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name: quantitative-physiology description: This skill should be used when calculating physiological parameters, modeling membrane transport, analyzing cardiovascular hemodynamics, computing renal clearance, simulating action potentials, or explaining quantitative relationships in any human physiological system. Use for physiology homework, medical calculations, computational biology modeling, and pharmacokinetic analysis. version: 3.0.0 equation_count: 248 source: "Quantitative Human Physiology: An Introduction, 3rd Edition - Joseph J. Feher (Elsevier 2026)"

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

Copyscripts/
├── 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

Copy# 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):

CopyQ = (πr⁴/8η) × (ΔP/L)

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

Fick's First Law (diffusion):

CopyJ = -D × (dC/dx)

Diffusion time scaling:

Copyt = x²/(2D)

Membrane Potential

Nernst equation (single ion equilibrium):

CopyE = (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):

CopyV_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:

CopyJ = J_max × [S] / (K_m + [S])

Hill equation (cooperativity):

CopyJ = J_max × [S]ⁿ / (K₀.₅ⁿ + [S]ⁿ)

Cross-Domain Equations

These foundational equations are used across multiple physiological systems:

Domain Reference Files

Load specific references for detailed domain analysis:

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

Example Usage

Calculate Nernst potential for K⁺:

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

Calculate cardiac output:

Copyfrom 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:

Copyfrom 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

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.