scholarly journals Classical Mathematical Models for Prediction of Response to Chemotherapy and Immunotherapy

2021 ◽  
Author(s):  
Narmin Ghaffari Laleh ◽  
Chiara Maria Lavinia Loeffler ◽  
Julia Grajek ◽  
Katerina Stankova ◽  
Alexander T. Pearson ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Mathematical Models ◽  
Early Treatment ◽  
Goodness Of Fit ◽  
Tumor Volume ◽  
Human Tumor ◽  
Gompertz Model ◽  
Text Book ◽  
Response To Chemotherapy ◽  
Volume Measurements

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest text-book models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemo-therapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment re-sponse, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we pro-vide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models.

scholarly journals Mathematical Models for Tumor Growth and the Reduction of Overtreatment

2018 ◽  
Vol 80 (01) ◽  
pp. 072-078 ◽  
Author(s):  
Berdine Heesterman ◽  
John-Melle Bokhorst ◽  
Lisa de Pont ◽  
Berit Verbist ◽  
Jean-Pierre Bayley ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Mathematical Models ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Age At Onset ◽  
Growth Curves ◽  
Magnetic Resonance Images ◽  
Coefficient Of Determination ◽  
Growth Data ◽  
Significant Difference

Background To improve our understanding of the natural course of head and neck paragangliomas (HNPGL) and ultimately differentiate between cases that benefit from early treatment and those that are best left untreated, we studied the growth dynamics of 77 HNPGL managed with primary observation. Methods Using digitally available magnetic resonance images, tumor volume was estimated at three time points. Subsequently, nonlinear least squares regression was used to fit seven mathematical models to the observed growth data. Goodness of fit was assessed with the coefficient of determination (R 2) and root-mean-squared error. The models were compared with Kruskal–Wallis one-way analysis of variance and subsequent post-hoc tests. In addition, the credibility of predictions (age at onset of neoplastic growth and estimated volume at age 90) was evaluated. Results Equations generating sigmoidal-shaped growth curves (Gompertz, logistic, Spratt and Bertalanffy) provided a good fit (median R 2: 0.996–1.00) and better described the observed data compared with the linear, exponential, and Mendelsohn equations (p < 0.001). Although there was no statistically significant difference between the sigmoidal-shaped growth curves regarding the goodness of fit, a realistic age at onset and estimated volume at age 90 were most often predicted by the Bertalanffy model. Conclusions Growth of HNPGL is best described by decelerating tumor growth laws, with a preference for the Bertalanffy model. To the best of our knowledge, this is the first time that this often-neglected model has been successfully fitted to clinically obtained growth data.

scholarly journals Mathematical models describing disappearance of Lucerne hay in the rumen using the nylon bag technique

2021 ◽  
Vol 50 (5) ◽  
Author(s):  
V. Palangi ◽  
M. Macit ◽  
A.R. Bayat
Keyword(s):  
Mathematical Models ◽  
Crude Protein ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Exponential Model ◽  
Parameter Estimates ◽  
Rumen Degradation ◽  
Degradation Data ◽  
Potential Use

It is essential to study the dynamics of rumen degradation of feeds before their potential use in formulating diets for ruminants. Various mathematical models have been developed to describe this degradation. The non-lagged exponential model (Model I), the lagged exponential model (Model II), the Gompertz model (Model III), and the generalized Mitscherlich model (Model IV) were examined using two alternative software (SAS and MATLAB) to determine their efficacy in accounting for variation in ruminal disappearance of dry matter (DM) and crude protein (CP) of lucerne hay from three cuttings. All models described DM degradability well (R2 >0.98). Only Models I and II converged when fitted to CP degradability data (R2 >0.98). It was concluded that any of these models could be used to describe the degradation of DM, whereas only Models I and II could be used to describe the degradation of CP from three cuttings of Lucerne hay. All the models that were fitted to the DM degradation data performed reasonably well, with only minor differences in goodness of fit. However, these models differed in values of the parameter estimates. Additionally, SAS failed to converge in the analyses of CP with Models III and IV, and MATLAB converged to nonsensical values with Model III. Model I might be recommended because it fitted the data well and required estimates of the fewest parameters Keywords: alfalfa hay, in situ digestion, model selection, nonlinear regression

The Novel Proteasome Inhibitor CEP-18770 Inhibits Myeloma Tumor Growth In Vitro and In Vivo and Enhances the Anti-MM Effects of Melphalan

Blood ◽  
2008 ◽  
Vol 112 (11) ◽  
pp. 843-843
Author(s):  
Eric SancheZ ◽  
Richard A Campbell ◽  
Jeffrey A Steinberg ◽  
Mingjie Li ◽  
Haiming Chen ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Arsenic Trioxide ◽  
Cell Lines ◽  
Proteasome Inhibitor ◽  
Tumor Volume ◽  
Single Agent ◽  
Human Tumor ◽  
The Novel

Abstract Proteasome inhibitors (PI) have been shown to be effective agents for the treatment of multiple myeloma (MM) and enhance the anti-tumor effects of a variety of chemotherapeutic drugs including melphalan and doxorubicin as well as arsenic trioxide (ATO). The novel proteasome inhibitor CEP-18770 has recently been shown to induce cytotoxic effects across a broad panel of human tumor cell lines including MM in vitro. However, little data exists on the in vivo anti-MM effects of this PI either alone or in combination with other active anti-MM drugs. First, we examined the anti-proliferative effects of treating MM cell lines in vitro with CEP-18770 alone and in combination with melphalan, arsenic trioxide (ATO) and doxorubicin. MM cell lines were cultured without fetal bovine serum and incubated in the presence of CEP-18770 alone and in combination with these agents for 48 hours. Cell growth was then measured using an MTS assay. First, RPMI8226 and U266 cells were tested in vitro using a constant concentration of melphalan or doxorubicin in combination with varying concentrations of CEP-18770 or varying concentrations of the chemotherapeutic agent with constant CEP-18770. Although single agent treatment showed marked anti-proliferative effects, combination indexes as calculated by the Chou-Talalay method showed synergistic anti- MM effects of CEP-18770 with either melphalan or doxorubicin in these MM cell lines. In addition, similar experiments were carried out evaluating the combination of ATO plus CEP-18770 in RPMI8226 cells and also showed synergism with this combination. Next, a series of in vivo studies were conducted using our SCID-hu models of MM including LAGλ-1, LAGκ-1A and LAGκ-1B. Mice receiving CEP-18770 at 0.1, 0.3, 1, and 3 mg/kg were injected twice weekly via intravenous injection throughout the study. CEP-18770 dosed at 10 mg/kg was administered via oral gavage twice weekly and mice dosed with melphalan received injections once weekly via intraperitoneal injection. Mice bearing intramuscularly implanted LAGλ-1 were treated with CEP-18770 or vehicle alone. Mice treated with the PI inhibited tumor growth as determined by human immunoglobulin (hIg) G levels and measurement of tumor volume (P = 0.0008) compared to mice receiving vehicle. A significant inhibition of both human paraprotein secretion and reduction of tumor growth was also observed in LAGk-1A-bearing mice treated with CEP-18770 at 1, 3 and 10 mg/kg (hIgG: P = 0.0001, P = 0.0002 and P = 0.0001, respectively; tumor volume: P = 0.0001, P = 0.0001 and P = 0.0001, respectively) and LAGk-1B-bearing mice treated with CEP-18770 at 3 and 10 mg/kg (hIgG: P = 0.0008 and P = 0.0034, respectively; tumor volume: P = 0.0008 and P = 0.0028, respectively) compared to mice receiving vehicle. Finally, the combination of CEP-18770 (1 mg/kg) plus melphalan (3 mg/kg) was tested in LAGk-1B-bearing mice. Mice treated with the combination showed markedly smaller tumors compared to treatment with vehicle (P = 0.0008) or melphalan alone (P = 0.0204). Mice treated with the PI alone or in combination with melphalan did not show any observed toxicity. Thus, these studies provide promising preclinical data to suggest the potent anti-MM effects of CEP-18770 both in vitro and in vivo and also suggest that this new PI may enhance the anti-MM effects of several active anti-MM agents including melphalan, doxorubicin and ATO.

PREDICTION POWER OF MATHEMATICAL MODELS FOR TUMOR GROWTH

1993 ◽  
Vol 01 (01) ◽  
pp. 69-78 ◽  
Author(s):  
M. MARUŠIĆ ◽  
S. VUK-PAVLOVIĆ
Keyword(s):  
Tumor Growth ◽  
Mathematical Models ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Gompertz Model ◽  
Multicellular Tumor Spheroids ◽  
Tumor Spheroids ◽  
Least Squares Minimization

We compared the Gompertz model, the generalized Gompertz model, the Piantadosi model, the autostimulation model and the polynomials for the power to predict growth of multicellular tumor spheroids as paradigms of the prevascular phase of tumor growth. For the comparison of models we developed a criterion that established the Gompertz model as the model with the best prediction power. The prediction power of the remaining models was ranked in declining order: the generalized Gompertz model; the mutually indistinguishable Piantadosi model and the autostimulation model; and the polynomials. The ranking of models was not affected by the applied minimization criteria of weighted least squares, unweighted least squares and fitting to logarithmically transformed data, but the prediction power was affected by these criteria. The best predictions were obtained by weighted least squares, closely followed by fitting to logarithmically transformed data. The unweighted least-squares minimization was much less applicable for prediction (and description) of growth.

Clinical pharmacokinetics (PK) and translational PK-pharmacodynamic (PD) modeling and simulation to predict antitumor response of various dosing schedules to guide the selection of a recommended phase II dose (RP2D) and schedule for the investigational agent MLN0128.

2013 ◽  
Vol 31 (15_suppl) ◽  
pp. 2567-2567 ◽  
Author(s):  
Chirag G. Patel ◽  
Mayank Patel ◽  
Arijit Chakravarty ◽  
Esha A. Gangolli ◽  
Elly Barry ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Tumor Volume ◽  
Clinical Investigation ◽  
Mammalian Target Of Rapamycin ◽  
Human Tumor ◽  
Growth Curves ◽  
Dose Schedule ◽  
Tumor Xenograft ◽  
Clinical Pharmacokinetics ◽  
Selection Of

2567 Background: MLN0128 (INK128) is an investigational oral, potent, and highly selective inhibitor of mammalian target of rapamycin complex 1 and 2 (mTORC1/2) currently in clinical investigation. In the phase1 study INK128-001, MLN0128 was administered once daily (QD), once weekly (QW), QDx3D/week, and QDx5D/week, with respective MTDs of 6, 40, 16, and 10 mg. To guide selection of dose/schedule for further investigation, PD modulation in skin (pS6, p4EBP1, pNDRG1, pPRAS40) was put into context of clinical PK in INK128-001. A preclinical translational dynamic-PK efficacy model was used to describe the relationship and determine PK drivers of efficacy in tumor xenograft models. This model was implemented using human PK parameters to predict tumor volume-time curves, which was utilized to help determine the optimal MLN0128 dose/schedule. Methods: Phoenix NLME v1.1 was used for compartmental modeling of clinical and preclinical PK data, and modeling the preclinical PK-efficacy relationship of MLN0128. PD activity in skin was measured by immunohistochemistry, reported as H scores. Tumor growth curves were simulated using NONMEM v7.2; predicted tumor growth curves were plotted in S-Plus v8.1. Results: Clinical skin PD data suggests exposure dependent inhibition of pS6, and p4EBP1. A two compartment PK model adequately described the PK characteristics of MLN0128 [mean (%CV) ka: ~5.305 h-1 (114), k12: ~0.490 h-1(85), k21: ~0.67 h-1(69), V/F: ~180 L (44), Tlag: 0.317 h (73)]. Simulation of human tumor volume-time curves suggest efficacy is dependent on schedule and that MLN0128 administered in more frequent schedules (QD, QDx5D) provides stronger antitumor effect vs less frequent schedules (QW, QDx3D). Conclusions: The results indicate that per unit MLN0128 plasma exposure, QD and QDx5D may be optimal in comparison with QDx3D and QW dosing. However, these results will also need to be put into context with the overall safety profile and respective MTDs and RP2Ds for each schedule with their resultant achievable total cycle dose by schedule. Clinical trial information: NCT01058707.

ANTITUMOR EFFECT OF COLLOIDAL SILVER BISILICATE IN EXPERIMENTAL IN VITRO AND IN VIVO STUDIES

2019 ◽  
Vol 65 (5) ◽  
pp. 760-765
Author(s):  
Margarita Tyndyk ◽  
Irina Popovich ◽  
A. Malek ◽  
R. Samsonov ◽  
N. Germanov ◽  
...  
Keyword(s):  
Antitumor Activity ◽  
Tumor Growth ◽  
Tumor Cells ◽  
Human Tumor ◽  
Significant Inhibition ◽  
In Vivo Studies ◽  
Ehrlich Carcinoma ◽  
In Vivo Experiments

The paper presents the results of the research on the antitumor activity of a new drug - atomic clusters of silver (ACS), the colloidal solution of nanostructured silver bisilicate Ag6Si2O7 with particles size of 1-2 nm in deionized water. In vitro studies to evaluate the effect of various ACS concentrations in human tumor cells cultures (breast cancer, colon carcinoma and prostate cancer) were conducted. The highest antitumor activity of ACS was observed in dilutions from 2.7 mg/l to 5.1 mg/l, resulting in the death of tumor cells in all studied cell cultures. In vivo experiments on transplanted Ehrlich carcinoma model in mice consuming 0.75 mg/kg ACS with drinking water revealed significant inhibition of tumor growth since the 14th day of experiment (maximally by 52% on the 28th day, p < 0.05) in comparison with control. Subcutaneous injections of 2.5 mg/kg ACS inhibited Ehrlich's tumor growth on the 7th and 10th days of the experiment (p < 0.05) as compared to control.

scholarly journals A generalized Gompertz growth model with applications and related birth-death processes

2020 ◽  
Author(s):  
Majid Asadi ◽  
Antonio Di Crescenzo ◽  
Farkhondeh A. Sajadi ◽  
Serena Spina
Keyword(s):  
Growth Model ◽  
Growth Curve ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Death Process ◽  
Birth Process ◽  
Failure Data ◽  
First Case ◽  
Gompertz Growth Model ◽  
Birth Death

AbstractIn this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $$d_2$$ d 2 -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.

scholarly journals Effects of Steady Low-Intensity Exercise on High-Fat Diet Stimulated Breast Cancer Progression Via the Alteration of Macrophage Polarization

2020 ◽  
Vol 19 ◽  
pp. 153473542094967
Author(s):  
Min Kyoon Kim ◽  
Yesl Kim ◽  
SeungHwa Park ◽  
Eunju Kim ◽  
Yerin Kim ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Tumor Growth ◽  
High Fat Diet ◽  
Tumor Volume ◽  
Macrophage Polarization ◽  
M2 Macrophage ◽  
High Fat ◽  
Low Intensity ◽  
M2 Macrophage Polarization ◽  
Low Intensity Exercise

Physical inactivity and high-fat diet, especially high saturated fat containing diet are established risk factors for breast cancer that are amenable to intervention. High-fat diet has been shown to induce tumor growth and metastasis by alteration of inflammation but steady exercise has anti-tumorigenic effects. However, the mechanisms underlying the effects of physical activity on high-fat diet stimulated breast cancer initiation and progression are currently unclear. In this study, we examined how the intensity of physical activity influences high fat diet-stimulated breast cancer latency and progression outcomes, and the possible mechanisms behind these effects. Five-week-old female Balb/c mice were fed either a control diet or a high-fat diet for 8 weeks, and then 4T1 mouse mammary tumor cells were inoculated into the mammary fat pads. Exercise training occurred before tumor cell injection, and tumor latency and tumor volume were measured. Mice with a high-fat diet and low-intensity exercise (HFLE) had a longer tumor latency period, slower tumor growth, and smaller tumor volume in the final tumor assessment compared with the control, high-fat diet control (HFDC), and high-fat diet with moderate-intensity exercise (HFME) groups. Steady low- and moderate-intensity exercise had no effect on cell proliferation but induced apoptosis by activating caspase-3 through the alteration of Bcl-2, Bcl-xL, and Bax expression. Furthermore, steady exercise reduced M2 macrophage polarization in breast tumor tissue, which has been linked to tumor growth. The myokine, myostatin, reduced M2 macrophage polarization through the inhibition of the JAK-STAT signaling pathway. These results suggest that steady low-intensity exercise could delay breast cancer initiation and growth and reduce tumor volume through the induction of tumor cell apoptosis and the suppression of M2 macrophage polarization.

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