questions we can answer with your core engineering knowledge.

Chapters 1-4: Cellular Physiology Overview Chapters 1-4: Cellular Physiology Cell structure and biochemical reactions Cellular homeostasis and membrane potential The action potential Cellular transport and communication Chapters 5-10: Systems Physiology Pharmacokinetics Tissue Mechanics Cardiovascular system I: The heart Cardiovascular system II: The vasculature The respiratory system The central nervous system

Pharmacokinetics Chapter 5

Kinetics Reaction kinetics Pharmacokinetics Tracer kinetics the fate of substances introduced into the body Pharmacodynamics Tracer kinetics Contrast agents/tracers used to measure flow and delivery

Concentration in blood/plasma ADME Distribution Concentration in blood/plasma Absorption Metabolism Substance Pharmacokinetics or PK is based on the ADME principle Excretion

Concentration in blood/plasma ADME Concentration in blood/plasma Absorption Substance Absorption Uptake into the blood stream (or specific tissue): Intravenous - injection/infusion Oral - tablet/suspension Inhalation

Concentration in blood/plasma ADME Distribution Concentration in blood/plasma Absorption Substance Distribution Uptake from blood into tissue/organ

Concentration in blood/plasma ADME Distribution Concentration in blood/plasma Absorption Substance Excretion Removal of substance and/or metabolites from the body Three routes: Kidney -> urine Liver (Biliary excretion) -> gut Lungs, e.g. anaesthetic gases Excretion

Concentration in blood/plasma ADME Distribution Concentration in blood/plasma Absorption Metabolism Substance Metabolism Substance is converted (in reactions) to other chemical compounds. Most (small-molecule) drug metabolism occurs in the liver. May deactivate a drug, although metabolites might be pharmacologically active. Excretion

Concentration in blood/plasma ADME Distribution Concentration in blood/plasma Absorption Metabolism Substance Excretion

Concentration in blood/plasma ADME Start with a simple model Absorption Distribution Metabolism Concentration in blood/plasma Substance Excretion

Concentration in blood/plasma One compartment model Excretion Concentration in blood/plasma Substance Single compartment Substance only in plasma cannot cross into tissue. Instantaneous input IV injection First order output renal excretion Plasma and urine samples are references.

Concentration in blood/plasma One compartment model Single compartment First order output rate constant: ke Instantaneous input Cp(0) SOLVE: Excretion Concentration in blood/plasma Substance

Concentration in blood/plasma One compartment model Single compartment First order output rate constant: ke Instantaneous input Cp(0) Excretion Concentration in blood/plasma Substance

Volume of distribution: One compartment model Volume of distribution: Volume of the ‘central’ compartment Not (necessarily) total body water volume. Half-life Time required for 50% elimination from the compartment In this case: Total body clearance rate of elimination per unit concentration

Concentration in blood/plasma One compartment model Excretion Concentration in blood/plasma Substance Single compartment Substance only in plasma cannot cross into tissue. Zero order input IV infusion implant First order output renal excretion

Concentration in blood/plasma One compartment model Single compartment First order output rate constant: ke Zero order input rate: k0 SOLVE: Excretion Concentration in blood/plasma Substance

One compartment model Single compartment First order output Instantaneous input Excretion Concentration in blood/plasma Substance Steady state (t→∞): Time to reach SS depends only on half-life:

Concentration in blood/plasma One compartment model Single compartment First order output rate constant: ke Zero order input rate: k0 until Tstop Excretion Concentration in blood/plasma Substance

One Compartment Model Generalise input: General solution: Convolution of input with impulse response function of the central compartment

Concentration in blood/plasma Absorption Add absorption Distribution Concentration in blood/plasma Absorption Metabolism Substance Excretion

Diffusion through a membrane: Absorption Diffusion equation: Diffusion through a membrane: Conc. c1 c2

Absorption Example: Gastrointestinal tract

Absorption Bioavailability rate & extent to which the substance is absorbed and becomes available at the site of interest e.g. how much of the drug from the tablet ends up in the blood. Absolute bioavailability: Comparison of substance applied via an absorption route (e.g. oral) to direct introduction to the circulation (i.e. IV injection). Relative bioavailability: Comparison between substance in different formulations and/or different routes of absorption. e.g. is this tablet formulation better than another?

Absorption Bioavailability Calculate from concentration-time curves, e.g. plasma samples Compare Area Under the Curve (AUC)

Concentration in blood/plasma Absorption Distribution Concentration in blood/plasma Absorption Metabolism Substance Excretion

Concentration in blood/plasma One compartment model Excretion Concentration in blood/plasma Substance Absorption Single compartment Substance only in plasma cannot cross into tissue. First order input Oral via GI tract First order output renal excretion

Concentration in blood/plasma One compartment model Excretion Concentration in blood/plasma Substance Absorption Single compartment First order output rate constant: ke First order input absorption rate: ka

Concentration in blood/plasma One compartment model Excretion Concentration in blood/plasma Substance Absorption At site of absorption: In the central compartment (plasma): Amount of substance being eliminated

One compartment model Concentration in blood/plasma Absorption Excretion Concentration in blood/plasma Substance Absorption Convert to concentration using Vc and also account for bioavailability: Elimination Absorption Called the Bateman function

Bateman function Semi-log plot: terminal slope determined by rate limiting constant - either ka or ke if ka > ke: terminal slope = -ke If ke > ka: terminal slope = -ka

Bateman function Method of residuals to determine rate constants:

Concentration in blood/plasma Distribution Add distribution Distribution Concentration in blood/plasma Absorption Metabolism Substance Excretion

Concentration in blood/plasma Two compartment model Two compartments Plasma + fast exchanging tissue Tissue Instantaneous input IV injection First order output renal excretion Excretion Concentration in blood/plasma Distribution Substance

Concentration in blood/plasma Two compartment model Two compartments rate constants: k12 and k21 First order output rate constant: ke Instantaneous input Cp(0)=D/V Central compartment: Peripheral compartment: Excretion Concentration in blood/plasma Distribution Substance

Concentration in blood/plasma Two compartment model SOLVE: Method of residuals: Excretion Concentration in blood/plasma Distribution Substance

Concentration in blood/plasma Two compartment model Two compartments Plasma + fast exchanging tissue Tissue First order input Oral administration First order output renal excretion Excretion Concentration in blood/plasma Distribution Substance Absorption

Concentration in blood/plasma Two compartment model Excretion Concentration in blood/plasma Distribution Substance Absorption

Non-linear pharmacokinetics are common at: Non-linear kinetics Non-linear pharmacokinetics are common at: Absorption process: Saturation of absorption processes, e.g. saturation of carrier molecules Change in blood flow or pH by drug Distribution Saturation of transport molecules Elimination Saturation of metabolizing enzymes Saturation of carrier-mediated transport in the kidneys

Michaelis-Menten Kinetics Non-linear kinetics Michaelis-Menten Kinetics Cp << Km - first order: Cp >> Km - zero order (saturated):

Physiology for Engineers Michael Chappell & Stephen Payne www.physiologyforengineers.org