Table 2.

Summary of system- and drug-related pharmacodynamic parameters estimated with clinical data and published in the literature to account for immuno-oncology treatments.

Parameter	Value	Units	Estimation	Indication	Treatment	Ref.
Tumor
Tumor growth
Lineal: a	$$\begin{gathered} T{S}_0=1.16\times {10}^{-6} \\ b=0.354 \end{gathered}$$	$$\begin{gathered} \mathrm{mm} \\ \mathrm{mm}/\mathrm{day} \end{gathered}$$	Colon cancer	Colon cancer	IL-2	[84]
$\mathrm{Exponential}: a TS$	$$\begin{gathered} T{S}_0=41.5 \\ b=0.0088-0.0017 \end{gathered}$$	$$\begin{gathered} \mathrm{mL} \\ {\mathrm{day}}^{-1} \end{gathered}$$	Melanoma patients [80]	Melanoma	Anti-PD1	[80]
	$$\begin{gathered} T{S}_0 shallow tumor=57.9 \\ T{S}_0 deep tumor=23.4 \\ b=0.00267 \end{gathered}$$	$$\begin{gathered} \mathrm{mm} \\ \mathrm{mm} \\ {\mathrm{day}}^{-1} \end{gathered}$$	Melanoma patients [81]	Melanoma	Anti-PD1	[81]
$\mathrm{Logistic}: a TS\left(1-bTS\right)$	$$\begin{gathered} a=2.065 \times {10}^{-1} \\ b=2.145\times {10}^{-10} \end{gathered}$$	$$\begin{gathered} {\mathrm{day}}^{-1} \\ {\mathrm{cell}}^{-1} \end{gathered}$$	Renal carcinoma [86,87]	Renal carcinoma	Sunitinib	[88]
	AD: $b=2.025$ AI: $a=0.006$	$$\begin{gathered} \mathrm{ng}/\mathrm{mL} \\ {\mathrm{day}}^{-1} \end{gathered}$$	Prostatic cancer [89]	Prostate	Intermittent ADT + DC vaccine	[90]
Tumor cell kill by CD8
$\mathrm{Fractional}: \frac{d{\left(CD8/TS\right)}^l}{s+{\left(CD8/TS\right)}^l}TS$	$$\begin{gathered} d=5.80 \\ l=1.36 \\ s=0.512-0.839 \end{gathered}$$	${\mathrm{day}}^{-1}$ None None	3 × 105 B16-BL6 cells [91]/Human [92]	Metastatic melanoma	Chemotherapy + TIL	[93]
	$$\begin{gathered} d=1.88-2.34 \\ l=1.81-2.09 \\ s=0.25 \end{gathered}$$	${\mathrm{day}}^{-1}$ None None	3 × 105 B16-BL6 cells [91]/Human [92]	Metastatic melanoma	Chemotherapy + TIL + IL2 + cancer vaccine	[94,95]
$\mathrm{Linear}: d CD8 TS$	$d=1.1\times {10}^{-6}$	${\mathrm{cell}}^{-1}\times { \mathrm{day}}^{-1}$	High grade gliomas patients [96]	Bladder	IL2 + BCG	[97,98]
Equation in [99]	$K_{death}=4$	${\mathrm{day}}^{-1}$	Assumed [99]	NSCLC	Anti-PD1	[99]
Tumor cell kill by NK cells
$c N TS$	$c=\left(3.23\times {10}^{-7}\right)$	${\mathrm{cell}}^{-1}\times {\mathrm{day}}^{-1}$	3 × 105 B16-BL6 cells [91]/Human [92]	Metastatic melanoma	Chemotherapy + TIL	[93]
	$c=\left(2.9077\times {10}^{-13}\right)$	${\mathrm{cell}}^{-1}\times { \mathrm{day}}^{-1}$	3 × 105 B16-BL6 cells [91]/Human [92]	Metastatic melanoma	Chemotherapy + TIL + IL2	[100]
	$c=\left(6.41\times {10}^{-11}\right)$	${\mathrm{cell}}^{-1}\times { \mathrm{day}}^{-1}$	3 × 105 B16-BL6 cells [91]/Human [92]	Metastatic melanoma	Chemotherapy + TIL + IL2 + IFNα	[95]
CD8 cells
Number of CD8 per microliter of blood
	1000	-	CD4+ count of 640-1175/µL humans	Melanoma	Pembrolizumab	[80]
CD8 recruitment by tumor
$\mathrm{By} \mathrm{CD}8 \mathrm{killing}: \frac{Vmax T{S}^2}{K_M+T{S}^2}CD8$	$$\begin{gathered} Vmax=\left(3.75\times {10}^{-2}\right) \\ {K}_M=2.0\times {10}^7 \end{gathered}$$	$$\begin{gathered} {\mathrm{day}}^{-1} \\ {\mathrm{cell}}^2 \end{gathered}$$	BCL 1 lymphoma of chimeric mice [91,92,93,94,95,96,97,98,99,100,101]/Human [92]	Metastatic melanoma	Chemotherapy + TIL	[93]
	$$\begin{gathered} Vmax=\left(32.49\times {10}^{-2}\right) \\ {K}_M=\left(23.66-5.66\right)\times {10}^7 \end{gathered}$$	$$\begin{gathered} {\mathrm{day}}^{-1} \\ {\mathrm{cell}}^2 \end{gathered}$$	BCL 1 lymphoma of chimeric mice [91,101]/Human [92]	Metastatic melanoma	Chemotherapy + TIL + IL2 + IFNα	[95]
$\frac{Vmax TS}{K_M+TS}CD8$	$$\begin{gathered} Vmax=\left(1.245\times {10}^{-2}\right) \\ {K}_M=2.019\times {10}^7 \end{gathered}$$	$$\begin{gathered} {\mathrm{day}}^{-1} \\ {\mathrm{cell}}^2 \end{gathered}$$	BCL 1 lymphoma of chimeric mice [91,92,93,94,95,96,97,98,99,100,101]/Human [92]	Metastatic melanoma	Chemotherapy + TIL + IL2	[100]
$\mathrm{By} \mathrm{BCG} \mathrm{killing}: \mathrm{By} \mathrm{CD}8 \mathrm{killing}: \frac{Vmax Ag}{K_M+Ag}IL2$	$$\begin{gathered} Vmax=1.45\times {10}^8 \\ {K}_M={10}^{10} \\ Vmax=1.514\times {10}^6 \\ {K}_M={10}^{10} \end{gathered}$$	$$\begin{gathered} {\mathrm{cell}}^{-1}\times {\mathrm{day}}^{-1}\times \mathrm{IL}{2}^{-1} \\ {\mathrm{cell}}^{-1} \\ {\mathrm{cell}}^{-1}\times {\mathrm{day}}^{-1}\times \mathrm{IL}{2}^{-1} \\ {\mathrm{cell}}^{-1} \end{gathered}$$	In vitro/Estimated bladder cancer patients [102] In vitro/Estimated bladder cancer patients [103]	Bladder	IL2 + BCG	[97]
CD8 activation by APCs
$\frac{e APC}{g+APC}$	$$\begin{gathered} e=20\times {10}^6 \\ g=400\times {10}^6 \end{gathered}$$	$$\begin{gathered} \mathrm{cells}\times {\mathrm{day}}^{-1} \\ \mathrm{cells} \end{gathered}$$	Preclinical experiments [104] Prostate cancer [105]	Prostate	Intermittent ADT + DC vaccine	[90]
NK cells
Production rate NK
$\mathrm{From} \mathrm{circulating} \mathrm{lymphocytes}:e L$	$e=8.68\times {10}^{-10}$	$\mathrm{L}\times {\mathrm{cell}}^{-1}\times { \mathrm{day}}^{-1}$	Preclinical experiments renal carcinoma [86,87]	Renal carcinoma	Sunitinib	[88]
NK recruitment
$\mathrm{By} \mathrm{tumor}: \frac{Vmax T{S}^2}{K_M+T{S}^2}N$	$$\begin{gathered} Vmax=\left(2.5\times {10}^{-2}\right) \\ {K}_M=2.02\times {10}^7 \end{gathered}$$	$$\begin{gathered} {\mathrm{day}}^{-1} \\ {\mathrm{cell}}^2 \end{gathered}$$	BCL 1 lymphoma of chimeric mice [91,92,93,94,95,96,97,98,99,100,101]/Human [92]	Metastatic melanoma	Chemotherapy + TIL + IFNα	[93,94,95]

TS—Tumor size, TS₀—Initial tumor size, AD—androgen dependent, AI—androgen independent, IL—Interleukin, NK—natural killer, TIL—Tumor infiltrate lymphocyte, ADT—androgen deprivation therapy, CIK—cytokine-induced killer cell, BCG—Bacillus Calmette Guérin, NSCLC—non-small cell lung cancer, CLL—chronic lymphocytic leucemia, APC—antigen presenting cells, DC—dendritic cells, BCL—B cell leukemia.