Tumor volume regression during and after chemo and radio therapy is a useful information for clinical decisions. Indeed, a quantitative, patient oriented, description of the response to treatment can guide towards the modification of the scheduled doses or the evaluation of the best time for surgery. We propose a macroscopic algorithm which permits to follow quantitatively the time evolution of the tumor volume during and after radiochemotherapy. The method, initially validated with different cell-lines implanted in mice, is then successfully applied to the available data for partially responding and complete recovery patients.

Faculty of Mathematics and Physics Charles University 5 Holešovičkách 2 18000 Prague Czech Republic

INFN Sezione di Catania 95123 Catania Italy

Istituto Oncologico del Mediterraneo 95029 Viagrande Italy

REM Radioterapia SRL 95029 Viagrande Italy

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Siegel R.L., Miller K.D., Fuchs H.E., Jemal A. Cancer statistics, 2022. CA Cancer J. Clin. 2022;72:7–33. doi: 10.3322/caac.21708. PubMed DOI

Thomas M., Rübe C., Hoffknecht P., Macha H.N., Freitag L., Linder A., Willich N., Hamm M., Sybrecht G.W., Ukena D., et al. Effect of preoperative chemoradiation in addition to preoperative chemotherapy: A randomised trial in stage III non-small-cell lung cancer. Lancet Oncol. 2008;9:636–648. doi: 10.1016/S1470-2045(08)70156-6. PubMed DOI

Albain K.S., Rusch V.W., Crowley J.J., Rice T.W., Turrisi A.T., 3rd, Weick J.K., Lonchyna V.A., Presant C.A., McKenna R.J., Gandara D.R. Concurrent cisplatin/etoposide plus chest radiotherapy followed by surgery for stages IIIA (N2) and IIIB non-small-cell lung cancer: Mature results of Southwest Oncology Group phase II study 8805. J. Clin. Oncol. 1995;13:1880–1892. PubMed

Choi N.C., Carey R.W., Daly W., Mathisen D., Wain J., Wright C., Lynch T., Grossbard M., Grillo H. Potential impact on survival of improved tumor downstaging and resection rate by preoperative twice-daily radiation and concurrent chemotherapy in stage IIIA non-small-cell lung cancer. J. Clin. Oncol. 1997;15:712–722. doi: 10.1200/JCO.1997.15.2.712. PubMed DOI

Spolverato G., Pucciarelli S., Bertorelle R., Rossi A.D., Nitti D. Predictive factors of the response of rectal cancer to neoadjuvant radiochemotherapy. Cancers. 2011;3:2176–2194. doi: 10.3390/cancers3022176. PubMed DOI PMC

Baskar R., Dai J., Wenlong N., Yeo R., Yeoh K.W. Biological response of cancer cells to radiation treatment. Front. Mol. Biosci. 2014;1:24. doi: 10.3389/fmolb.2014.00024. PubMed DOI PMC

Fleming F., Påhlman L., Monson J. Neoadjuvant therapy in rectal cancer. Dis. Colon Rectum. 2011;54:901–902. doi: 10.1007/DCR.0b013e31820eeb37. PubMed DOI

Hahnfeldt P., Panigrahy D., Folkman J., Hlatky L. Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 1999;59:4770–4775. PubMed

Steel G.G. Growth Kinetics of Tumours. Clarendon Press; Oxford, UK: 1977.

Wheldon T.E. Mathematical Models in Cancer Research. Adam Hilger Publisher; Bristol, UK: 1988.

Norton L. A Gompertzian model of human breast cancer growth. Cancer Res. 1988;48:7067–7071. PubMed

Yorke E., Fuks Z., Norton L., Whitmore W., Ling C.C. Modeling the development of metastases from primary and locally recurrent tumors: Comparison with a clinical data base for prostatic cancer. Cancer Res. 1993;53:2987–2993. PubMed

Vaghi C., Rodallec A., Fanciullino R., Ciccolini J., Mochel J.P., Mastri M., Benzekry S. Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors. PLoS Comput. Biol. 2020;16:e1007178. doi: 10.1371/journal.pcbi.1007178. PubMed DOI PMC

Gompertz B. On the nature of the function expressive of the law of human mortality and a new mode of determining life contingencies. Philos. Trans. R. Soc. 1825;115:513–583. PubMed PMC

Jung H., Kruger H.J., Brammer I., Zywietz F., Beck-Bomholdt H.P. Cell population kinetics of the rhabdomyosarcoma R1H of the rat after single doses of X rays. Int. J. Radiat. Biol. 1990;57:567–589. doi: 10.1080/09553009014552701. PubMed DOI

Hansen O., Grau C., Bentzen S.M., Overgaard J. Repopulation in the SCCVII squamous cell carcinoma assessed by an in vivo-in vitro excision essay. Radioth. Oncol. 1996;32:137–144. doi: 10.1016/0167-8140(96)01728-8. PubMed DOI

O’Donoghue J.A. The response of tumours with Gompertzian growth characteristics to fractionated radiotherapy. Int. J. Radiat. Biol. 1997;72:325–339. doi: 10.1080/095530097143329. PubMed DOI

Norton L., Simon R. Tumor size, sensitivity to therapy and the design of treatment protocols. Cancer Treat. Rep. 1976;61:1307–1317. PubMed

Norton L., Simon R. The Norton-Simon hypothesis revisited. Cancer Treat. Rep. 1986;70:163–169. PubMed

Dzutsev A., Goldszmid R.S., Viaud S., Zitvogel L., Trinchieri G. The role of the microbiota in inflammation, carcinogenesis, and cancer therapy. Eur. J. Immunol. 2015;45:17–31. doi: 10.1002/eji.201444972. PubMed DOI

Serna G., Ruiz-Pace F., Hernando J., Alonso L., Fasani R., Landolfi S., Comas R., Jimenez J., Elez E., Bullman S., et al. Fusobacterium nucleatum persistence and risk of recurrence after preoperative treatment in locally advanced rectal cancer. Ann. Oncol. 2020;31:1366–1375. doi: 10.1016/j.annonc.2020.06.003. PubMed DOI PMC

Yi Y., Shen L., Shi W., Xia F., Zhang H., Wang Y., Zhang J., Wang Y., Sun X., Zhang Z., et al. Gut Microbiome Components Predict Response to Neoadjuvant Chemoradiotherapy in Patients with Locally Advanced Rectal Cancer: A Prospective, Longitudinal Study. Clin. Cancer Res. 2021;27:1329–1340. doi: 10.1158/1078-0432.CCR-20-3445. PubMed DOI

Amugongo L., Green A., Cobben D., van Herk M., McWilliam A., Osorio E. Identification of modes of tumor regression in non-small cell lung cancer patients during radiotherapy. Med. Phys. 2022;49:370–381. doi: 10.1002/mp.15320. PubMed DOI

Dahlberg W., Azzam E., Yu Y., Little J. Response of human tumor cells of varying radiosensitivity and radiocurability to fractionated irradiation. Cancer Res. 1999;59:5365–5369. PubMed

Lewin T.D., Byrne H.M., Maini P.K., Caudell J.J., Moros E.G., Enderling H. The importance of dead material within a tumour on the dynamics in response to radiotherapy. Phys. Med. Biol. 2020;65:015007. doi: 10.1088/1361-6560/ab4c27. PubMed DOI

Zahid M.U., Mohsin N., Mohamed A.S., Caudell J.J., Harrison L.B., Fuller C.D., Moros E.G., Enderling H. Forecasting Individual Patient Response to Radiotherapy in Head and Neck Cancer with a Dynamic Carrying Capacity Model. Int. J. Radiat. Oncol. Biol. Phys. 2021;111:693–704. doi: 10.1016/j.ijrobp.2021.05.132. PubMed DOI PMC

Castorina P., Castorina L., Ferini G. Non-Homogeneous Tumor Growth and Its Implications for Radiotherapy: A Phenomenological Approach. J. Pers. Med. 2021;11:527. doi: 10.3390/jpm11060527. PubMed DOI PMC

Ferini G., Valenti V., Tripoli A., Illari S.I., Molino L., Parisi S., Cacciola A., Lillo S., Giuffrida D., Pergolizzi S. Lattice or oxygen-guided radiotherapy: What if they converge? Possible future directions in the era of immunotherapy. Cancers. 2021;13:3290. doi: 10.3390/cancers13133290. PubMed DOI PMC

Ferini G., Castorina P., Valenti V., Illari S., Sachpazidis I., Castorina L., Marrale M., Pergolizzi S. A Novel Radiotherapeutic Approach to Treat Bulky Metastases Even From Cutaneous Squamous Cell Carcinoma: Its Rationale and a Look at the Reliability of the Linear-Quadratic Model to Explain Its Radiobiological Effects. Front. Oncol. 2022;12:809279. doi: 10.3389/fonc.2022.809279. PubMed DOI PMC

El-Benhawy S., Sadek N., Kamel M., Sharaf A., Abderhman I., Morsi M., Abobakr A. Study the relationship of endothelial damage / dysfunction due to occupational exposure to low dose ionizing radiation versus high dose exposure during radiotherapy. Cancer Treat. Res. Commun. 2020;25:100215. doi: 10.1016/j.ctarc.2020.100215. PubMed DOI

Vadalà R., Santacaterina A., Sindoni A., Platania A., Arcudi A., Ferini G., Mazzei M., Marletta D., Rifatto C., Risoleti E., et al. Stereotactic body radiotherapy in non-operable lung cancer patients. Clin. Transl. Oncol. 2016;18:1158–1159. doi: 10.1007/s12094-016-1552-7. PubMed DOI

Parisi S., Ferini G., Cacciola A., Lillo S., Tamburella C., Santacaterina A., Bottari A., Brogna A., Ferrantelli G., Pontoriero A., et al. A non-surgical COMBO-therapy approach for locally advanced unresectable pancreatic adenocarcinoma: Preliminary results of a prospective study. Radiol. Medica. 2022;127:214–219. doi: 10.1007/s11547-021-01441-w. PubMed DOI

Mattonen S., Ward A., Palma D. Pulmonary imaging after stereotactic radiotherapy-does RECIST still apply? Br. J. Radiol. 2016;89:20160113. doi: 10.1259/bjr.20160113. PubMed DOI PMC

Mattonen S., Huang K., Ward A., Senan S., Palma D. New techniques for assessing response after hypofractionated radiotherapy for lung cancer. J. Thorac. Dis. 2014;6:375–386. PubMed PMC

Castorina P., Delsanto P.P., Guiot C. Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences. Phys. Rev. Lett. 2006;96:188701. doi: 10.1103/PhysRevLett.96.188701. PubMed DOI

Castorina P., Blanchard P. Unified approach to growth and aging in biological, technical and biotechnical systems. SpringerPlus. 2012;1:7. doi: 10.1186/2193-1801-1-7. PubMed DOI PMC

Meyer P.S., Ausubel J.H. Carrying Capacity: A Model with Logistically Varying Limits. Technol. Forecast. Soc. Chang. 1999;61:209–214. doi: 10.1016/S0040-1625(99)00022-0. DOI

Royama T. Analytical Population Dynamics. Volume 10 Springer Science & Business Media; Berlin/Heidelberg, Germany: 2012.

Begin R., Kleijnen J.P., Engels B., Philippens M., Asselen B., Raaymakers B., Reerink O., Ridder M., Intven M. Tumor volume regression during preoperative chemoradiotherapy for rectal cancer: A prospective observational study with weekly MRI. Acta Oncol. 2018;57:723–727. doi: 10.1080/0284186X.2017.1400689. PubMed DOI

Bostel T., Dreher C., Wollschläger D., Mayer A., König F., Bickelhaupt S., Schlemmer H., Huber P., Sterzing F., Bäumer P., et al. Exploring MR regression patterns in rectal cancer during neoadjuvant radiochemotherapy with daily T2- and diffusion-weighted MRI. Radiat. Oncol. 2020;15:171. doi: 10.1186/s13014-020-01613-4. PubMed DOI PMC

Puglisi C., Giuffrida R., Borzì G., Mattia P.D., Costa A., Colarossi C., Deiana E., Picardo M., Colarossi L., Mare M., et al. Radiosensitivity of Cancer Stem Cells Has Potential Predictive Value for Individual Responses to Radiotherapy in Locally Advanced Rectal Cancer. Cancers. 2020;12:3672. doi: 10.3390/cancers12123672. PubMed DOI PMC

Quantitative Method for Monitoring Tumor Evolution During and After Therapy

Forecasting Individual Patients' Best Time for Surgery in Colon-Rectal Cancer by Tumor Regression during and after Neoadjuvant Radiochemotherapy