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Guillevin R, Naudin M, Fayolle P, Giraud C, Le Guillou X, Thomas C, Herpe G, Miranville A, Fernandez-Maloigne C, Pellerin L, Guillevin C. Diagnostic and Therapeutic Issues in Glioma Using Imaging Data: The Challenge of Numerical Twinning. J Clin Med 2023; 12:7706. [PMID: 38137775 PMCID: PMC10744312 DOI: 10.3390/jcm12247706] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 11/28/2023] [Accepted: 12/11/2023] [Indexed: 12/24/2023] Open
Abstract
Glial tumors represent the leading etiology of primary brain tumors. Their particularities lie in (i) their location in a highly functional organ that is difficult to access surgically, including for biopsy, and (ii) their rapid, anisotropic mode of extension, notably via the fiber bundles of the white matter, which further limits the possibilities of resection. The use of mathematical tools enables the development of numerical models representative of the oncotype, genotype, evolution, and therapeutic response of lesions. The significant development of digital technologies linked to high-resolution NMR exploration, coupled with the possibilities offered by AI, means that we can envisage the creation of digital twins of tumors and their host organs, thus reducing the use of physical sampling.
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Affiliation(s)
- Rémy Guillevin
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Mathieu Naudin
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Pierre Fayolle
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Clément Giraud
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Xavier Le Guillou
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
- Department of Genetic, University Hospital Center of Poitiers, 86000 Poitiers, France
| | - Clément Thomas
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Guillaume Herpe
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | - Alain Miranville
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
| | | | - Luc Pellerin
- IRMETIST Laboratory, INSERM U1313, University of Poitiers and University Hospital Center of Poitiers, 86000 Poitiers, France
| | - Carole Guillevin
- Department of Imaging, University Hospital Center of Poitiers, 86000 Poitiers, France
- Labcom I3M, University of Poitiers, 86000 Poitiers, France
- DACTIM-MIS Team, Laboratoire de Mathématiques Appliquées LMA, CNRS UMR 7348, 86021 Poitiers, France
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2
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Elmeliegy M, Den Haese J, Talati C, Wetzler M, Jusko WJ. Towards better combination regimens of cytarabine and FLT3 inhibitors in acute myeloid leukemia. Cancer Chemother Pharmacol 2020; 86:325-337. [PMID: 32748108 DOI: 10.1007/s00280-020-04114-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2020] [Accepted: 06/03/2020] [Indexed: 12/14/2022]
Abstract
BACKGROUND AML patients with FLT3/ITD mutations have poor response to cytarabine-based chemotherapy. FLT3 inhibitors (FLT3i) may resensitize cells to cytarabine (CYT). Improving treatment outcome of this combination may benefit from a mechanistic extrapolation approach from in vitro data. METHODS The effects of CYT and several FLT3i on cell proliferation and cell cycle kinetics were examined in AML cell lines. The effect of FLT3i (quizartinib, midostaurin, sorafenib) on cell proliferation and cell cycle kinetics was assessed in AML cell lines with differing FLT3 status; HEL (negligible expression of wild-type FLT3), EOL1 (wild-type FLT3), MV4-11 (FLT3-ITD resulting in constitutively active isoform). Semi-mechanistic cell cycle models for CYT and FLT3i were developed. Clinical CYT and quizartinib pharmacokinetic dosage regimens were modeled. Survival of AML patients was described via a hazard model. Simulations exploring different CYT/quizartinib regimens were conducted with the goal of improving treatment outcome. RESULTS FLT3 status was associated with sensitivity to CYT (HEL cells most sensitive > EOL1 > MV4-11 cells). This order of sensitivity is reversed for FLT3i. Cytarabine induced apoptosis in the S-phase while all FLT3i induced apoptosis and cell cycle arrest at G1 phase. Simulations of candidate clinical regimens predict better cell kill upon adding quizartinib simultaneously with or immediately after CYT exposure. Overall survival was predicted to be significantly better with quizartinib 200 mg administered every 48 h vs every 24 h in patients with FLT3 aberrations. CONCLUSION Simultaneous administration of quizartinib and CYT every other day is a promising combination regimen for AML patients with FLT3 mutations.
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Affiliation(s)
- Mohamed Elmeliegy
- Pfizer, Inc., 10555 Science Center Dr., San Diego, CA, 92121, USA. .,Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, NY, 14214, USA.
| | - Jason Den Haese
- Department of Medicine, Roswell Park Cancer Institute, Elm and Carlton Streets, Buffalo, NY, USA.,Department of Biology and Mathematics, D'Youville College, Buffalo, NY, USA
| | - Chetasi Talati
- Department of Medicine, Roswell Park Cancer Institute, Elm and Carlton Streets, Buffalo, NY, USA.,Department of Malignant Hematology, Moffitt Cancer Center, Tampa, FL, USA
| | - Meir Wetzler
- Department of Medicine, Roswell Park Cancer Institute, Elm and Carlton Streets, Buffalo, NY, USA
| | - William J Jusko
- Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, NY, 14214, USA
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3
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Perrillat-Mercerot A, Guillevin C, Miranville A, Guillevin R. Using mathematics in MRI data management for glioma assesment. J Neuroradiol 2019; 48:282-290. [PMID: 31811826 DOI: 10.1016/j.neurad.2019.11.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Revised: 10/25/2019] [Accepted: 11/26/2019] [Indexed: 12/01/2022]
Abstract
Our aim is to review the mathematical tools usefulness in MR data management for glioma diagnosis and treatment optimization. MRI does not give access to organs variations in hours or days. However a lot of multiparametric data are generated. Mathematics could help to override this paradox, the aim of this article is to show how. We first make a review on mathematical modelling using equations. Afterwards we present statistical analysis. We provide detailed examples in both sections. We finally conclude, giving some clues on in silico models.
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Affiliation(s)
- A Perrillat-Mercerot
- UMR CNRS 7348, SP2MI, équipe DACTIM-MIS, laboratoire de mathématiques et applications, université de Poitiers, boulevard Marie-et-Pierre-Curie, Téléport 2, 86962 Chasseneuil Futuroscope cedex, France.
| | - C Guillevin
- UMR CNRS 7348, SP2MI, équipe DACTIM-MIS, laboratoire de mathématiques et applications, université de Poitiers, boulevard Marie-et-Pierre-Curie, Téléport 2, 86962 Chasseneuil Futuroscope cedex, France; CHU de Poitiers, 2, rue de la Milétrie, 86021 Poitiers, France.
| | - A Miranville
- UMR CNRS 7348, SP2MI, équipe DACTIM-MIS, laboratoire de mathématiques et applications, université de Poitiers, boulevard Marie-et-Pierre-Curie, Téléport 2, 86962 Chasseneuil Futuroscope cedex, France.
| | - R Guillevin
- UMR CNRS 7348, SP2MI, équipe DACTIM-MIS, laboratoire de mathématiques et applications, université de Poitiers, boulevard Marie-et-Pierre-Curie, Téléport 2, 86962 Chasseneuil Futuroscope cedex, France; CHU de Poitiers, 2, rue de la Milétrie, 86021 Poitiers, France.
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4
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Williams KS, Secomb TW, El-Kareh AW. Additive Damage Models for Cellular Pharmacodynamics of Radiation-Chemotherapy Combinations. Bull Math Biol 2017; 80:1236-1258. [PMID: 28849417 DOI: 10.1007/s11538-017-0316-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Accepted: 07/03/2017] [Indexed: 11/28/2022]
Abstract
Many cancer patients receive combination treatments with radiation and chemotherapy. Available mathematical models for cellular pharmacodynamics have limited ability to represent observed in vitro responses to radiochemotherapy. Here, a family of additive damage models is proposed to describe cell kill resulting from radiochemotherapy with fixed schedule and variable doses. The pathways by which the agents produce cellular damage are assumed to converge in a single cell death process, so that survival depends on total damage, which can be represented as a sum of contributions from the various damage pathways. Heterogeneity in response across the cell population is ascribed to variations in the damage threshold for cell kill. The family of proposed models includes effects of one or two pathways of damage for each agent, saturation in drug responses, and cooperative or antagonistic interactions between agents. Models from this family with 4-7 unknown parameters are tested for their ability to fit 218 in vitro literature data sets for a range of drugs and cell lines. Overall, the additive damage models are found to outperform models based on the existing concept of independent cell kill, according to the corrected Akaike Information Criterion. The results are used to assess the importance of the various effects included in the models. These additive damage models have potential applications to the optimization of treatment and to the analysis and interpretation of in vitro screening data for new drug-radiation combinations.
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Affiliation(s)
| | - Timothy W Secomb
- Program in Applied Mathematics, University of Arizona, Tucson, AZ, USA.,Microcirculation Division, University of Arizona, Tucson, AZ, USA.,Department of Physiology, University of Arizona, Tucson, AZ, USA
| | - Ardith W El-Kareh
- Program in Applied Mathematics, University of Arizona, Tucson, AZ, USA. .,Microcirculation Division, University of Arizona, Tucson, AZ, USA.
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5
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Miao X, Koch G, Ait-Oudhia S, Straubinger RM, Jusko WJ. Pharmacodynamic Modeling of Cell Cycle Effects for Gemcitabine and Trabectedin Combinations in Pancreatic Cancer Cells. Front Pharmacol 2016; 7:421. [PMID: 27895579 PMCID: PMC5108803 DOI: 10.3389/fphar.2016.00421] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Accepted: 10/24/2016] [Indexed: 12/28/2022] Open
Abstract
Combinations of gemcitabine and trabectedin exert modest synergistic cytotoxic effects on two pancreatic cancer cell lines. Here, systems pharmacodynamic (PD) models that integrate cellular response data and extend a prototype model framework were developed to characterize dynamic changes in cell cycle phases of cancer cell subpopulations in response to gemcitabine and trabectedin as single agents and in combination. Extensive experimental data were obtained for two pancreatic cancer cell lines (MiaPaCa-2 and BxPC-3), including cell proliferation rates over 0-120 h of drug exposure, and the fraction of cells in different cell cycle phases or apoptosis. Cell cycle analysis demonstrated that gemcitabine induced cell cycle arrest in S phase, and trabectedin induced transient cell cycle arrest in S phase that progressed to G2/M phase. Over time, cells in the control group accumulated in G0/G1 phase. Systems cell cycle models were developed based on observed mechanisms and were used to characterize both cell proliferation and cell numbers in the sub G1, G0/G1, S, and G2/M phases in the control and drug-treated groups. The proposed mathematical models captured well both single and joint effects of gemcitabine and trabectedin. Interaction parameters were applied to quantify unexplainable drug-drug interaction effects on cell cycle arrest in S phase and in inducing apoptosis. The developed models were able to identify and quantify the different underlying interactions between gemcitabine and trabectedin, and captured well our large datasets in the dimensions of time, drug concentrations, and cellular subpopulations.
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Affiliation(s)
- Xin Miao
- Department of Pharmaceutical Sciences, University at Buffalo, State University of New York Buffalo, NY, USA
| | - Gilbert Koch
- Department of Pharmaceutical Sciences, University at Buffalo, State University of New YorkBuffalo, NY, USA; Pediatric Pharmacology and Pharmacometrics, University of Basel, Children's HospitalBasel, Switzerland
| | - Sihem Ait-Oudhia
- Department of Pharmaceutics, Center for Pharmacometrics and Systems Pharmacology (Orlando), College of Pharmacy, University of Florida Orlando, FL, USA
| | - Robert M Straubinger
- Department of Pharmaceutical Sciences, University at Buffalo, State University of New York Buffalo, NY, USA
| | - William J Jusko
- Department of Pharmaceutical Sciences, University at Buffalo, State University of New York Buffalo, NY, USA
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Fuentes-Garí M, Misener R, García-Munzer D, Velliou E, Georgiadis MC, Kostoglou M, Pistikopoulos EN, Panoskaltsis N, Mantalaris A. A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity. J R Soc Interface 2016; 12:20150276. [PMID: 26040591 DOI: 10.1098/rsif.2015.0276] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Acute myeloid leukaemia is characterized by marked inter- and intra-patient heterogeneity, the identification of which is critical for the design of personalized treatments. Heterogeneity of leukaemic cells is determined by mutations which ultimately affect the cell cycle. We have developed and validated a biologically relevant, mathematical model of the cell cycle based on unique cell-cycle signatures, defined by duration of cell-cycle phases and cyclin profiles as determined by flow cytometry, for three leukaemia cell lines. The model was discretized for the different phases in their respective progress variables (cyclins and DNA), resulting in a set of time-dependent ordinary differential equations. Cell-cycle phase distribution and cyclin concentration profiles were validated against population chase experiments. Heterogeneity was simulated in culture by combining the three cell lines in a blinded experimental set-up. Based on individual kinetics, the model was capable of identifying and quantifying cellular heterogeneity. When supplying the initial conditions only, the model predicted future cell population dynamics and estimated the previous heterogeneous composition of cells. Identification of heterogeneous leukaemia clones at diagnosis and post-treatment using such a mathematical platform has the potential to predict multiple future outcomes in response to induction and consolidation chemotherapy as well as relapse kinetics.
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Affiliation(s)
- María Fuentes-Garí
- Biological Systems Engineering Laboratory, Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
| | - Ruth Misener
- Department of Computing, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
| | - David García-Munzer
- Biological Systems Engineering Laboratory, Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
| | - Eirini Velliou
- Department of Chemical and Process Engineering, University of Surrey, Guildford GU2 7XH, UK
| | | | | | | | - Nicki Panoskaltsis
- Department of Hematology, Imperial College London, Northwick Park and St Mark's Campus, Harrow HA1 3UJ, UK
| | - Athanasios Mantalaris
- Biological Systems Engineering Laboratory, Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
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7
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Fuentes-Garí M, Misener R, Georgiadis MC, Kostoglou M, Panoskaltsis N, Mantalaris A, Pistikopoulos EN. Selecting a Differential Equation Cell Cycle Model for Simulating Leukemia Treatment. Ind Eng Chem Res 2015. [DOI: 10.1021/acs.iecr.5b01150] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
| | | | | | | | - Nicki Panoskaltsis
- Centre
for Haematology, Imperial College London, Northwick Park Campus, HA1
3LY, London, U.K
| | | | - Efstratios N. Pistikopoulos
- Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States
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8
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Abstract
Population balance modeling is undergoing phenomenal growth in its applications, and this growth is accompanied by multifarious reviews. This review aims to fortify the model's fundamental base, as well as point to a variety of new applications, including modeling of crystal morphology, cell growth and differentiation, gene regulatory processes, and transfer of drug resistance. This is accomplished by presenting the many faces of population balance equations that arise in the foregoing applications.
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Affiliation(s)
| | - Meenesh R. Singh
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94704
- Joint Center for Artificial Photosynthesis, Lawrence Berkeley National Laboratory, Berkeley, California 94720
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9
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Falgreen S, Laursen MB, Bødker JS, Kjeldsen MK, Schmitz A, Nyegaard M, Johnsen HE, Dybkær K, Bøgsted M. Exposure time independent summary statistics for assessment of drug dependent cell line growth inhibition. BMC Bioinformatics 2014; 15:168. [PMID: 24902483 PMCID: PMC4127655 DOI: 10.1186/1471-2105-15-168] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2013] [Accepted: 05/27/2014] [Indexed: 12/17/2022] Open
Abstract
Background In vitro generated dose-response curves of human cancer cell lines are
widely used to develop new therapeutics. The curves are summarised by simplified
statistics that ignore the conventionally used dose-response curves’
dependency on drug exposure time and growth kinetics. This may lead to suboptimal
exploitation of data and biased conclusions on the potential of the drug in
question. Therefore we set out to improve the dose-response assessments by
eliminating the impact of time dependency. Results First, a mathematical model for drug induced cell growth inhibition was formulated
and used to derive novel dose-response curves and improved summary statistics that
are independent of time under the proposed model. Next, a statistical analysis
workflow for estimating the improved statistics was suggested consisting of 1)
nonlinear regression models for estimation of cell counts and doubling times, 2)
isotonic regression for modelling the suggested dose-response curves, and 3)
resampling based method for assessing variation of the novel summary statistics.
We document that conventionally used summary statistics for dose-response
experiments depend on time so that fast growing cell lines compared to slowly
growing ones are considered overly sensitive. The adequacy of the mathematical
model is tested for doxorubicin and found to fit real data to an acceptable
degree. Dose-response data from the NCI60 drug screen were used to illustrate the
time dependency and demonstrate an adjustment correcting for it. The applicability
of the workflow was illustrated by simulation and application on a doxorubicin
growth inhibition screen. The simulations show that under the proposed
mathematical model the suggested statistical workflow results in unbiased
estimates of the time independent summary statistics. Variance estimates of the
novel summary statistics are used to conclude that the doxorubicin screen covers a
significant diverse range of responses ensuring it is useful for biological
interpretations. Conclusion Time independent summary statistics may aid the understanding of drugs’
action mechanism on tumour cells and potentially renew previous drug sensitivity
evaluation studies.
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Affiliation(s)
- Steffen Falgreen
- Department of Haematology, Aalborg University Hospital, Aalborg, Denmark.
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10
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Pefani E, Panoskaltsis N, Mantalaris A, Georgiadis MC, Pistikopoulos EN. Design of optimal patient-specific chemotherapy protocols for the treatment of acute myeloid leukemia (AML). Comput Chem Eng 2013. [DOI: 10.1016/j.compchemeng.2013.02.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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11
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Hamed SS, Straubinger RM, Jusko WJ. Pharmacodynamic modeling of cell cycle and apoptotic effects of gemcitabine on pancreatic adenocarcinoma cells. Cancer Chemother Pharmacol 2013; 72:553-63. [PMID: 23835677 DOI: 10.1007/s00280-013-2226-6] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2012] [Accepted: 06/08/2013] [Indexed: 01/19/2023]
Abstract
PURPOSE The standard of care for treating patients with pancreatic adenocarcinomas includes gemcitabine (2',2'-difluorodeoxycytidine). Gemcitabine primarily elicits its response by stalling the DNA replication forks of cells in the S phase of the cell cycle. To provide a quantitative framework for characterizing the cell cycle and apoptotic effects of gemcitabine, we developed a pharmacodynamic model in which the activation of cell cycle checkpoints or cell death is dependent on gemcitabine exposure. METHODS Three pancreatic adenocarcinoma cell lines (AsPC-1, BxPC-3, and MiaPaca-2) were exposed to varying concentrations (0-100,000 ng/mL) of gemcitabine over a period of 96 h in order to quantify proliferation kinetics and cell distributions among the cell cycle phases. The model assumes that the drug can inhibit cycle-phase transitioning in each of the 3 phases (G1, S, and G2/M) and can cause apoptosis of cells in G1 and G2/M phases. Fitting was performed using the ADAPT5 program. RESULTS The time course of gemcitabine effects was well described by the model, and parameters were estimated with good precision. Model predictions and experimental data show that gemcitabine induces cell cycle arrest in the S phase at low concentrations, whereas higher concentrations induce arrest in all cell cycle phases. Furthermore, apoptotic effects of gemcitabine appear to be minimal and take place at later time points. CONCLUSION The pharmacodynamic model developed provides a quantitative, mechanistic interpretation of gemcitabine efficacy in 3 pancreatic cancer cell lines, and provides useful insights for rational selection of chemotherapeutic agents for combination therapy.
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Affiliation(s)
- Salaheldin S Hamed
- Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical Sciences, University at Buffalo, Buffalo, NY 14214, USA
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12
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Mathematical modeling to distinguish cell cycle arrest and cell killing in chemotherapeutic concentration response curves. J Pharmacokinet Pharmacodyn 2011; 38:385-403. [DOI: 10.1007/s10928-011-9199-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2010] [Accepted: 04/16/2011] [Indexed: 12/18/2022]
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13
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Affiliation(s)
- Eric Sherer
- School of Chemical Engineering Purdue University West Lafayette, Indiana 47907
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14
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Sherer E, Tocce E, Hannemann RE, Rundell AE, Ramkrishna D. Identification of age-structured models: cell cycle phase transitions. Biotechnol Bioeng 2008; 99:960-74. [PMID: 17787014 DOI: 10.1002/bit.21633] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
A methodology is developed that determines age-specific transition rates between cell cycle phases during balanced growth by utilizing age-structured population balance equations. Age-distributed models are the simplest way to account for varied behavior of individual cells. However, this simplicity is offset by difficulties in making observations of age distributions, so age-distributed models are difficult to fit to experimental data. Herein, the proposed methodology is implemented to identify an age-structured model for human leukemia cells (Jurkat) based only on measurements of the total number density after the addition of bromodeoxyuridine partitions the total cell population into two subpopulations. Each of the subpopulations will temporarily undergo a period of unbalanced growth, which provides sufficient information to extract age-dependent transition rates, while the total cell population remains in balanced growth. The stipulation of initial balanced growth permits the derivation of age densities based on only age-dependent transition rates. In fitting the experimental data, a flexible transition rate representation, utilizing a series of cubic spline nodes, finds a bimodal G(0)/G(1) transition age probability distribution best fits the experimental data. This resolution may be unnecessary as convex combinations of more restricted transition rates derived from normalized Gaussian, lognormal, or skewed lognormal transition-age probability distributions corroborate the spline predictions, but require fewer parameters. The fit of data with a single log normal distribution is somewhat inferior suggesting the bimodal result as more likely. Regardless of the choice of basis functions, this methodology can identify age distributions, age-specific transition rates, and transition-age distributions during balanced growth conditions.
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Affiliation(s)
- E Sherer
- School of Chemical Engineering, Forney Hall of Chemical Engineering, 480 Stadium Mall Way, Purdue University, West Lafayette, Indiana 47907, USA
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15
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Sherer E, Hannemann RE, Rundell A, Ramkrishna D. Estimation of likely cancer cure using first- and second-order product densities of population balance models. Ann Biomed Eng 2007; 35:903-15. [PMID: 17440813 DOI: 10.1007/s10439-007-9310-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2006] [Accepted: 03/30/2007] [Indexed: 10/23/2022]
Abstract
The objective of chemotherapy is to eradicate all cancerous cells. However, due to the stochastic behavior of cells, the elimination of all cancerous cells must be discussed probabilistically. We hypothesize, and demonstrate in the results, that the mean and standard deviation of a cancer cell population, derived through the probabilistic interpretation of population balance equations, are sufficient to estimate the likelihood of cancer eradication. Our analysis of a binary cell division model reveals that an expected cancer population that is six standard deviations less than one cell provides a good estimate for the treatment durations that nearly ensures treatment successes. This approximation is evaluated and tested on two other physiologically likely scenarios: variable patient response to chemotherapy and the presence of a dormant population. We find that early identification of individual patient susceptibility to the chemotherapeutic agent is extremely important to all patients as treatment adjustments for non-responders greatly enhances their likelihood of cure while responders need not be subjected to needlessly harsh treatments. Presence of a dormant population increases both the required treatment duration and population variability, but the same estimation method holds. This work is a step toward using stochastic models for a quantitative evaluation of chemotherapy.
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Affiliation(s)
- Eric Sherer
- School of Chemical Engineering, Forney Hall of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA
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