journal article Jan 01, 2025

Mathematical modeling and sensitivity analysis of hypoxia-activated drugs

View at Publisher Save 10.3934/math.20251130
Topics

No keywords indexed for this article. Browse by subject →

References
58
[1]
The tumour microenvironment after radiotherapy: mechanisms of resistance and recurrence

Holly E. Barker, James T. E. Paget, Aadil A. Khan et al.

Nature Reviews Cancer 10.1038/nrc3958
[2]
Transport of drugs from blood vessels to tumour tissue

Mark W. Dewhirst, Timothy W. Secomb

Nature Reviews Cancer 10.1038/nrc.2017.93
[3]
M. S. Abdo, K. Shah, H. A. Wahash, S. K. Panchal, On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative, <i>Chaos Soliton. Fract.</i>, <b>135</b> (2020), 109867. https://doi.org/10.1016/j.chaos.2020.109867 10.1016/j.chaos.2020.109867
[4]
S. Kumar, A. Ahmadian, R. Kumar, D. Kumar, J. Singh, D. Baleanu, et al., An efficient numerical method for the fractional SIR epidemic model of infectious disease by using Bernstein wavelets, <i>Mathematics</i>, <b>8</b> (2020), 558. https://doi.org/10.3390/math8040558 10.3390/math8040558
[5]
P. Pandey, Y. M. Chu, J. F. Gómez-Aguilar, H. Jahanshahi, A. A. Aly, A novel fractional mathematical model of the COVID-19 epidemic considering quarantine and latent time, <i>Results Phys.</i>, <b>26</b> (2021), 104286. https://doi.org/10.1016/j.rinp.2021.104286 10.1016/j.rinp.2021.104286
[6]
K. Hattaf, Useful results for the qualitative analysis of generalized Hattaf mixed fractional differential equations with applications to medicine, <i>Computation</i>, <b>13</b> (2025), 167. https://doi.org/10.3390/computation13070167 10.3390/computation13070167
[7]
M. El Younoussi, Z. Hajhouji, K. Hattaf, N. Yousfi, Dynamics of a reaction-diffusion fractional-order model for M1 oncolytic virotherapy with CTL immune response, <i>Chaos Soliton. Fract.</i>, <b>157</b> (2022), 11957. https://doi.org/10.1016/j.chaos.2022.111957 10.1016/j.chaos.2022.111957
[8]
Critical Analysis of FDA-Approved Dual Inhibitor Cabenuva to HIV Replication Kinetics: A Mathematical Study

Tushar Ghosh, Priti Kumar Roy

Математическая биология и биоинформатика 10.17537/2025.20.236
[9]
A. K. Bag, S. Ghosh, A. N. Chatterjee, P. K. Roy, A mathematical framework investigating the impact of Chemo-iPSC therapy for the dynamics of cervical cancer, <i>J. Appl. Math. Comput.</i>, <b>71</b> (2025), 6061–6093. https://doi.org/10.1007/s12190-025-02476-2 10.1007/s12190-025-02476-2
[10]
S. Chakraborty, X. Z. Li, P. K. Roy, How can HPV-induced cervical cancer be controlled by a combination of drug therapy? A mathematical study, <i>Int. J. Biomath.</i>, <b>12</b> (2019), 1950070. https://doi.org/10.1142/S1793524519500700 10.1142/s1793524519500700
[11]
K. O. Hicks, F. B. Pruijn, T. W. Secomb, M. P. Hay, R. Hsu, J. M. Brown, et al., Use of three-dimensional tissue cultures to model extravascular transport and predict in vivo activity of hypoxia-targeted anticancer drugs, <i>J. Natl. Cancer I.</i>, <b>98</b> (2006), 1118–1128. https://doi.org/10.1093/jnci/djj306 10.1093/jnci/djj306
[12]
Y. Li, S. P. Patel, J. Roszik, Y. Qin, Hypoxia-driven immunosuppressive metabolites in the tumor microenvironment: New approaches for combinational immunotherapy, <i>Front. Immunol.</i>, <b>9</b> (2018), 1591. https://doi.org/10.3389/fimmu.2018.01591 10.3389/fimmu.2018.01591
[13]
Z. Fu, A. M. Mowday, J. B. Smaill, I. F. Hermans, A. V. Patterson, Tumour hypoxia-mediated immunosuppression: Mechanisms and therapeutic approaches to improve cancer immunotherapy, <i>Cells</i>, <b>10</b> (2021), 1006. https://doi.org/10.3390/cells10051006 10.3390/cells10051006
[14]
J. C. Forster, L. G. Marcu, E. Bezak, Approaches to combat hypoxia in cancer therapy and the potential for in silico models in their evaluation, <i>Phys. Medica</i>, <b>64</b> (2019), 145–156. https://doi.org/10.1016/j.ejmp.2019.07.006 10.1016/j.ejmp.2019.07.006
[15]
L. Possenti, P. Vitullo, A. Cicchetti, P. Zunino, T. Rancati, Modeling hypoxia-induced radiation resistance and the impact of radiation sources, <i>Comput. Biolo. Med.</i>, <b>173</b> (2024), 108334. https://doi.org/10.1016/j.compbiomed.2024.108334 10.1016/j.compbiomed.2024.108334
[16]
E. Sausville, Respecting cancer drug transportability: A basis for successful lead selection, <i>J. NatL. Cancer Inst.</i>, <b>98</b> (2006), 98. https://doi.org/10.1093/jnci/djj327 10.1093/jnci/djj327
[17]
F. B. Pruijn, K. Patel, M. P. Hay, W. R. Wilson, K. O. Hicks, Prediction of tumour tissue diffusion coefficients of hypoxia-activated prodrugs from physicochemical parameters, <i>Aust. J. Chem.</i>, <b>61</b> (2008), 687–693. https://doi.org/10.1071/CH08240 10.1071/ch08240
[18]
Y. Li, L. Zhao, X. F. Li, Targeting hypoxia: Hypoxia-activated prodrugs in cancer therapy, <i>Front. Oncol.</i>, <b>11</b> (2021), 700407. https://doi.org/10.3389/fonc.2021.700407 10.3389/fonc.2021.700407
[19]
A. Linninger, K. A. Mardal, P. Zunino, <i>Quantitative approaches to microcirculation: Mathematical models, computational methods and data analysis</i>, Cham: Springer, 2024. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1007/978-3-031-58519-7">https://doi.org/10.1007/978-3-031-58519-7</ext-link>
[20]
L. Cattaneo, P. Zunino, Computational models for fluid exchange between microcirculation and tissue interstitium, <i>Netw. Heterog. Media</i>, <b>9</b> (2014), 135–159. https://doi.org/10.3934/nhm.2014.9.135 10.3934/nhm.2014.9.135
[21]
L. Possenti, S. di Gregorio, F. M. Gerosa, G. Raimondi, G. Casagrande, M. L. Costantino, et al., A computational model for microcirculation including Fahraeus-Lindqvist effect, plasma skimming, and fluid exchange with the tissue interstitium, <i>Int. J. Numer. Meth. Bio.</i>, <b>35</b> (2019), e3165. https://doi.org/10.1002/cnm.3165 10.1002/cnm.3165
[22]
L. Possenti, A. Cicchetti, R. Rosati, D. Cerroni, M. L. Costantino, T. Rancati, et al., A mesoscale computational model for microvascular oxygen transfer, <i>Ann. Biomed. Eng.</i>, <b>49</b> (2021), 3356–3373. https://doi.org/10.1007/s10439-021-02807-x 10.1007/s10439-021-02807-x
[23]
L. Cattaneo, P. Zunino, A computational model of drug delivery through microcirculation to compare different tumor treatments, <i>Int. J. Numer. Meth. Bio.</i>, <b>30</b> (2014), 1347–1371. https://doi.org/10.1002/cnm.2661 10.1002/cnm.2661
[24]
L. Possenti, S. Di Gregorio, G. Casagrande, M. L. Costantino, T. Rancati, P. Zunino, A global sensitivity analysis approach applied to a multiscale model of microvascular flow, <i>Comput. Method. Biomec.</i>, <b>23</b> (2020), 1215–1224. https://doi.org/10.1080/10255842.2020.1793964 10.1080/10255842.2020.1793964
[25]
P. Vitullo, L. Cicci, L. Possenti, A. Coclite, M. L. Costantino, P. Zunino, Sensitivity analysis of a multi-physics model for the vascular microenvironment, <i>Int. J. Numer. Meth. Bio.</i>, <b>39</b> (2023), e3752. https://doi.org/10.1002/cnm.3752 10.1002/cnm.3752
[26]
A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, et al., <i>Global sensitivity analysis: The primer</i>, John Wiley &amp; Sons, 2008. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1002/9780470725184">https://doi.org/10.1002/9780470725184</ext-link> 10.1002/9780470725184
[27]
P. Vitullo, A. Colombo, N. R. Franco, A. Manzoni, P. Zunino, Nonlinear model order reduction for problems with microstructure using mesh-informed neural networks, <i>Finite Elem. Anal. Des.</i>, <b>229</b> (2024), 104068. https://doi.org/10.1016/j.finel.2023.104068 10.1016/j.finel.2023.104068
[28]
A. R. Pries, T. W. Secomb, Microvascular blood viscosity in vivo and the endothelial surface layer, <i>Am. J. Physiol. Heart C.</i>, <b>289</b> (2005), 6. https://doi.org/10.1152/ajpheart.00297.2005 10.1152/ajpheart.00297.2005
[29]
M. Jarzyńska. The application of practical Kedem-Katchalsky equations in membrane transport, <i>Centr. Eur. J. Phys.</i>, <b>4</b> (2006), 429–438. https://doi.org/10.2478/s11534-006-0034-x 10.1152/ajpheart.00297.2005
[30]
J. M. Brown, SR 4233 (tirapazamine): A new anticancer drug exploiting hypoxia in solid tumors, <i>Br. J. Cancer</i>, <b>67</b> (1993), 1163–1170. https://doi.org/10.1038/bjc.1993.220 10.1038/bjc.1993.220
[31]
K. O. Hicks, F. B. Pruijn, J. R. Sturman, W. A. Denny, W. R. Wilson, Multicellular resistance to tirapazamine is due to restricted extravascular transport: A pharmacokinetic/pharmacodynamic study in HT29 multicellular layer cultures, <i>Cancer Res.</i>, <b>63</b> (2003), 5970–5977.
[32]
K. O. Hicks, B. G. Siim, J. K. Jaiswal, F. B. Pruijn, A. M. Fraser, R. Patel, et al., Pharmacokinetic/pharmacodynamic modeling identifies SN30000 and SN29751 as tirapazamine analogues with improved tissue penetration and hypoxic cell killing in tumors, <i>Clin. Cancer Res.</i>, <b>16</b> (2010), 4946–4957. https://doi.org/10.1158/1078-0432.CCR-10-1439 10.1158/1078-0432.ccr-10-1439
[33]
H. Zou, P. Banerjee, S. S. Y. Leung, X. Yan, Application of pharmacokinetic-pharmacodynamic modeling in drug delivery: development and challenges, <i>Front. Pharmacol.</i>, <b>11</b> (2020), 997. https://doi.org/10.3389/fphar.2020.00997 10.3389/fphar.2020.00997
[34]
Extravascular Transport of Drugs in Tumor Tissue:  Effect of Lipophilicity on Diffusion of Tirapazamine Analogues in Multicellular Layer Cultures

Frederik B. Pruijn, Joanna R. Sturman, H. D. Sarath Liyanage et al.

Journal of Medicinal Chemistry 10.1021/jm049549p
[35]
B. G. Siim, P. L. Van Zijl, J. M. Brown, Tirapazamine-induced DNA damage measured using the comet assay correlates with cytotoxicity towards hypoxic tumour cells in vitro, <i>Br. J. Cancer</i>, <b>73</b> (1996), 952–960. https://doi.org/10.1038/bjc.1996.187 10.1038/bjc.1996.187
[36]
M. Di Paola, F. P. Pinnola, M. Zingales, A discrete mechanical model of fractional hereditary materials, <i>Meccanica</i>, <b>48</b> (2013), 1573–1586. https://doi.org/10.1007/s11012-012-9685-4 10.1007/s11012-012-9685-4
[37]
L. T. Baxter, R. K. Jain, Transport of fluid and macromolecules in tumors. Ⅰ. Role of interstitial pressure and convection, <i>Microvasc. Res.</i>, <b>37</b> (1989), 77–104. https://doi.org/10.1016/0026-2862(89)90074-5 10.1016/0026-2862(89)90074-5
[38]
L. T. Baxter, R. K. Jain, Transport of fluid and macromolecules in tumors Ⅱ. Role of heterogeneous perfusion and lymphatics, <i>Microvasc. Res.</i>, <b>40</b> (1990), 246–263. https://doi.org/10.1016/0026-2862(90)90023-k 10.1016/0026-2862(90)90023-k
[39]
R. B. Bird, W. E. Stewart, E. N. Lightfoot, <i>Transport phenomena</i>, John Wiley &amp; Sons, 2002.
[40]
M. Prosi, P. Zunino, K. Perktold, A. Quarteroni, Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: A new methodology for the model setup with applications to the study of disturbed luminal flow, <i>J. Biomech.</i>, <b>38</b> (2005), 903–917. https://doi.org/10.1016/j.jbiomech.2004.04.024 10.1016/j.jbiomech.2004.04.024
[41]
A. Bressan, <i>Hyperbolic systems of conservation laws: The one-dimensional cauchy problem</i>, 2000. 10.1093/oso/9780198507000.001.0001
[42]
L. C. Evans, <i>Partial differential equations</i>, American Mathematical Society, 2010. 10.1090/gsm/019
[43]
P. Hartman, <i>Ordinary differential equations</i>, Society for Industrial and Applied Mathematics, 2002. 10.1137/1.9780898719222
[44]
C. D'Angelo, A. Quarteroni, On the coupling of 1D and 3D diffusion-reaction equations: Application to tissue perfusion problems, <i>Math. Mod. Method. Appl. Sci.</i>, <b>18</b> (2008), 1481–1504. https://doi.org/10.1142/S0218202508003108 10.1142/s0218202508003108
[45]
T. Köppl, E. Vidotto, B. Wohlmuth, P. Zunino, Mathematical modeling, analysis, and numerical approximation of second-order elliptic problems with inclusions, <i>Math. Mod. Method. Appl. Sci.</i>, <b>28</b> (2018), 953–978. https://doi.org/10.1142/S0218202518500252 10.1142/s0218202518500252
[46]
I. G. Gjerde, K. Kumar, J. M. Nordbotten, B. Wohlmuth, Splitting method for elliptic equations with line sources, <i>ESAIM Math. Model. Num.</i>, <b>53</b> (2019), 1715–1739. https://doi.org/10.1051/m2an/2019027 10.1051/m2an/2019027
[47]
F. Laurino, P. Zunino, Derivation and analysis of coupled PDEs on manifolds with high dimensionality gap arising from topological model reduction, <i>ESAIM Math. Model. Num.</i>, <b>53</b> (2019), 2047–2080. https://doi.org/10.1051/m2an/2019042 10.1051/m2an/2019042
[48]
M. Kuchta, F. Laurino, K. Mardal, P. Zunino, Analysis and approximation of mixed-dimensional PDEs on 3D-1D domains coupled with Lagrange multipliers, <i>SIAM J. Numer. Anal.</i>, <b>59</b> (2021), 558–582. https://doi.org/10.1137/20M1329664 10.1137/20m1329664
[49]
L. Heltai, P. Zunino, Reduced Lagrange multiplier approach for non-matching coupling of mixed-dimensional domains, <i>Math. Mod. Method. Appl. Sci.</i>, <b>33</b> (2023), 2425–2462. https://doi.org/10.1142/S0218202523500525 10.1142/s0218202523500525
[50]
Factorial Sampling Plans for Preliminary Computational Experiments

Max D. Morris

Technometrics 10.1080/00401706.1991.10484804

Showing 50 of 58 references

Metrics
1
Citations
58
References
Details
Published
Jan 01, 2025
Vol/Issue
10(11)
Pages
25504-25544
Cite This Article
Alessandro Coclite, Riccardo Montanelli Eccher, Luca Possenti, et al. (2025). Mathematical modeling and sensitivity analysis of hypoxia-activated drugs. AIMS Mathematics, 10(11), 25504-25544. https://doi.org/10.3934/math.20251130