Zpankz 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.