The same tissue is many chemistries at once.
Oxygen, acidity and pressure are not constants inside a tumour. They vary steeply over short distances, and each one changes what a compound does when it gets there. An average across the mass describes nowhere in it.
The problem
Tumour vasculature is irregular. Some regions are well perfused, some are barely reached, and the distance between the two can be under a hundred micrometres. Oxygen falls away from vessels. Metabolism turns acidic where oxygen is short. Fluid pressure rises toward the centre where drainage is poor.
Each of those is a chemistry change, and each one changes drug behaviour. Hypoxia alters which death pathways are even available. Acidity changes the ionisation of a molecule, which changes whether it crosses a membrane at all. Pressure changes which way fluid moves.
What LURA computes
The gradients are carried as fields on the same geometry the transport problem is solved on, and they are solved together, because they are not independent. Perfusion sets oxygen. Oxygen sets metabolic state. Metabolic state sets acidity. Acidity feeds back into how the compound moves.
- Oxygen tension, from the vascular geometry and consumption
- Acidity, from the metabolic state that oxygen supply produces
- Interstitial pressure, from supply and from poor drainage
- The compound behaviour those local conditions imply, at that position
What comes out
The tumour stops being one environment and becomes a set of them, each with its own answer. That is the point. It lets a project say which fraction of a mass is in a state where the compound works, and which fraction is in a state where it does not — and then ask what would change that split.
It also explains a common and frustrating result honestly. When a compound performs well in culture and poorly in vivo, the difference is often not the molecule. It is that the assay was run in one chemistry and the tissue contains several.
What this does not claim
These are modelled fields, computed from the vascular and tissue description supplied. They are not imaging of a specific patient tumour, and LURA does not present them as measurement.
The provenance of every coefficient is carried with the result: measured values, values from matched tissue, and class priors are labelled differently, and a result standing mostly on priors says so on its face.