The growth law of primary breast cancer as inferred from mammography screening trials data

The prognostic potential of mammographic growth rate of invasive breast cancer in the Nijmegen breast cancer screening cohort

OBJECTIVES

Insight into the aggressiveness of potential breast cancers found in screening may optimize recall decisions. Specific growth rate (SGR), measured on mammograms, may provide valuable prognostic information. This study addresses the association of SGR with prognostic factors and overall survival in patients with invasive carcinoma of no special type (NST) from a screened population.

METHODS

In this historic cohort study, 293 women with NST were identified from all participants in the Nijmegen screening program (2003-2007). Information on clinicopathological factors was retrieved from patient files and follow-up on vital status through municipalities. On consecutive mammograms, tumor volumes were estimated. After comparing five growth functions, SGR was calculated using the best-fitting function. Regression and multivariable survival analyses described associations between SGR and prognostic factors as well as overall survival.

RESULTS

Each one standard deviation increase in SGR was associated with an increase in the Nottingham prognostic index by 0.34 [95% confidence interval (CI): 0.21-0.46]. Each one standard deviation increase in SGR increased the odds of a tumor with an unfavorable subtype (based on histologic grade and hormone receptors; odds ratio 2.14 [95% CI: 1.45-3.15]) and increased the odds of diagnosis as an interval cancer (versus screen-detected; odds ratio 1.57 [95% CI: 1.20-2.06]). After a median of 12.4 years of follow-up, 78 deaths occurred. SGR was not associated with overall survival (hazard ratio 1.12 [95% CI: 0.87-1.43]).

CONCLUSIONS

SGR may indicate prognostically relevant differences in tumor aggressiveness if serial mammograms are available. A potential association with cause-specific survival could not be determined and is of interest for future research.

Tumor Doubling Time and Screening Interval

The goal of screening is to detect breast cancers when still curable to decrease breast cancer-specific mortality. Breast cancer screening in the United States is routinely performed with digital mammography and digital breast tomosynthesis. This article reviews breast cancer doubling time by tumor subtype and examines the impact of doubling time on breast cancer screening intervals. By the article's end, the reader will be better equipped to have informed discussions with patients and medical professionals regarding the benefits and disadvantages of the currently recommended screening mammography intervals.

Impact of a Categorical AI System for Digital Breast Tomosynthesis on Breast Cancer Interpretation by Both General Radiologists and Breast Imaging Specialists

Purpose To evaluate performance improvements of general radiologists and breast imaging specialists when interpreting a set of diverse digital breast tomosynthesis (DBT) examinations with the aid of a custom-built categorical artificial intelligence (AI) system. Materials and Methods A fully balanced multireader, multicase reader study was conducted to compare the performance of 18 radiologists (nine general radiologists and nine breast imaging specialists) reading 240 retrospectively collected screening DBT mammograms (mean patient age, 59.8 years ± 11.3 [SD]; 100% women), acquired between August 2016 and March 2019, with and without the aid of a custom-built categorical AI system. The area under the receiver operating characteristic curve (AUC), sensitivity, and specificity across general radiologists and breast imaging specialists reading with versus without AI were assessed. Reader performance was also analyzed as a function of breast cancer characteristics and patient subgroups. Results Every radiologist demonstrated improved interpretation performance when reading with versus without AI, with an average AUC of 0.93 versus 0.87, demonstrating a difference in AUC of 0.06 (95% CI: 0.04, 0.08; P < .001). Improvement in AUC was observed for both general radiologists (difference of 0.08; P < .001) and breast imaging specialists (difference of 0.04; P < .001) and across all cancer characteristics (lesion type, lesion size, and pathology) and patient subgroups (race and ethnicity, age, and breast density) examined. Conclusion A categorical AI system helped improve overall radiologist interpretation performance of DBT screening mammograms for both general radiologists and breast imaging specialists and across various patient subgroups and breast cancer characteristics. Keywords: Computer-aided Diagnosis, Screening Mammography, Digital Breast Tomosynthesis, Breast Cancer, Screening, Convolutional Neural Network (CNN), Artificial Intelligence Supplemental material is available for this article. © RSNA, 2024.

Modeling tumor growth using fractal calculus: Insights into tumor dynamics

Important concepts like fractal calculus and fractal analysis, the sum of squared residuals, and Aikaike's information criterion must be thoroughly understood in order to correctly fit cancer-related data using the proposed models. The fractal growth models employed in this work are classified in three main categories: Sigmoidal growth models (Logistic, Gompertz, and Richards models), Power Law growth model, and Exponential growth models (Exponential and Exponential-Lineal models)". We fitted the data, computed the sum of squared residuals, and determined Aikaike's information criteria using Matlab and the web tool WebPlotDigitizer. In addition, the research investigates "double-size cancer" in the fractal temporal dimension with respect to various mathematical models.

Potential Mechanisms of miR-143/Krupple Like Factor 5 Axis in Impeding the Proliferation of Michigan Cancer Foundation-7 Breast Cancer Cell Line

Breast cancer is one of the most prevailing cancers in females, while the cancerous heterogeneity hinders its early diagnosis and subsequent therapy. miR-143-3p is a critical mediator in malignancy development and tumorigenesis as a tumor suppressor. Its role in various tumor entities has been investigated, such as colon cancer and breast cancer. Using MCF-7 breast cancer cell model, we planned to explore the underlying mechanisms of miR-143/KLF-5 axis in retarding breast cancer cells growth. Bioinformatics analysis searched the target KLF5 of miR-143, and the miR-143-targeted mimic and inhibitor were employed to detect the changes of KLF5. After transfection of mimic miR-143, the CCK-8 reagent assessed cell proliferation. Based on optimal stimulation time, miR-143 stimulation model was established, followed by determining expression of KLF5, EGFR and PCNA via western blot and qPCR. Eventually, siRNA-KLF5 was applied to silencing KLF5 level to evaluate its role in MCF-7 cells. The transcription and translation levels of KLF5 were diminished in miR-143-mimic transfected MCF-7 cells, while enhanced in miR-143-inhibitor transfected MCF-7 cells. When MCF-7 cells were transfected with miR-143-mimic at different time points, 48 hours was found to be the optimal transfection time, with reduced transcription and translation levels of KLF5, EGFR and PCNA. The transcription and translation levels of PNCA and EGFR were declined after silencing KLF5 by siRNA. miR-143/KLF5 axis could retard the proliferation of MCF-7 breast cancer cells.

Robust breast cancer detection in mammography and digital breast tomosynthesis using an annotation-efficient deep learning approach

Breast cancer remains a global challenge, causing over 600,000 deaths in 2018 (ref. ¹). To achieve earlier cancer detection, health organizations worldwide recommend screening mammography, which is estimated to decrease breast cancer mortality by 20-40% (refs. ^2,3). Despite the clear value of screening mammography, significant false positive and false negative rates along with non-uniformities in expert reader availability leave opportunities for improving quality and access^4,5. To address these limitations, there has been much recent interest in applying deep learning to mammography^6-18, and these efforts have highlighted two key difficulties: obtaining large amounts of annotated training data and ensuring generalization across populations, acquisition equipment and modalities. Here we present an annotation-efficient deep learning approach that (1) achieves state-of-the-art performance in mammogram classification, (2) successfully extends to digital breast tomosynthesis (DBT; '3D mammography'), (3) detects cancers in clinically negative prior mammograms of patients with cancer, (4) generalizes well to a population with low screening rates and (5) outperforms five out of five full-time breast-imaging specialists with an average increase in sensitivity of 14%. By creating new 'maximum suspicion projection' (MSP) images from DBT data, our progressively trained, multiple-instance learning approach effectively trains on DBT exams using only breast-level labels while maintaining localization-based interpretability. Altogether, our results demonstrate promise towards software that can improve the accuracy of and access to screening mammography worldwide.

Unification of aggregate growth models by emergence from cellular and intracellular mechanisms

Multicellular aggregate growth is regulated by nutrient availability and removal of metabolites, but the specifics of growth dynamics are dependent on cell type and environment. Classical models of growth are based on differential equations. While in some cases these classical models match experimental observations, they can only predict growth of a limited number of cell types and so can only be selectively applied. Currently, no classical model provides a general mathematical representation of growth for any cell type and environment. This discrepancy limits their range of applications, which a general modelling framework can enhance. In this work, a hybrid cellular Potts model is used to explain the discrepancy between classical models as emergent behaviours from the same mathematical system. Intracellular processes are described using probability distributions of local chemical conditions for proliferation and death and simulated. By fitting simulation results to a generalization of the classical models, their emergence is demonstrated. Parameter variations elucidate how aggregate growth may behave like one classical growth model or another. Three classical growth model fits were tested, and emergence of the Gompertz equation was demonstrated. Effects of shape changes are demonstrated, which are significant for final aggregate size and growth rate, and occur stochastically.

The initial engraftment of tumor cells is critical for the future growth pattern: a mathematical study based on simulations and animal experiments

Background

Xenograft mouse tumor models are used to study mechanisms of tumor growth and metastasis formation and to investigate the efficacy of different therapeutic interventions. After injection the engrafted cells form a local tumor nodule. Following an initial lag period of several days, the size of the tumor is measured periodically throughout the experiment using calipers. This method of determining tumor size is error prone because the measurement is two-dimensional (calipers do not measure tumor depth). Primary tumor growth can be described mathematically by suitable growth functions, the choice of which is not always obvious. Growth parameters provide information on tumor growth and are determined by applying nonlinear curve fitting.

Methods

We used self-generated synthetic data including random measurement errors to research the accuracy of parameter estimation based on caliper measured tumor data. Fit metrics were investigated to identify the most appropriate growth function for a given synthetic dataset. We studied the effects of measuring tumor size at different frequencies on the accuracy and precision of the estimated parameters. For curve fitting with fixed initial tumor volume, we varied this fixed initial volume during the fitting process to investigate the effect on the resulting estimated parameters. We determined the number of surviving engrafted tumor cells after injection using ex vivo bioluminescence imaging, to demonstrate the effect on experiments of incorrect assumptions about the initial tumor volume.

Results

To select a suitable growth function, measurement data from at least 15 animals should be considered. Tumor volume should be measured at least every three days to estimate accurate growth parameters. Daily measurement of the tumor volume is the most accurate way to improve long-term predictability of tumor growth. The initial tumor volume needs to have a fixed value in order to achieve meaningful results. An incorrect value for the initial tumor volume leads to large deviations in the resulting growth parameters.

Conclusions

The actual number of cancer cells engrafting directly after subcutaneous injection is critical for future tumor growth and distinctly influences the parameters for tumor growth determined by curve fitting.

Stochastic Evolution of Pancreatic Cancer Metastases During Logistic Clonal Expansion

Despite recent progress in diagnostic and multimodal treatment approaches, most cancer deaths are still caused by metastatic spread and the subsequent growth of tumor cells in sites distant from the primary organ. So far, few quantitative studies are available that allow for the estimation of metastatic parameters and the evaluation of alternative treatment strategies. Most computational studies have focused on situations in which the tumor cell population expands exponentially over time; however, tumors may eventually be subject to resource and space limitations so that their growth patterns deviate from exponential growth to adhere to density-dependent growth models. In this study, we developed a stochastic evolutionary model of cancer progression that considers alterations in metastasis-related genes and intercellular growth competition leading to density effects described by logistic growth. Using this stochastic model, we derived analytical approximations for the time between the initiation of tumorigenesis and diagnosis, the expected number of metastatic sites, the total number of metastatic cells, the size of the primary tumor, and survival. Furthermore, we investigated the effects of drug administration and surgical resection on these quantities and predicted outcomes for different treatment regimens. Parameter values used in the analysis were estimated from data obtained from a pancreatic cancer rapid autopsy program. Our theoretical approach allows for flexible modeling of metastatic progression dynamics.

A Multiscale Agent-Based Model of Ductal Carcinoma In Situ

OBJECTIVE

we present a multiscale agent-based model of Ductal Carcinoma in Situ (DCIS) in order to gain a detailed understanding of the cell-scale population dynamics, phenotypic distributions, and the associated interplay of important molecular signaling pathways that are involved in DCIS ductal invasion into the duct cavity (a process we refer to as duct advance rate here).

METHODS

DCIS is modeled mathematically through a hybridized discrete cell-scale model and a continuum molecular scale model, which are explicitly linked through a bidirectional feedback mechanism.

RESULTS

we find that duct advance rates occur in two distinct phases, characterized by an early exponential population expansion, followed by a long-term steady linear phase of population expansion, a result that is consistent with other modeling work. We further found that the rates were influenced most strongly by endocrine and paracrine signaling intensity, as well as by the effects of cell density induced quiescence within the DCIS population.

CONCLUSION

our model analysis identified a complex interplay between phenotypic diversity that may provide a tumor adaptation mechanism to overcome proliferation limiting conditions, allowing for dynamic shifts in phenotypic populations in response to variation in molecular signaling intensity. Further, sensitivity analysis determined DCIS axial advance rates and calcification rates were most sensitive to cell cycle time variation.

SIGNIFICANCE

this model may serve as a useful tool to study the cell-scale dynamics involved in DCIS initiation and intraductal invasion, and may provide insights into promising areas of future experimental research.

Brain Metastases: Insights from Statistical Modeling of Size Distribution

BACKGROUND AND PURPOSE

Brain metastases are a common finding on brain MRI. However, the factors that dictate their size and distribution are incompletely understood. Our aim was to discover a statistical model that can account for the size distribution of parenchymal metastases in the brain as measured on contrast-enhanced MR imaging.

MATERIALS AND METHODS

Tumor volumes were calculated on the basis of measured tumor diameters from contrast-enhanced T1-weighted spoiled gradient-echo images in 68 patients with untreated parenchymal metastatic disease. Tumor volumes were then placed in rank-order distributions and compared with 11 different statistical curve types. The resultant R ² values to assess goodness of fit were calculated. The top 2 distributions were then compared using the likelihood ratio test, with resultant R values demonstrating the relative likelihood of these distributions accounting for the observed data.

RESULTS

Thirty-nine of 68 cases best fit a power distribution (mean R ² = 0.938 ± 0.050), 20 cases best fit an exponential distribution (mean R ² = 0.957 ± 0.050), and the remaining cases were scattered among the remaining distributions. Likelihood ratio analysis revealed that 66 of 68 cases had a positive mean R value (1.596 ± 1.316), skewing toward a power law distribution.

CONCLUSIONS

The size distributions of untreated brain metastases favor a power law distribution. This finding suggests that metastases do not exist in isolation, but rather as part of a complex system. Furthermore, these results suggest that there may be a relatively small number of underlying variables that substantially influence the behavior of these systems. The identification of these variables could have a profound effect on our understanding of these lesions and our ability to treat them.

Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors

Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported population-level correlation between the Gompertz parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous population parameter estimation, we propose a reduced Gompertz function consisting of a single individual parameter (and one population parameter). Leveraging the population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.

Personal response to immune checkpoint inhibitors of patients with advanced melanoma explained by a computational model of cellular immunity, tumor growth, and drug

Immune checkpoint inhibitors, such as pembrolizumab, are transforming clinical oncology. Yet, insufficient overall response rate, and accelerated tumor growth rate in some patients, highlight the need for identifying potential responders. To construct a computational model, identifying response predictors, and enabling immunotherapy personalization. The combined dynamics of cellular immunity, pembrolizumab, and the melanoma cancer were modeled by a set of ordinary differential equations. The model relies on a scheme of T memory stem cells, progressively differentiating into effector CD8⁺ T cells, and additionally includes T cell exhaustion, reinvigoration and senescence. Clinical data of a pembrolizumab-treated patient with advanced melanoma (Patient O’) were used for model calibration and simulations. Virtual patient populations, varying in one parameter or more, were generated for retrieving clinical studies. Simulations captured the major features of Patient O’s disease, displaying a good fit to her clinical data. A temporary increase in tumor burden, as implied by the clinical data, was obtained only when assuming aberrant self-renewal rates. Variation in effector T cell cytotoxicity was sufficient for simulating dynamics that vary from rapid progression to complete cure, while variation in tumor immunogenicity has a delayed and limited effect on response. Simulations of a-specific clinical trial were in good agreement with the clinical results, demonstrating positive correlations between response to pembrolizumab and the ratio of reinvigoration to baseline tumor load. These results were obtained by assuming inter-patient variation in the toxicity of effector CD8+ T cells, and in their intrinsic division rate, as well as by assuming that the intrinsic division rate of cancer cells is correlated with the baseline tumor burden. In conclusion, hyperprogression can result from lower patient-specific effector cytotoxicity, a temporary increase in tumor load is unlikely to result from real tumor growth, and the ratio of reinvigoration to tumor load can predict personal response to pembrolizumab. Upon further validation, the model can serve for immunotherapy personalization.

Investigation of solid tumor progression with account of proliferation/migration dichotomy via Darwinian mathematical model

A new continuous spatially-distributed model of solid tumor growth and progression is presented. The model explicitly accounts for mutations/epimutations of tumor cells which take place upon their division. The tumor grows in normal tissue and its progression is driven only by competition between populations of malignant cells for limited nutrient supply. Two reasons for the motion of tumor cells in space are taken into consideration, i.e., their intrinsic motility and convective fluxes, which arise due to proliferation of tumor cells. The model is applied to investigation of solid tumor progression under phenotypic alterations that inversely affect cell proliferation rate and cell motility by increasing the value of one of the parameters at the expense of another.It is demonstrated that the crucial feature that gives evolutionary advantage to a cell population is the speed of its intergrowth into surrounding normal tissue. Of note, increase in tumor intergrowth speed in not always associated with increase in motility of tumor cells. Depending on the parameters of functions, that describe phenotypic alterations, tumor cellular composition may evolve towards: (1) maximization of cell proliferation rate, (2) maximization of cell motility, (3) non-extremum values of cell proliferation rate and motility. Scenarios are found, where after initial tendency for maximization of cell proliferation rate, the direction of tumor progression sharply switches to maximization of cell motility, which is accompanied by decrease in total speed of tumor growth.

Machine learning-based prediction of breast cancer growth rate in vivo

Background

Determining the rate of breast cancer (BC) growth in vivo, which can predict prognosis, has remained elusive despite its relevance for treatment, screening recommendations and medicolegal practice. We developed a model that predicts the rate of in vivo tumour growth using a unique study cohort of BC patients who had two serial mammograms wherein the tumour, visible in the diagnostic mammogram, was missed in the first screen.

Methods

A serial mammography-derived in vivo growth rate (SM-INVIGOR) index was developed using tumour volumes from two serial mammograms and time interval between measurements. We then developed a machine learning-based surrogate model called Surr-INVIGOR using routinely assessed biomarkers to predict in vivo rate of tumour growth and extend the utility of this approach to a larger patient population. Surr-INVIGOR was validated using an independent cohort.

Results

SM-INVIGOR stratified discovery cohort patients into fast-growing versus slow-growing tumour subgroups, wherein patients with fast-growing tumours experienced poorer BC-specific survival. Our clinically relevant Surr-INVIGOR stratified tumours in the discovery cohort and was concordant with SM-INVIGOR. In the validation cohort, Surr-INVIGOR uncovered significant survival differences between patients with fast-growing and slow-growing tumours.

Conclusion

Our Surr-INVIGOR model predicts in vivo BC growth rate during the pre-diagnostic stage and offers several useful applications.

Growth dynamics in naturally progressing chronic lymphocytic leukaemia

How the genomic features of a patient's cancer relate to individual disease kinetics remains poorly understood. Here we used the indolent growth dynamics of chronic lymphocytic leukaemia (CLL) to analyse the growth rates and corresponding genomic patterns of leukaemia cells from 107 patients with CLL, spanning decades-long disease courses. We found that CLL commonly demonstrates not only exponential expansion but also logistic growth, which is sigmoidal and reaches a certain steady-state level. Each growth pattern was associated with marked differences in genetic composition, the pace of disease progression and the extent of clonal evolution. In a subset of patients, whose serial samples underwent next-generation sequencing, we found that dynamic changes in the disease course of CLL were shaped by the genetic events that were already present in the early slow-growing stages. Finally, by analysing the growth rates of subclones compared with their parental clones, we quantified the growth advantage conferred by putative CLL drivers in vivo.

Cellular interactions constrain tumor growth

A tumor is made up of a heterogeneous collection of cell types, all competing on a fitness landscape mediated by microenvironmental conditions that dictate their interactions. Despite the fact that much is known about cell signaling, cellular cooperation, and the functional constraints that affect cellular behavior, the specifics of how these constraints (and the range over which they act) affect the macroscopic tumor growth laws that govern total volume, mass, and carrying capacity remain poorly understood. We develop a statistical mechanics approach that focuses on the total number of possible states each cell can occupy and show how different assumptions on correlations of these states give rise to the many different macroscopic tumor growth laws used in the literature. Although it is widely understood that molecular and cellular heterogeneity within a tumor is a driver of growth, here we emphasize that focusing on the functional coupling of states at the cellular level is what determines macroscopic growth characteristics.

A software tool for the quantification of metastatic colony growth dynamics and size distributions in vitro and in vivo

The majority of cancer-related deaths are due to metastasis, hence improved methods to biologically and computationally model metastasis are required. Computational models rely on robust data that is machine-readable. The current methods used to model metastasis in mice involve generating primary tumors by injecting human cells into immune-compromised mice, or by examining genetically engineered mice that are pre-disposed to tumor development and that eventually metastasize. The degree of metastasis can be measured using flow cytometry, bioluminescence imaging, quantitative PCR, and/or by manually counting individual lesions from metastatic tissue sections. The aforementioned methods are time-consuming and do not provide information on size distribution or spatial localization of individual metastatic lesions. In this work, we describe and provide a MATLAB script for an image-processing based method designed to obtain quantitative data from tissue sections comprised of multiple subpopulations of disseminated cells localized at metastatic sites in vivo. We further show that this method can be easily adapted for high throughput imaging of live or fixed cells in vitro under a multitude of conditions in order to assess clonal fitness and evolution. The inherent variation in mouse studies, increasing complexity in experimental design which incorporate fate-mapping of individual cells, result in the need for a large cohort of mice to generate a robust dataset. High-throughput imaging techniques such as the one that we describe will enhance the data that can be used as input for the development of computational models aimed at modeling the metastatic process.

Does breast cancer growth rate really depend on tumor subtype? Measurement of tumor doubling time using serial ultrasonography between diagnosis and surgery

BACKGROUND

Breast cancer growth is generally expected to differ between tumor subtypes. We aimed to evaluate tumor doubling time (DT) using ultrasonography and verify whether each tumor subtype has a unique DT.

METHODS

This retrospective study included 265 patients with invasive breast cancer who received serial ultrasonography between diagnosis and surgery. Tumor diameters were measured in three directions and DTs were calculated according to an exponential growth model using the volume change during serial ultrasonography. We investigated the relationships between DT, tumor subtype, and histopathological factors.

RESULTS

Volumes did not change in 95 (36%) of 265 tumors and increased in 170 (64%) tumors during serial ultrasonography (mean interval, 56.9 days). The mean volume increases of all tumors and volume-increased tumors were 22.1% and 34.5%, respectively. Triple-negative tumors had greater volume increases (40% vs. 20%, p = 0.001) and shorter DT (124 vs. 185 days, p = 0.027) than estrogen receptor (ER)+/human epidermal growth factor receptor 2 (HER2)- tumors. Volume-increased tumors had higher Ki-67 indices than those of volume-stable tumors in ER+/HER2- (p = 0.002) and ER+/HER2+ tumors (p = 0.011) and higher histological grades in all tumors except triple-negative tumors (p < 0.001). Triple-negative tumors with DTs < 90 days (short-DT) showed higher Ki-67 indices than those with DTs > 90 days (long-DT) (p = 0.008). In ER+/HER2- tumors, histological grades were higher for short-DT than for long-DT tumors (p = 0.022).

CONCLUSION

Differences in tumor DT depending on breast cancer subtype, Ki-67 index, and histological grade were confirmed using serial ultrasonography even during preoperative short interval.

Evolution of model specific relative growth rate: Its genesis and performance over Fisher's growth rates

Growth curve models play an instrumental role to quantify the growth of biological processes and have immense practical applications across disciplines. In the modelling approach, the absolute growth rate and relative growth rate (RGR) are two most commonly used measures of growth rates. RGR is empirically estimated by Fisher (1921) assuming exponential growth between two consecutive time points and remains invariant under any choice of the underlying growth model. In this article, we propose a new measure of RGR, called modified RGR, which is sensitive to the choice of underlying growth law. The mathematical form of the growth equations are utilized to develop the formula for model dependent growth rates and can be easily computed for commonly used growth models. We compare the efficiency of Fisher's measure of RGR and modified RGR to infer the true growth profile. To achieve this, we develop a goodness of fit testing procedure using Gompertz model as a test bed. The relative efficiency of the two rate measures is compared by generating power curves of the goodness of fit testing procedure. The asymptotic distributions of the associated test statistics are elaborately studied under Gompertz set up. The simulation experiment shows that the proposed formula has better discriminatory power than the existing one in identifying the true profile. The claim is also verified using existing real data set on fish growth. An algorithm for the model selection mechanism is also proposed based on the modified RGR and is generalized for some commonly used other growth models. The proposed methodology may serve as a valuable tool in growth studies in different research areas.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

14C BOMB-PULSE DATING AND STABLE ISOTOPE ANALYSIS FOR GROWTH RATE AND DIETARY INFORMATION IN BREAST CANCER?

The purpose of this study was to perform an initial investigation of the possibility to determine breast cancer growth rate with (14)C bomb-pulse dating. Tissues from 11 breast cancers, diagnosed in 1983, were retrieved from a regional biobank. The estimated average age of the majority of the samples overlapped the year of collection (1983) within 3σ Thus, this first study of tumour tissue has not yet demonstrated that (14)C bomb-pulse dating can obtain information on the growth of breast cancer. However, with further refinement, involving extraction of cell types and components, there is a possibility that fundamental knowledge of tumour biology might still be gained by the bomb-pulse technique. Additionally, δ (13)C and δ (15)N analyses were performed to obtain dietary and metabolic information, and to serve as a base for improvement of the age determination.

Suppression of RAF/MEK or PI3K synergizes cytotoxicity of receptor tyrosine kinase inhibitors in glioma tumor-initiating cells

Background

The majority of glioblastomas have aberrant receptor tyrosine kinase (RTK)/RAS/phosphoinositide 3 kinase (PI3K) signaling pathways and malignant glioma cells are thought to be addicted to these signaling pathways for their survival and proliferation. However, recent studies suggest that monotherapies or inappropriate combination therapies using the molecular targeted drugs have limited efficacy possibly because of tumor heterogeneities, signaling redundancy and crosstalk in intracellular signaling network, indicating necessity of rationale and methods for efficient personalized combination treatments. Here, we evaluated the growth of colonies obtained from glioma tumor-initiating cells (GICs) derived from glioma sphere culture (GSC) in agarose and examined the effects of combination treatments on GICs using targeted drugs that affect the signaling pathways to which most glioma cells are addicted.

Methods

Human GICs were cultured in agarose and treated with inhibitors of RTKs, non-receptor kinases or transcription factors. The colony number and volume were analyzed using a colony counter, and Chou-Talalay combination indices were evaluated. Autophagy and apoptosis were also analyzed. Phosphorylation of proteins was evaluated by reverse phase protein array and immunoblotting.

Results

Increases of colony number and volume in agarose correlated with the Gompertz function. GICs showed diverse drug sensitivity, but inhibitions of RTK and RAF/MEK or PI3K by combinations such as EGFR inhibitor and MEK inhibitor, sorafenib and U0126, erlotinib and BKM120, and EGFR inhibitor and sorafenib showed synergy in different subtypes of GICs. Combination of erlotinib and sorafenib, synergistic in GSC11, induced apoptosis and autophagic cell death associated with suppressed Akt and ERK signaling pathways and decreased nuclear PKM2 and β-catenin in vitro, and tended to improve survival of nude mice bearing GSC11 brain tumor. Reverse phase protein array analysis of the synergistic treatment indicated involvement of not only MEK and PI3K signaling pathways but also others associated with glucose metabolism, fatty acid metabolism, gene transcription, histone methylation, iron transport, stress response, cell cycle, and apoptosis.

Conclusion

Inhibiting RTK and RAF/MEK or PI3K could induce synergistic cytotoxicity but personalization is necessary. Examining colonies in agarose initiated by GICs from each patient may be useful for drug sensitivity testing in personalized cancer therapy.

Electronic supplementary material

The online version of this article (doi:10.1186/s12967-016-0803-2) contains supplementary material, which is available to authorized users.

Robust nonparametric estimation of monotone regression functions with interval-censored observations

Nonparametric estimation of monotone regression functions is a classical problem of practical importance. Robust estimation of monotone regression functions in situations involving interval-censored data is a challenging yet unresolved problem. Herein, we propose a nonparametric estimation method based on the principle of isotonic regression. Using empirical process theory, we show that the proposed estimator is asymptotically consistent under a specific metric. We further conduct a simulation study to evaluate the performance of the estimator in finite sample situations. As an illustration, we use the proposed method to estimate the mean body weight functions in a group of adolescents after they reach pubertal growth spurt.

In Vivo Tumor Growth Rate Measured by US in Preoperative Period and Long Term Disease Outcome in Breast Cancer Patients

OBJECTIVE

The aim of our study was to evaluate the effect of tumor growth rate, calculated from tumor size measurements by US, on breast cancer patients' outcome.

PATIENTS AND METHODS

Breast cancer patients who received at least two serial breast ultrasonographies (US) in our institution during preoperative period and were surgically treated between 2002 and 2010 were reviewed. Tumor growth rate was determined by specific growth rate (SGR) using the two time point tumor sizes by US.

RESULTS

A total of 957 patients were analyzed. The median duration between initial and second US was 28 days (range, 8-140). The median initial tumor size was 1.7 cm (range, 0.4-7.0) and median second size was 1.9 cm (range, 0.3-7.2). 523 (54.6%) cases had increase in size. The median SGR(x10-2) was 0.59 (range, -11.90~31.49) and mean tumor doubling time was 14.51 days. Tumor growth rate was higher when initial tumor size was smaller. Lymphovascular invasion, axillary lymph node metastasis, and higher histologic grade were significantly associated with higher SGR. SGR was significantly associated with disease-free survival (DFS) in a univariate analysis (p = 0.04), but not in a multivariate Cox analysis (p>0.05). High SGR was significantly associated with worse DFS in a subgroup of initial tumor size >2 cm (p = 0.018), but not in those with tumor size <2 cm (p>0.05).

CONCLUSION

Our results showed that tumor growth rate measured by US in a relatively short time interval was associated with other worse prognostic factors and DFS, but it was not an independent prognostic factor in breast cancer patients.

Estimating Tumor Growth Rates In Vivo

In this paper, we develop methods for inferring tumor growth rates from the observation of tumor volumes at two time points. We fit power law, exponential, Gompertz, and Spratt’s generalized logistic model to five data sets. Though the data sets are small and there are biases due to the way the samples were ascertained, there is a clear sign of exponential growth for the breast and liver cancers, and a 2/3’s power law (surface growth) for the two neurological cancers.

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations

There has been increasing awareness in the wider biological community of the role of clonal phenotypic heterogeneity in playing key roles in phenomena such as cellular bet-hedging and decision making, as in the case of the phage-λ lysis/lysogeny and B. Subtilis competence/vegetative pathways. Here, we report on the effect of stochasticity in growth rate, cellular memory/intermittency, and its relation to phenotypic heterogeneity. We first present a linear stochastic differential model with finite auto-correlation time, where a randomly fluctuating growth rate with a negative average is shown to result in exponential growth for sufficiently large fluctuations in growth rate. We then present a non-linear stochastic self-regulation model where the loss of coherent self-regulation and an increase in noise can induce a shift from bounded to unbounded growth. An important consequence of these models is that while the average change in phenotype may not differ for various parameter sets, the variance of the resulting distributions may considerably change. This demonstrates the necessity of understanding the influence of variance and heterogeneity within seemingly identical clonal populations, while providing a mechanism for varying functional consequences of such heterogeneity. Our results highlight the importance of a paradigm shift from a deterministic to a probabilistic view of clonality in understanding selection as an optimization problem on noise-driven processes, resulting in a wide range of biological implications, from robustness to environmental stress to the development of drug resistance.

Modeling drug resistance in a conjoint normal-tumor setting

Background

In this paper, we modify our previously developed conjoint tumor-normal cell model in order to make a distinction between tumor cells that are responsive to chemotherapy and those that may show resistance.

Results

Using this newly developed core model, the evolution of three cell types: normal, tumor, and drug-resistant tumor cells, is studied through a series of numerical simulations. In addition, we illustrate critical factors that cause different dynamical patterns for normal and tumor cells. Among these factors are the co-dependency of the normal and tumor cells, the cells’ response mechanism to a single or multiple chemotherapeutic treatment, the drug administration sequence, and the treatment starting time.

Conclusion

The results provide us with a deeper understanding of the possible evolution of normal, drug-responsive, and drug-resistant tumor cells during the cancer progression, which may contribute to improving the therapeutic strategies.

Cancer stem cells: small subpopulation or evolving fraction?

This review discusses quantitative modeling studies of stem and non-stem cancer cell interactions and the fraction of cancer stem cells.

Lifespan based pharmacokinetic-pharmacodynamic model of tumor growth inhibition by anticancer therapeutics

Accurate prediction of tumor growth is critical in modeling the effects of anti-tumor agents. Popular models of tumor growth inhibition (TGI) generally offer empirical description of tumor growth. We propose a lifespan-based tumor growth inhibition (LS TGI) model that describes tumor growth in a xenograft mouse model, on the basis of cellular lifespan T. At the end of the lifespan, cells divide, and to account for tumor burden on growth, we introduce a cell division efficiency function that is negatively affected by tumor size. The LS TGI model capability to describe dynamic growth characteristics is similar to many empirical TGI models. Our model describes anti-cancer drug effect as a dose-dependent shift of proliferating tumor cells into a non-proliferating population that die after an altered lifespan T_A. Sensitivity analysis indicated that all model parameters are identifiable. The model was validated through case studies of xenograft mouse tumor growth. Data from paclitaxel mediated tumor inhibition was well described by the LS TGI model, and model parameters were estimated with high precision. A study involving a protein casein kinase 2 inhibitor, AZ968, contained tumor growth data that only exhibited linear growth kinetics. The LS TGI model accurately described the linear growth data and estimated the potency of AZ968 that was very similar to the estimate from an established TGI model. In the case study of AZD1208, a pan-Pim inhibitor, the doubling time was not estimable from the control data. By fixing the parameter to the reported in vitro value of the tumor cell doubling time, the model was still able to fit the data well and estimated the remaining parameters with high precision. We have developed a mechanistic model that describes tumor growth based on cell division and has the flexibility to describe tumor data with diverse growth kinetics.

Classical mathematical models for description and prediction of experimental tumor growth

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

Analysis of inter-patient variations in tumour growth rate

Purpose

Inter-patient variations in tumour growth rate are usually interpreted as biological heterogeneity among patients due to, e.g., genetic variability. However, these variations might be a result of non-exponential, e.g. the Gompertzian, tumour growth kinetics. The aim was to study if the natural tumour growth deceleration, i.e. non-exponential growth, is a dominant factor in such variations.

Materials and methods

The correlation between specific growth rate (SGR) and the logarithm of tumour volume, Ln(V), was calculated for tumours in patients with meningioma, hepatocellular carcinoma, pancreatic carcinoma, primary lung cancer, post-chemotherapy regrowth of non-small cell lung cancer (NSCLC), and in nude mice transplanted with human midgut carcinoid GOT1, a tumour group which is biologically more homogeneous than patient groups.

Results

The correlation between SGR and Ln(V) was statistically significant for meningioma, post-chemotherapy regrowth of NSCLC, and the mouse model, but not for any other patient groups or subgroups, based on differentiation and clinical stage.

Conclusion

This method can be used to evaluate the homogeneity of tumour growth kinetics among patients. Homogeneity of post-chemotherapy regrowth pattern of NSCLC suggests that, in contrast to untreated tumours, the remaining resistant cells or stem cells (if exist) might have similar biological characteristics among these patients.

A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis

Population modeling of tumor size dynamics has recently emerged as an important tool in pharmacometric research. A series of new mixed-effects models have been reported recently, and we present herein a synthetic view of models with published mathematical equations aimed at describing the dynamics of tumor size in cancer patients following anticancer drug treatment. This selection of models will constitute the basis for the Drug Disease Model Resources (DDMoRe) repository for models on oncology.

Simplifying the complexity of resistance heterogeneity in metastasis

The main goal of treatment regimens for metastasis is to control growth rates, not eradicate all cancer cells. Mathematical models offer methodologies that incorporate high-throughput data with dynamic effects on net growth. The ideal approach would simplify, but not over-simplify, a complex problem into meaningful and manageable estimators that predict the response of a patient to specific treatments. We explore here three fundamental approaches with different assumptions concerning resistance mechanisms in which the cells are categorized into either discrete compartments or described by a continuous range of resistance levels. We argue in favor of modeling resistance as a continuum, and demonstrate how integrating cellular growth rates, density-dependent versus exponential growth, and intratumoral heterogeneity improves predictions concerning the resistance heterogeneity of metastases.

Bridging population and tissue scale tumor dynamics: a new paradigm for understanding differences in tumor growth and metastatic disease

To provide a better understanding of the relationship between primary tumor growth rates and metastatic burden, we present a method that bridges tumor growth dynamics at the population level, extracted from the SEER database, to those at the tissue level. Specifically, with this method, we are able to relate estimates of tumor growth rates and metastatic burden derived from a population-level model to estimates of the primary tumor vascular response and the circulating tumor cell (CTC) fraction derived from a tissue-level model. Variation in the population-level model parameters produces differences in cancer-specific survival and cure fraction. Variation in the tissue-level model parameters produces different primary tumor dynamics that subsequently lead to different growth dynamics of the CTCs. Our method to bridge the population and tissue scales was applied to lung and breast cancer separately, and the results were compared. The population model suggests that lung tumors grow faster and shed a significant number of lethal metastatic cells at small sizes, whereas breast tumors grow slower and do not significantly shed lethal metastatic cells until becoming larger. Although the tissue-level model does not explicitly model the metastatic population, we are able to disengage the direct dependency of the metastatic burden on primary tumor growth by introducing the CTC population as an intermediary and assuming dependency. We calibrate the tissue-level model to produce results consistent with the population model while also revealing a more dynamic relationship between the primary tumor and the CTCs. This leads to exponential tumor growth in lung and power law tumor growth in breast. We conclude that the vascular response of the primary tumor is a major player in the dynamics of both the primary tumor and the CTCs, and is significantly different in breast and lung cancer.

Computer simulation of the metastatic progression

A novel computer model based on a discrete event simulation procedure describes quantitatively the processes underlying the metastatic cascade. Analytical functions describe the size of the primary tumor and the metastases, while a rate function models the intravasation events of the primary tumor and metastases. Events describe the behavior of the malignant cells until the formation of new metastases. The results of the computer simulations are in quantitative agreement with clinical data determined from a patient with hepatocellular carcinoma in the liver. The model provides a more detailed view on the process than a conventional mathematical model. In particular, the implications of interventions on metastasis formation can be calculated.

Parameter non-identifiability of the Gyllenberg-Webb ODE model

An ODE model introduced by Gyllenberg and Webb (Growth Develop Aging 53:25-33, 1989) describes tumour growth in terms of the dynamics between proliferating and quiescent cell states. The passage from one state to another and vice versa is modelled by two functions r0 and ri depending on the total tumour size. As these functions do not represent any observable quantities, they have to be identified from the observations. In this paper we show that there is an infinite number of pairs (r0, ri) corresponding to the same solution of the ODE system and the functions (r0, ri) will be classified in terms of this equivalence. Surprisingly, the technique used for this classification permits a uniqueness proof of the solution of the ODE model in a non-Lipschitz case. The reasoning can be widened to a more general setting including an extension of the Gyllenberg-Webb model with a nonlinear birth rate. The relevance of this result is discussed in a preclinical application scenario.

Tumor growth dynamics: insights into evolutionary processes

Identifying the types of event that drive tumor evolution and progression is crucial for understanding cancer. We suggest that the analysis of tumor growth dynamics can provide a window into tumor biology and evolution by connecting them with the types of genetic change that have occurred. Although fundamentally important, the documentation of tumor growth kinetics is more sparse in the literature than is the molecular analysis of cells. Here, we provide a historical summary of tumor growth patterns and argue that they can be classified into five basic categories. We then illustrate how those categories can provide insights into events that drive tumor progression, by discussing a particular evolutionary model as an example and encouraging such analysis in a more general setting.

A new method to estimate parameters of the growth model for metastatic tumours

Purpose

Knowledge of natural tumour growth is valuable for understanding tumour biology, optimising screening programs, prognostication, optimal scheduling of chemotherapy, and assessing tumour spread. However, mathematical modelling in individuals is hampered by the limited data available. We aimed to develop a method to estimate parameters of the growth model and formation rate of metastases in individual patients.

Materials and methods

Data from one patient with liver metastases from a primary ileum carcinoid and one patient with lung metastases from a primary renal cell carcinoma were used to demonstrate this new method. Metastatic growth models were estimated by direct curve fitting, as well as with the new proposed method based on the relationship between tumour growth rate and tumour volume. The new model was derived from the Gompertzian growth model by eliminating the time factor (age of metastases), which made it possible to perform the calculations using data from all metastases in each patient. Finally, the formation time of each metastasis and, consecutively, the formation rate of metastases in each patient were estimated.

Results

With limited measurements in clinical studies, fitting different growth curves was insufficient to estimate true tumour growth, even if patients were followed for several years. Growth of liver metastases was well described with a general growth model for all metastases. However, the lung metastases from renal cell carcinoma were better described by heterogeneous exponential growth with various growth rates.

Conclusion

Analysis of the regression of tumour growth rate with the logarithm of tumour volume can be used to estimate parameters of the tumour growth model and metastasis formation rates, and therefore the number and size distribution of metastases in individuals.

Tumor evolution in space: the effects of competition colonization tradeoffs on tumor invasion dynamics

We apply competition colonization tradeoff models to tumor growth and invasion dynamics to explore the hypothesis that varying selection forces will result in predictable phenotypic differences in cells at the tumor invasive front compared to those in the core. Spatially, ecologically, and evolutionarily explicit partial differential equation models of tumor growth confirm that spatial invasion produces selection pressure for motile phenotypes. The effects of the invasive phenotype on normal adjacent tissue determine the patterns of growth and phenotype distribution. If tumor cells do not destroy their environment, colonizer and competitive phenotypes coexist with the former localized at the invasion front and the latter, to the tumor interior. If tumors cells do destroy their environment, then cell motility is strongly selected resulting in accelerated invasion speed with time. Our results suggest that the widely observed genetic heterogeneity within cancers may not be the stochastic effect of random mutations. Rather, it may be the consequence of predictable variations in environmental selection forces and corresponding phenotypic adaptations.

The model muddle: in search of tumor growth laws

In this article, we will trace the historical development of tumor growth laws, which in a quantitative fashion describe the increase in tumor mass/volume over time. These models are usually formulated in terms of differential equations that relate the growth rate of the tumor to its current state and range from the simple one-parameter exponential growth model to more advanced models that contain a large number of parameters. Understanding the assumptions and consequences of such models is important, as they often underpin more complex models of tumor growth. The conclusion of this brief survey is that although much improvement has occurred over the last century, more effort and new models are required if we are to understand the intricacies of tumor growth.

A review of mathematical models of cancer-immune interactions in the context of tumor dormancy

The role of the immune system in tumor dormancy is now well established. In an immune-induced dormant state, potentially lethal cancer cells persist in a state where growth is restricted, to little or no increase, by the host's immune response. To describe this state in the context of cancer progression and immune response, basic temporal (spatially homogeneous) quantitative predator-prey constructs are discussed, along with some current and proposed augmentations that incorporate potentially significant biological phenomena such as the cancer cell transition to a quiescent state or the time delay in T-cell activation. Advances in cancer-immune modeling that describe complex interactions underlying the ability of the immune system to both promote and inhibit tumor growth are emphasized. Finally, the review concludes by discussing future mathematical challenges and their biological significance.

Translational pharmacokinetic-pharmacodynamic modeling from nonclinical to clinical development: a case study of anticancer drug, crizotinib

Attrition risk related to efficacy is still a major reason why new chemical entities fail in clinical trials despite recently increased understanding of translational pharmacology. Pharmacokinetic-pharmacodynamic (PKPD) analysis is key to translating in vivo drug potency from nonclinical models to patients by providing a quantitative assessment of in vivo drug potency with mechanistic insight of drug action. The pharmaceutical industry is clearly moving toward more mechanistic and quantitative PKPD modeling to have a deeper understanding of translational pharmacology. This paper summarizes an anticancer drug case study describing the translational PKPD modeling of crizotinib, an orally available, potent small molecule inhibitor of multiple tyrosine kinases including anaplastic lymphoma kinase (ALK) and mesenchymal-epithelial transition factor (MET), from nonclinical to clinical development. Overall, the PKPD relationships among crizotinib systemic exposure, ALK or MET inhibition, and tumor growth inhibition (TGI) in human tumor xenograft models were well characterized in a quantitative manner using mathematical modeling: the results suggest that 50% ALK inhibition is required for >50% TGI whereas >90% MET inhibition is required for >50% TGI. Furthermore, >75% ALK inhibition and >95% MET inhibition in patient tumors were projected by PKPD modeling during the clinically recommended dosing regimen, twice daily doses of crizotinib 250 mg (500 mg/day). These simulation results of crizotinib-mediated ALK and MET inhibition appeared consistent with the currently reported clinical responses. In summary, the present paper presents an anticancer drug example to demonstrate that quantitative PKPD modeling can be used for predictive translational pharmacology from nonclinical to clinical development.