Micropharmacology: An In Silico Approach for Assessing Drug Efficacy Within a Tumor Tissue

Abstract

Systemic chemotherapy is one of the main anticancer treatments used for most kinds of clinically diagnosed tumors. However, the efficacy of these drugs can be hampered by the physical attributes of the tumor tissue, such as tortuous vasculature, dense and fibrous extracellular matrix, irregular cellular architecture, tumor metabolic gradients, and non-uniform expression of the cell membrane receptors. This can impede the transport of therapeutic agents to tumor cells in sufficient quantities. In addition, tumor microenvironments undergo dynamic spatio-temporal changes during tumor progression and treatment, which can also obstruct drug efficacy. To examine ways to improve drug delivery on a cell-to-tissue scale (single-cell pharmacology), we developed the microscale pharmacokinetics/pharmacodynamics (microPKPD) modeling framework. Our model is modular and can be adjusted to include only the mathematical equations that are crucial for a biological problem under consideration. This modularity makes the model applicable to a broad range of pharmacological cases. As an illustration, we present two specific applications of the microPKPD methodology that help to identify optimal drug properties. The hypoxia-activated drugs example uses continuous drug concentrations, diffusive–advective transport through the tumor interstitium, and passive transmembrane drug uptake. The targeted therapy example represents drug molecules as discrete particles that move by diffusion and actively bind to cell receptors. The proposed modeling approach takes into account the explicit tumor tissue morphology, its metabolic landscape and/or specific receptor distribution. All these tumor attributes can be assessed from patients’ diagnostic biopsies; thus, the proposed methodology can be developed into a tool suitable for personalized medicine, such as neoadjuvant chemotherapy.

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References

  1. Bae YH, Park K (2011) Targeted drug delivery to tumors: myths, reality and possibility. J Control Release 153(3):198–205

    Article  Google Scholar 

  2. Bloch N, Weiss G, Szekely S, Harel D (2015) An interactive tool for animating biology, and its use in spatial and temporal modeling of a cancerous tumor and its microenvironment. PLoS ONE 10(7):e0133484

    Article  Google Scholar 

  3. Casciari JJ, Sotirchos SV, Sutherland RM (1992) Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH. J Cell Physiol 151(2):386–394

    Article  Google Scholar 

  4. Chauhan VP, Stylianopoulos T, Boucher Y, Jain R (2011) Delivery of molecular and nanoscale medicine to tumors: transport barriers and strategies. Ann Rev Chem Biomol Eng 2:281–98

    Article  Google Scholar 

  5. Choi IK, Strauss R, Richter M, Yun CO, Lieber A (2013) Strategies to increase drug penetration in solid tumors. Front Oncol 3:193

    Article  Google Scholar 

  6. Cortez R (2001) The method of regularized stokeslets. SIAM J Sci Comput 23:1204–1225

    MathSciNet  Article  MATH  Google Scholar 

  7. Cortez R, Fauci L, Medovikov A (2005) The method of regularized stokeslets in three dimensions: analysis, validation, and application to helical swimming. Phys Fluids 17:031504

    MathSciNet  Article  MATH  Google Scholar 

  8. Curtis LT, Wu M, Lowengrub J, Decuzzi P, Frieboes HB (2015) Computational modeling of tumor response to drug release from vasculature-bound nanoparticles. PLoS ONE 10(12):e0144888

    Article  Google Scholar 

  9. Dewhirst MW, Secomb TW (2017) Transport of drugs from blood vessels to tumour tissue. Nat Rev Cancer 17:738–750

    Article  Google Scholar 

  10. Dubach JM, Vinegoni C, Mazitschek R, Fumene-Feruglio P, Cameron LA, Weissleder R (2014) In vivo imaging of specific drug-target binding at subcellular resolution. Nat Commun 5:3946

    Article  Google Scholar 

  11. Dubach JM, Kim E, Yang K, Cuccarese M, Giedt RJ, Meimetis LG, Vinegoni C, Weissleder R (2017) Quantitating drug-target engagement in single cells in vitro and in vivo. Nat Chem Biol 13(2):168–173

    Article  Google Scholar 

  12. Durymanov MO, Rosenkranz AA, Sobolev AS (2015) Current approaches for improving intratumoral accumulation and distribution of nanomedicines. Theranostics 5(9):1007–1020

    Article  Google Scholar 

  13. Finley RS (2003) Overview of targeted therapies for cancer. Am J Health-Syst Pharm 60(9):S4–S10

    Article  Google Scholar 

  14. Fisher R, Pusztai L, Swanton C (2013) Cancer heterogeneity: implications for targeted therapeutics. Br J Cancer 108:479–485

    Article  Google Scholar 

  15. Foehrenbacher A, Patel K, Abbattista MR, Guise CP, Secomb TW, Wilson WR, Hicks KO (2013a) The role of bystander effects in the antitumor activity of the hypoxia-activated pro-drug pr-104. Front Oncol 3:263

    Google Scholar 

  16. Foehrenbacher A, Secomb TW, Wilson WR, Hicks KO (2013b) Design of optimized hypoxia-activated prodrugs using pharmacokinetic/pharmacodynamic modeling. Front Oncol 3:214

    Google Scholar 

  17. Fukumura D, Duda DG, Munn LL, Jain RK (2010) Tumor microvasculature and microenvironment: Novel insights through intravital imaging in pre-clinical models. Microcirculation 17(3):206–225

    Article  Google Scholar 

  18. Gevertz JL (2011) Computational modeling of tumor response to vascular-targeting therapies, part I: validation. Comput Math Methods Med 2011:ID830515

  19. Huang M, Shen AJ, Ding J, Geng MY (2014) Molecularly targeted cancer therapy: some lessons from the past decade. Trends Pharmacol Sci 35:41–50

    Article  Google Scholar 

  20. Hunter FW, Wouters BG, Wilson WR (2016) Hypoxia-activated prodrugs: paths forward in the era of personalised medicine. Br J Cancer 114:1071–1077

    Article  Google Scholar 

  21. Jain RK, Stylianopoulos T (2010) Delivering nanomedicine to solid tumors. Nat Rev Clin Oncol 7:653

    Article  Google Scholar 

  22. Junttila MR, de Sauvage FJ (2013) Influence of tumour micro-environment heterogeneity on therapeutic response. Nature 501(7467):346–354

    Article  Google Scholar 

  23. Kanigel-Winner K, Steinkamp MP, Lee RJ, Swat M, Muller CY, Moses ME, Jiang Y, Wilson BS (2016) Spatial modeling of drug delivery routes for treatment of disseminated ovarian cancer. Cancer Res 76(6):1320–1334

    Article  Google Scholar 

  24. Karolak A, Markov DA, McCawley LJ, Rejniak KA (2018) Toward personalized computational oncology: from spatial models of tumor spheroids, to organoids, to tissues. J R Soc Interface 15:20170703

    Article  Google Scholar 

  25. Kim M, Gillies RJ, Rejniak KA (2013) Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues. Front Oncol 3:278

    Google Scholar 

  26. Laughney AM, Kim E, Sprachman MM, Miller MA, Kohler RH, Yang KS, Orth JD, Mitchison TJ, Weissleder R (2014) Single-cell pharmacokinetic imaging reveals a therapeutic strategy to overcome drug resistance to the microtubule inhibitor eribulin. Sci Transl Med 6(261):261ra152

    Article  Google Scholar 

  27. Lindsay D, Garvey CM, Mumenthaler SM, Foo J, Komarova NL (2016) Leveraging hypoxia-activated prodrugs to prevent drug resistance in solid tumors. PLoS Comput Biol 12:e1005077

    Article  Google Scholar 

  28. Lloyd MC, Rejniak KA, Brown JS, Gatenby RA, Minor E, Bui MM (2015) Pathology to enhance precision medicine in oncology: lessons of landscape ecology. Adv Anat Pathol 22:267–272

    Article  Google Scholar 

  29. Mallarkey G, Coombes RC (2013) Targeted therapies in medical oncology: successes, failures and next steps. Ther Adv Med Oncol 5(1):5–16

    Article  Google Scholar 

  30. Marusyk A, Almendro V, Polyak K (2012) Intra-tumour heterogeneity: a looking glass for cancer? Nat Rev Cancer 12:323

    Article  Google Scholar 

  31. McKeage MJ, Gu Y, Wilson WR, Hill A, Amies K, Melink TJ, Jameson MB (2011) A phase I trial of PR-104, a pre-prodrug of the bioreductive prodrug PR-104a, given weekly to solid tumour patients. BMC Cancer 11:432

    Article  Google Scholar 

  32. Michor F, Weaver VM (2014) Understanding tissue context influences on intratumour heterogeneity. Nat Cell Biol 16(4):301–302

    Article  Google Scholar 

  33. Mitchell MJ, Jain RK, Langer R (2017) Engineering and physical sciences in oncology: challenges and opportunities. Nat Rev Cancer 17:659–675

    Article  Google Scholar 

  34. Perez-Velazquez J, Gevertz JL, Karolak A, Rejniak KA (2016) Microenvironmental niches and sanctuaries: a route to acquired resistance. Adv Exp Med Biol 936:149–164

    Article  Google Scholar 

  35. Phillips RM (2016) Targeting the hypoxic fraction of tumours using hypoxia-activated prodrugs. Cancer Chemother Pharmacol 77:441–457

    Article  Google Scholar 

  36. Powathil GG, Swat M, Chaplain MA (2015) Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling. Cancer Biol 30:13–20

    Article  Google Scholar 

  37. Prasetyanti PR, Medema JP (2017) Intra-tumor heterogeneity from a cancer stem cell perspective. Mol Cancer 16:41

    Article  Google Scholar 

  38. Rejniak KA, McCawley LJ (2010) Current trends in mathematical modeling of tumor-microenvironment interactions: a survey of tools and applications. Exp Biol Med 235:411–423

    Article  Google Scholar 

  39. Rejniak KA, Estrella V, Chen T, Cohen AS, Lloyd MC, Morse DL (2013) The role of tumor tissue architecture in treatment penetration and efficacy: an integrative study. Front Oncol 3:111

    Article  Google Scholar 

  40. Rejniak KA, Lloyd MC, Reed DR, Bui MM (2015) Diagnostic assessment of osteosarcoma chemoresistance based on virtual clinical trials. Med Hypotheses 85:348–354

    Article  Google Scholar 

  41. Robertson-Tessi M, Gillies RJ, Gatenby R, Anderson A (2015) Impact of metabolic heterogeneity on tumor growth, invasion, and treatment outcomes. Cancer Res 75(8):1567–1579

    Article  Google Scholar 

  42. Schmidt MM, Wittrup KD (2009) A modeling analysis of the effects of molecular size and binding affinity on tumor targeting. Mol Cancer Ther 8(10):2861–2871

    Article  Google Scholar 

  43. Sun JD, Liu Q, Wang J, Ahluwalia D, Ferraro D, Wang Y, Duan JX, Ammons WS, Curd JG, Matteucci MD, Hart CP (2011) Selective tumor hypoxia targeting by hypoxia-activated prodrug TH-302 inhibits tumor growth in preclinical models of cancer. Clin Cancer Res 18(3):758–770

    Article  Google Scholar 

  44. Tannock IF, Lee CM, Tunggal JK, Cowan DSM, Egorin MJ (2002) Limited penetration of anticancer drugs through tumor tissue: a potential cause of resistance of solid tumors to chemotherapy. Clin Cancer Res 8(3):878–884

    Google Scholar 

  45. Tellez-Gabriel M, Ory B, Lamoureux F, Heymann MF, Heymann D (2016) Tumour heterogeneity: the key advantages of single-cell analysis. Int J Mol Sci 17:2142

    Article  Google Scholar 

  46. Thomas GD, Chappell MJ, Dykes PW, Ramsden DB, Godfrey KR, Ellis JR, Bradwell AR (1989) Effect of dose, molecular size, affinity, and protein binding on tumor uptake of antibody or ligand: a biomathematical model. Cancer Res 49(12):3290–3296

    Google Scholar 

  47. Thurber GM, Yang KS, Reiner T, Kohler RH, Sorger P, Mitchison T, Weissleder R (2013) Single-cell and subcellular pharmacokinetic imaging allows insight into drug action in vivo. Nat Commun 4:1504

    Article  Google Scholar 

  48. Thurber GM, Reiner T, Yang KS, Kohler RH, Weissleder R (2014) Effect of small-molecule modification on single-cell pharmacokinetics of PARP inhibitors. Mol Cancer Ther 13(4):986–995

    Article  Google Scholar 

  49. Tlupova S, Cortez R (2009) Boundary integral solutions of coupled Stokes and Darcy flows. J Comput Phys 228:158–179

    MathSciNet  Article  MATH  Google Scholar 

  50. Vinegoni C, Dubach JM, Thurber GM, Miller MA, Mazitschek R, Weissleder R (2015) Advances in measuring single-cell pharmacology in vivo. Drug Discov Today 20(9):1087–1092

    Article  Google Scholar 

  51. Weiss GJ, Infante JR, Chiorean EG, Borad MJ, Bendell JC, Molina JR, Tibes R, Ramanathan RK, Lewandowski K, Jones SF, Lacouture ME, Langmuir VK, Lee H, Kroll S, Burris HA (2011) Phase 1 study of the safety, tolerability, and pharmacokinetics of TH-302, a hypoxia-activated prodrug, in patients with advanced solid malignancies. Clin Cancer Res 17(9):2997–3004

    Article  Google Scholar 

  52. Wilson WR, Hay MP (2011) Targeting hypoxia in cancer therapy. Nat Rev Cancer 11:393–410

    Article  Google Scholar 

  53. Wilson WR, Hicks KO, Pullen SM, Ferry DM, Helsby NA, Patterson AV (2007) Bystander effects of bioreductive drugs: potential for exploiting pathological tumor hypoxia with dinitrobenzamide mustards. Radiat Res 167:625–636

    Article  Google Scholar 

  54. Wojtkowiak JW, Cornnell HC, Matsumoto S, Saito K, Takakusagi Y, Dutta P, Kim M, Zhang X, Leos R, Bailey KM, Martinez G, Lloyd MC, Weber C, Mitchell JB, Lynch RM, Baker AF, Gatenby RA, Rejniak KA, Hart C, Krishna MC, Gillies RJ (2015) Pyruvate sensitizes pancreatic tumors to hypoxia-activated prodrug TH-302. Cancer Metab 3:2

    Article  Google Scholar 

  55. Yeh JJ, Kim WY (2015) Targeting tumor hypoxia with hypoxia-activated prodrugs. J Clin Oncol 33(13):1505–1508

    Article  Google Scholar 

  56. Yu X, Zhang Y, Chen C, Yao Q, Li M (2010) Targeted drug delivery in pancreatic cancer. Biochim Biophys Acta 1805(1):97

    Google Scholar 

  57. Ziemys A, Klemm S, Milosevic M, Yokoi K, Ferrari M, Kojic M (2016) Computational analysis of drug transport in tumor microenvironment as a critical compartment for nanotherapeutic pharmacokinetics. Drug Deliv 23(23):2524–2531

    Google Scholar 

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Correspondence to Katarzyna A. Rejniak.

Additional information

This work was supported by the U01-CA202229 Physical Sciences Oncology Project (PSOP) Grant from the US National Institutes of Health, National Cancer Institute (NIH/NCI) and the American Cancer Society-Moffitt Institutional Grant. This publication was made possible by the NIH/NCI U54-CA193489 and NIH/NCI R01-CA077575 Grants, and by the Shared Resources at the H. Lee Moffitt Cancer Center & Research Institute, an NCI designated Comprehensive Cancer Center, through the NIH P30-CA076292 Grant.

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Karolak, A., Rejniak, K.A. Micropharmacology: An In Silico Approach for Assessing Drug Efficacy Within a Tumor Tissue. Bull Math Biol 81, 3623–3641 (2019). https://doi.org/10.1007/s11538-018-0402-x

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Keywords

  • Drug penetration
  • microPKPD
  • Single-cell pharmacology
  • Tumor tissue architecture
  • Targeted therapeutics
  • Hypoxia-activated pro-drugs