Table 2 Description of parameter values involved in the IL-7 dynamics
Parameter | Description (units) | Baseline values |
|---|---|---|
\(a_{i}\) | CD8\(^{+}\) T cells doubling time (day\(^{-1}\)) | 2.0794 |
\(d_{i}\) | CD8\(^{+}\) T cells half-life (day\(^{-1}\)) | 0.4 |
\(d_{t}\) | Killing rate of tumour cells by immune effector cells (day\(^{-1}\)) | \(10^{-6}\) |
\(k_{ei}\) | IL-7 half life (day\(^{-1}\)) | 2.14 |
M | Carrying capacity of immune cells | \(10^{9}\) |
\(f_{i}R_{i}\) | Influx of IL-7 secreted by immune cells, into the vasculature ((pg/ml)/cell/day) | \(10.925\times 10^{-6}\) |
\(f_{hi}R_{hi}N_{h}\) | Healthy cells shedding influx of IL-7 (pg/day) | \(1.9548\times 10^{4}\) (low shedding); or \(7.1724\times 10^{4}\) (high shedding) |
\(c_{IL7}\) | Cut-off limit of IL-7 assay (for healthy vs. disease states), when the biomarker is produced by both immune and healthy cells (pg/ml) | 3.8 (low threshold) or 18 (high threshold) |
\(d_{IL7}\) | Detection limit of IL-7 assay (i.e., min concentration of IL-7 detectable in plasma), when the biomarker is produced by the immune cells alone (pg/ml) | 1.0 |
\(V_{pl}\) | Mean plasma volume in a 70-year female patient (ml) | 3150 |
\(D_{T}^{t}\) | Tumour detection time based on the CA-125 biomarker (days) | To be determined |
\(D_{T}^{i}\) | Tumour detection time based on the IL-7 biomarker (days) | To be determined |