 codex/thermodilution-equal-area-curves.py

"""Illustrative equal-area thermal indicator curves; Python 3.14 / Matplotlib 3.10.

Run from _media; output is thermodilution-equal-area-curves.png in cwd.
Curves are A*t*exp(-t/tau)/tau**2, with analytic integral A=1 K s.
They illustrate a conservation calculation, not patient data.
"""
from pathlib import Path
import math
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

A = 1.0  # K s, exact integral from zero to infinity
seconds = [i / 100 for i in range(1601)]
fig, ax = plt.subplots(figsize=(7.2, 3.8), dpi=100, facecolor='white')
for tau, color in ((1.0, '#1766a5'), (2.0, '#c15b18')):
    deficit = [A * t * math.exp(-t / tau) / tau**2 for t in seconds]
    ax.plot(seconds, deficit, color=color, linewidth=2.3,
            label=rf'$\tau={tau:g}$ s; peak ${A/(math.e*tau):.3f}$ K')
ax.set(xlim=(0, 16), ylim=(0, .42), xlabel='Time after indicator arrival (s)',
       ylabel='Temperature deficit (K)',
       title='Equal thermal area, different peak temperatures')
ax.text(.98, .95, 'Both full integrals: 1 K s\nSynthetic curves; no patient data',
        transform=ax.transAxes, ha='right', va='top', fontsize=10)
ax.legend(loc='center right', frameon=False, fontsize=10)
ax.spines[['top', 'right']].set_visible(False)
ax.grid(axis='y', color='#dddddd', linewidth=.6)
fig.tight_layout()
fig.savefig(Path('thermodilution-equal-area-curves.png'), facecolor='white', dpi=100)
plt.close(fig)