## Abstract

### Background

The clinical impact of hypoxia in solid tumours is indisputable and yet questions about the sensitivity of hypoxia-PET imaging have impeded its uptake into routine clinical practice. Notably, the binding rate of hypoxia-sensitive PET tracers is slow, comparable to the rate of diffusive equilibration in some tissue types, including mucinous and necrotic tissue. This means that tracer uptake on the scale of a PET imaging voxel—large enough to include such tissue *and* hypoxic cells—can be as much determined by tissue transport properties as it is by hypoxia. Dynamic PET imaging of 20 patients with pancreatic ductal adenocarcinoma was used to assess the impact of transport on surrogate metrics of hypoxia: the tumour-to-blood ratio [TBR(*t*)] at time *t* post-tracer injection and the trapping rate *k*
_{3} inferred from a two-tissue compartment model. Transport quantities obtained from this model included the vascular influx and efflux rate coefficients, *k*
_{1} and *k*
_{2}, and the distribution volume *v*
_{
d
}≡*k*
_{1}/(*k*
_{2}+*k*
_{3}).

### Results

Correlations between voxel- and whole tumour-scale *k*
_{3} and TBR values were weak to modest: the population average of the Pearson correlation coefficients (*r*) between voxel-scale *k*
_{3} and TBR (1 h) [TBR(2 h)] values was 0.10 [0.01] in the 20 patients, while the correlation between tumour-scale *k*
_{3} and TBR(2 h) values was 0.58. Using Patlak’s formula to correct uptake for the distribution volume, correlations became strong (*r*=0.80[0.52] and *r*=0.93, respectively). The distribution volume was substantially below unity for a large fraction of tumours studied, with *v*
_{
d
} ranging from 0.68 to 1 (population average, 0.85). Surprisingly, *k*
_{3} values were strongly correlated with *v*
_{
d
} in all patients. A model was proposed to explain this in which *k*
_{3} is a combination of the hypoxia-sensitive tracer binding rate *k*
_{b} and the rate *k*
_{eq} of equilibration in slow-equilibrating regions occupying a volume fraction 1−*v*
_{
d
} of the imaged tissue. This model was used to calculate the proposed hypoxia surrogate marker *k*
_{b}.

### Conclusions

Hypoxia-sensitive PET tracers are slow to reach diffusive equilibrium in a substantial fraction of pancreatic tumours, confounding quantification of hypoxia using both static (TBR) and dynamic (*k*
_{3}) PET imaging. TBR is reduced by distribution volume effects and *k*
_{3} is enhanced by slow equilibration. We proposed a novel model to quantify tissue transport properties and hypoxia-sensitive tracer binding in order to improve the sensitivity of hypoxia-PET imaging.