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

1. Bulk flow: Pressure-driven (Poiseuille)
2. Diffusion: Concentration-driven (Fick)
3. 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

1. Membrane → Action Potential: Nernst → GHK → HH membrane current → Na/K currents
2. Oxygen Cascade: Hill saturation → O₂ content → O₂ delivery → Fick principle
3. Renal Clearance: RPF → filtration fraction → GFR → clearance → fractional excretion
4. 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

1. Identify the process: Flow, diffusion, electrical, kinetics?
2. List knowns with units: Enforce dimensional consistency
3. Select equation module: Match process to appropriate domain
4. Calculate: Use .compute() method with parameters
5. Validate: Check result against physiological ranges
6. Interpret: Explain biological significance

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