A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Most of the cancer growth models have described the exponential growth patterns at the very initial stage with low cell population density. Eventually, decreasing the tumor growth rate at higher cell population densities because of deficiency in resources such as space and nutrients. However, recent studies at clinical and preclinical investigations of cancer initiation or reappaearance showed a population dynamics evincing that the growth rate increases as cell number increases. Hence, showing behaviour analogous to cooperative mechanism in the ecosystem and ecological effect called Allee effect. Based on these observations with two arguments i.e. change in initial population and growth rate. In this paper, the novel mathematical model of tumor growth kinetics with Allee effect under fuzzy environment is proposed. In this model the Generalized Hukuhara derivative approach is utilized to solve the fuzzy differential equations. Moreover, it is showen that the change in initial value and growth rate affects the cell density with the Allee effect under the fuzzy environment. Finally the superiority of model has been showen with the help of numerical simulation.

Hyperprogression after Immunotherapy: Nivolumab. Analysis of Imaging Findings Associated with Hyperprogression and Tumor Growth Kinetics

Introduction The increased use of new checkpoint inhibitors in cancer therapy has led to the discovery of new unconventional responses, like pseudoprogression and hyperprogression disease (HPD). The study documents imaging findings of HPD and analyzes the growth kinetics in advanced metastatic cancers patients treated with immunotherapy. Methods We retrospectively reviewed patients treated with anti-PD-1 (anti-progressive disease-1) antibody therapy (nivolumab) between January 2017 and December 2017 at our institute. The patients who exhibited early and rapid progression rates after initiation of immunotherapy were further analyzed for tumor growth kinetics (TGKs) and imaging findings. All prebaseline, baseline, and post nivolumab imaging were retrospectively reviewed to assess the TGKs, time to treatment failure (TTF), and rate of progression according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. Results Four patients with HPD had peculiar imaging appearance of unilateral circumferential nodular pleural thickening along with conglomerate pleural masses and effusions. Both primary and secondary sites progressed along with the appearance of new lesions in all these patients. The mean progression-free survival (PFS) was 32 days using Kaplan Meier analysis. Conclusion The unique and recurring imaging pattern of disease progression in patients with HPD as reported in our case series in addition to TGK ratio, and TTF may prove to be of additional help in early identification of this unique and ghastly outcome.

Correspondence between formulations of Avrami and Gompertz equations for untreated tumor growth kinetics

The classical and modified equations of Kolmogorov-Johnson-Mehl-Avrami are compared with the equations of conventional Gompertz andMontijano-Bergues-Bory-Gompertz, in the frame of growth kinetics of tumors. For this, different analytical and numerical criteria are usedto demonstrate the similarity between them, in particular the distance of Hausdorff. The results show that these equations are similar fromthe mathematical point of view and the parameters of the Gompertz equation are explicitly related to those of the Avrami equation. It isconcluded that Modified Kolmogorov-Johnson-Mehl-Avrami and Montijano-Bergues-Bory-Gompertz equations can be used to describe thegrowth kinetics of unperturbed tumors.

NIMG-64. IMPACT OF TUMOR LOCATION ON IMAGE-DERIVED VOLUME, PROLIFERATION RATE AND GROWTH VELOCITY IN GLIOBLASTOMA PATIENTS

INTRODUCTION Glioblastoma (GBM) is the most common malignant primary brain tumor in adults with a median overall survival (OS) of 15months. Despite advancements in treatments, prognosis is dismal and the prognostic significance of tumor location is not entirely understood. METHODOLOGY: In our study, we investigated sex-specific volumetric, tumor growth kinetics, and outcome differences among GBMs in various brain locations. Primary GBM patients with pretreatment magnetic resonance imaging (MRI) data (N=289, 173 males, 116 females) were selected from our brain tumor repository. Tumor abnormality was segmented on T1-weighted post-gadolinium contrast agent (T1Gd) MRIs. We utilized the Harvard-Oxford brain atlases to determine the location of GBMs. RESULTS Overall, our study found smaller tumors in the left hemisphere. This may be expected as left-hemispheric GBM symptoms could present earlier, leading to earlier diagnosis and treatment. However, when the cohort was split by sex, we found this observation significant for females only in the parietal lobe (p < 0.0001). Further, female GBMs demonstrated smaller necrotic volume in the left hemisphere (p = 0.030). Sex-specific differences in incidence were noted in the temporal and occipital lobes (2M:1F). Comparing tumor growth kinetics in different brain locations and hemispheres, females had significantly lower tumor proliferation rates in the left hemisphere (p = 0.009) and lower tumor proliferation rates in the left frontal lobe (p = 0.031). Controlling for treatment, patients with frontal lobe tumors had significantly longer OS compared to those with GBMs in the temporal lobe (p = 0.046, 312 days). Differences in growth velocities were noted between frontal and parietal lobe with frontal GBMs having lower velocities in comparison to parietal lobe GBMs. CONCLUSION Together, our results demonstrate that tumor growth and proliferation rates may vary based on location and sex. Additional research is needed to further explore the clinical significance of tumor location.

Three-Dimensional Modeling of Avascular Tumor Growth in Both Static and Dynamic Culture Platforms

Microfluidic cell culture platforms are ideal candidates for modeling the native tumor microenvironment because they can precisely reconstruct in vivo cellular behavior. Moreover, mathematical modeling of tumor growth can pave the way toward description and prediction of growth pattern as well as improving cancer treatment. In this study, a modified mathematical model based on concentration distribution is applied to tumor growth in both conventional static culture and dynamic microfluidic cell culture systems. Apoptosis and necrosis mechanisms are considered as the main inhibitory factors in the model, while tumor growth rate and nutrient consumption rate are modified in both quiescent and proliferative zones. We show that such modification can better predict the experimental results of tumor growth reported in the literature. Using numerical simulations, the effects of the concentrations of the nutrients as well as the initial tumor radius on the tumor growth are investigated and discussed. Furthermore, tumor growth is simulated by taking into account the dynamic perfusion into the proposed model. Subsequently, tumor growth kinetics in a three-dimensional (3D) microfluidic device containing a U-shaped barrier is numerically studied. For this case, the effect of the flow rate of culture medium on tumor growth is investigated as well. Finally, to evaluate the impact of the trap geometry on the tumor growth, a comparison is made between the tumor growth kinetics in two frequently used traps in microfluidic cell culture systems, i.e., the U-shaped barrier and microwell structures. The proposed model can provide insight into better predicting the growth and development of avascular tumor in both static and dynamic cell culture platforms.

Hyperprogressive disease (HPD) during nivolumab (Nivo) or irinotecan (IRI) as salvage line in patients with metastatic gastric cancer (MGC).

126 Background: Nivo was approved in heavily treated MGC patients in September 2017 in Japan. HPD have been reported in patients with various tumor types treated with anti-PD-1/PD-L1 antibody therapy, but no data was existed in gastric cancer. Methods: We retrospectively compared tumor growth kinetics (TGK) on Nivo or IRI as salvage line and TGK on last treatment in patients with MGC in our hospital. The TGK ratio (TGKR, ratio of the slope of tumor growth before treatment and the slope of tumor growth on treatment) was calculated. HPD was defined as a TGKR ≥ 2. Results: 51 patients have been treated Nivo (n = 31) or IRI (n = 20) as salvage line before Aug 2018 in our hospital. The median age was 67 years (range 37-81) in Nivo and 68 years (range 46-80) in IRI.; 20 males and 11 females in Nivo and 16 males and 4 females in IRI; PS 0-1/2 score 19/12 in Nivo and 19/1 in IRI. Thirty-five patients (Nivo : IRI = 16:19) had target lesions according to RECIST 1.1 and performed CT pre, baseline and during treatment. HPD were observed in seven patients (44%) with Nivo. On the contrary, only one patient (5%) experienced HPD with IRI. Median PFS and OS (HPD vs. non-HPD) were 2.1 versus 3.5 months (HR: 0.29 (0.083-0.98), p = 0.046) and 5.3 versus 6.6 months (HR: 0.44 (0.078-2.5), p = 0.35) with Nivo. The rate of grade3-4 irAEs were colitis (6%), interstitial pneumonia (6%), and mytosis (3%) with Nivo. No treatment-related death and pseudo-progression were observed. Conclusions: HPD is more common with Nivo compared with IRI in patients with MGC as salvage line and associated with poor PFS in patients treated with Nivo. Further analysis will be warranted.