Quantitative Human Physiology

Overview

248 atomic equations across 9 physiological domains with full dependency tracking. Each equation is a standalone Python module with compute functions, parameters, and metadata.

Architecture

scripts/ ├── foundations/ # 20 equations - transport, diffusion, thermodynamics ├── membrane/ # 18 equations - channels, pumps, potential ├── excitable/ # 22 equations - action potentials, muscle ├── nervous/ # 27 equations - synapses, sensory, motor ├── cardiovascular/ # 31 equations - heart, circulation, hemodynamics ├── respiratory/ # 41 equations - ventilation, gas exchange ├── renal/ # 30 equations - filtration, clearance ├── gastrointestinal/ # 34 equations - digestion, absorption └── endocrine/ # 25 equations - hormones, feedback

Quick Import

Import entire domains

from scripts import cardiovascular, respiratory, renal

Import specific equations

from scripts.cardiovascular.cardiac import cardiac_output, ejection_fraction from scripts.respiratory.gas_exchange import alveolar_gas_equation from scripts.renal.clearance import clearance, filtered_load

Import foundations used across domains

from scripts.foundations.transport import poiseuille_flow from scripts.foundations.thermodynamics import nernst_equation

Core Principles

Conservation Laws

• Mass: Input = Output + Accumulation

• Energy: Follow thermodynamic constraints

• Charge: Maintain electroneutrality

Transport Classification

• Bulk flow: Pressure-driven (Poiseuille)

• Diffusion: Concentration-driven (Fick)

• Active transport: ATP-coupled pumps

Essential Equations

Transport

Poiseuille's Law (laminar flow):

Q = (πr⁴/8η) × (ΔP/L)

Flow scales with radius⁴. Doubling vessel radius → 16× flow.

Fick's First Law (diffusion):

J = -D × (dC/dx)

Diffusion time scaling:

t = x²/(2D)

Membrane Potential

Nernst equation (single ion equilibrium):

E = (RT/zF) × ln(C_out/C_in)

At 37°C: E ≈ (61.5/z) × log₁₀(C_out/C_in) mV

Goldman-Hodgkin-Katz (multiple ions):

V_m = (RT/F) × ln[(P_K[K]_o + P_Na[Na]_o + P_Cl[Cl]_i) / (P_K[K]_i + P_Na[Na]_i + P_Cl[Cl]_o)]

Kinetics

Michaelis-Menten:

J = J_max × [S] / (K_m + [S])

Hill equation (cooperativity):

J = J_max × [S]ⁿ / (K₀.₅ⁿ + [S]ⁿ)

Cross-Domain Equations

These foundational equations are used across multiple physiological systems:

Equation Primary Also Used In Import

Nernst foundations membrane, excitable, nervous, cardiovascular, renal from scripts.foundations.thermodynamics import nernst_equation

Fick Diffusion foundations respiratory, renal, cardiovascular from scripts.foundations.diffusion import fick_flux

Poiseuille foundations cardiovascular, renal from scripts.foundations.transport import poiseuille_flow

Michaelis-Menten foundations renal, gastrointestinal, endocrine from scripts.foundations.kinetics import michaelis_menten

Hill foundations excitable, cardiovascular, respiratory, endocrine from scripts.foundations.kinetics import hill_equation

Henderson-Hasselbalch foundations respiratory, renal from scripts.foundations.thermodynamics import henderson_hasselbalch

Starling Forces cardiovascular renal, gastrointestinal from scripts.cardiovascular.microcirculation import starling_filtration

Goldman-Hodgkin-Katz membrane excitable, nervous, cardiovascular from scripts.membrane.potential import ghk_potential

Domain Reference Files

Load specific references for detailed domain analysis:

Domain Reference Equations Key Topics

Physical Foundations references/physical-foundations.md

20 Poiseuille, Laplace, diffusion, thermodynamics

Membranes & Transport references/membranes-transport.md

18 Channels, pumps, osmosis, Donnan equilibrium

Excitable Cells references/excitable-cells.md

22 Action potentials, Hodgkin-Huxley, muscle

Nervous System references/nervous-system.md

27 Synapses, sensory, motor control

Cardiovascular references/cardiovascular.md

31 Frank-Starling, hemodynamics, ECG

Respiratory references/respiratory.md

41 Lung mechanics, V/Q matching, acid-base

Renal references/renal.md

30 GFR, tubular function, countercurrent

Gastrointestinal references/gastrointestinal.md

34 Secretion, absorption, motility

Endocrine references/endocrine.md

25 Hormone kinetics, HPA axis, feedback

Dependency Graph

See graph/dependency-graph.json for full equation dependencies.

Key Dependency Chains

• Membrane → Action Potential: Nernst → GHK → HH membrane current → Na/K currents

• Oxygen Cascade: Hill saturation → O₂ content → O₂ delivery → Fick principle

• Renal Clearance: RPF → filtration fraction → GFR → clearance → fractional excretion

• HPA Axis: CRH dynamics → ACTH dynamics → Cortisol dynamics → feedback gain

Functional Clusters

See graph/clusters.json for equation groupings by physiological function:

• Transport & Fluid Mechanics (7 equations)

• Electrochemical Gradients (5 equations)

• Excitation-Contraction Coupling (5 equations)

• Oxygen Transport Cascade (6 equations)

• Acid-Base Homeostasis (5 equations)

• Renal Filtration & Clearance (6 equations)

• Hormone Kinetics & Feedback (5 equations)

• Synaptic & Neural Signaling (5 equations)

• GI Secretion & Absorption (5 equations)

• Cardiovascular Regulation (5 equations)

Physical Constants

Constant Symbol Value Units

Gas constant R 8.314 J/(mol·K)

Faraday constant F 96,485 C/mol

Body temperature T 310 K

Example Usage

Calculate Nernst potential for K⁺:

from scripts.foundations.thermodynamics import nernst_equation E_K = nernst_equation.compute(z=1, C_out=4, C_in=140) # ≈ -95 mV

Calculate cardiac output:

from scripts.cardiovascular.cardiac import cardiac_output CO = cardiac_output.compute(heart_rate=70, stroke_volume=0.070) # 4.9 L/min

Calculate GFR from Starling forces:

from scripts.renal.glomerular import gfr_from_nfp, net_filtration_pressure NFP = net_filtration_pressure.compute(P_gc=50, P_bs=15, pi_gc=25, pi_bs=0) GFR = gfr_from_nfp.compute(Kf=12.5, NFP=NFP) # mL/min

Physiological Reference Values

Parameter Normal Range

Resting membrane potential -70 to -90 mV

Cardiac output 4-8 L/min

Blood pressure 120/80 mmHg

GFR 90-120 mL/min

Arterial pH 7.35-7.45

PaO₂ 80-100 mmHg

PaCO₂ 35-45 mmHg

Problem-Solving Workflow

• Identify the process: Flow, diffusion, electrical, kinetics?

• List knowns with units: Enforce dimensional consistency

• Select equation module: Match process to appropriate domain

• Calculate: Use .compute() method with parameters

• Validate: Check result against physiological ranges

• Interpret: Explain biological significance

Load domain-specific references when detailed mechanisms needed beyond core equations.