Logic & Formulation
The HMI Torch is not a random number generator. It is powered by a formal mathematical core that
quantifies physiological stability.
1. The Canonical Transform
Physiological units are messy. Heart rate is in bpm, Creatinine in mg/dL, pH is logarithmic. To compare
them, we first normalize everything into a standard Deviation Space.
For any parameter $P$, we calculate its deviation $D$ from the Basal Reference ($B$):
D = |(P - B) / B|
This separates the magnitude of the problem from the units of the measurement.
2. Organ Stability Index (OSI)
An organ is not defined by one number. The Heart is defined by Rate, Output, Pressure, and Electrical
stability. The OSI is a weighted aggregation of these normalized deviations.
An OSI of 100% means perfect adherence to the Basal Reference. As deviations accumulate,
the OSI drops non-linearly. We use a penalty function that punishes larger deviations more severely than
small ones, mimicking biological tipping points.
3. Global Homeostasis Index (GHI)
The GHI is the single “Health Score” visible on the dashboard. It is NOT an average of
the organs.
The body works in series, not parallel. A failure in the Lungs triggers failure in the Heart. Therefore,
the GHI is calculated using a limiting factor approach.
GHI = Min(Organ_OSI) * Weight + Avg(Other_OSIs) * (1-Weight)
This ensures that a single failing organ drags the entire system score down, alerting the user to the
bottleneck.
4. Cascade Risk
Perhaps the most novel metric is “Cascade Risk”. This measures the inter-organ strain.
If the Heart is compensating (high rate) but the Kidneys are failing (low GFR), the system is under
tension.
Cascade Risk quantifies the probability that the current state will degrade into a multi-organ failure if
no action is taken. It is the “Velocity” of the crash.
A Deterministic Core
These equations are hard-coded. They do not change. We call this the “Frozen Core”. This ensures that if
you put the same inputs in today, tomorrow, or 10 years from now, you will get the exact same result. It
is a calibratable standard.