Spatial interactions modulate tumor growth and immune infiltration.

Lenia, a cellular automata framework used in artificial life, provides a natural setting to implement mathematical models of cancer incorporating features such as morphogenesis, homeostasis, motility, reproduction, growth, stimuli response, evolvability, and adaptation. Historically, agent-based models of cancer progression have been constructed with rules that govern birth, death and migration, with attempts to map local rules to emergent global growth dynamics. In contrast, Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining an interaction kernel governing density-dependent growth dynamics. Lenia can recapitulate a range of cancer model classifications including local or global, deterministic or stochastic, non-spatial or spatial, single or multi-population, and off or on-lattice. Lenia is subsequently used to develop data-informed models of 1) single-population growth dynamics, 2) multi-population cell-cell competition models, and 3) cell migration or chemotaxis. Mathematical modeling provides important mechanistic insights. First, short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects. Next, we find that asymmetric interaction tumor-immune kernels lead to poor immune response. Finally, modeling recapitulates immune-ECM interactions where patterns of collagen formation provide immune protection, indicated by an emergent inverse relationship between disease stage and immune coverage.

To modulate or to skip: De-escalating PARP inhibitor maintenance therapy in ovarian cancer using adaptive therapy.

Toxicity and emerging drug resistance pose important challenges in poly-adenosine ribose polymerase inhibitor (PARPi) maintenance therapy of ovarian cancer. We propose that adaptive therapy, which dynamically reduces treatment based on the tumor dynamics, might alleviate both issues. Utilizing in vitro time-lapse microscopy and stepwise model selection, we calibrate and validate a differential equation mathematical model, which we leverage to test different plausible adaptive treatment schedules. Our model indicates that adjusting the dosage, rather than skipping treatments, is more effective at reducing drug use while maintaining efficacy due to a delay in cell kill and a diminishing dose-response relationship. In vivo pilot experiments confirm this conclusion. Although our focus is toxicity mitigation, reducing drug use may also delay resistance. This study enhances our understanding of PARPi treatment scheduling and illustrates the first steps in developing adaptive therapies for new treatment settings. A record of this paper's transparent peer review process is included in the supplemental information.

Tumor-immune metaphenotypes orchestrate an evolutionary bottleneck that promotes metabolic transformation.

Introduction: Metabolism plays a complex role in the evolution of cancerous tumors, including inducing a multifaceted effect on the immune system to aid immune escape. Immune escape is, by definition, a collective phenomenon by requiring the presence of two cell types interacting in close proximity: tumor and immune. The microenvironmental context of these interactions is influenced by the dynamic process of blood vessel growth and remodelling, creating heterogeneous patches of well-vascularized tumor or acidic niches. Methods: Here, we present a multiscale mathematical model that captures the phenotypic, vascular, microenvironmental, and spatial heterogeneity which shapes acid-mediated invasion and immune escape over a biologically-realistic time scale. The model explores several immune escape mechanisms such as i) acid inactivation of immune cells, ii) competition for glucose, and iii) inhibitory immune checkpoint receptor expression (PD-L1). We also explore the efficacy of anti-PD-L1 and sodium bicarbonate buffer agents for treatment. To aid in understanding immune escape as a collective cellular phenomenon, we define immune escape in the context of six collective phenotypes (termed "meta-phenotypes"): Self-Acidify, Mooch Acid, PD-L1 Attack, Mooch PD-L1, Proliferate Fast, and Starve Glucose. Results: Fomenting a stronger immune response leads to initial benefits (additional cytotoxicity), but this advantage is offset by increased cell turnover that leads to accelerated evolution and the emergence of aggressive phenotypes. This creates a bimodal therapy landscape: either the immune system should be maximized for complete cure, or kept in check to avoid rapid evolution of invasive cells. These constraints are dependent on heterogeneity in vascular context, microenvironmental acidification, and the strength of immune response. Discussion: This model helps to untangle the key constraints on evolutionary costs and benefits of three key phenotypic axes on tumor invasion and treatment: acid-resistance, glycolysis, and PD-L1 expression. The benefits of concomitant anti-PD-L1 and buffer treatments is a promising treatment strategy to limit the adverse effects of immune escape.

Second-Order Effects of Chemotherapy Pharmacodynamics and Pharmacokinetics on Tumor Regression and Cachexia.

Drug dose response curves are ubiquitous in cancer biology, but these curves are often used to measure differential response in first-order effects: the effectiveness of increasing the cumulative dose delivered. In contrast, second-order effects (the variance of drug dose) are often ignored. Knowledge of second-order effects may improve the design of chemotherapy scheduling protocols, leading to improvements in tumor response without changing the total dose delivered. By considering treatment schedules with identical cumulative dose delivered, we characterize differential treatment outcomes resulting from high variance schedules (e.g. high dose, low dose) and low variance schedules (constant dose). We extend a previous framework used to quantify second-order effects, known as antifragility theory, to investigate the role of drug pharmacokinetics. Using a simple one-compartment model, we find that high variance schedules are effective for a wide range of cumulative dose values. Next, using a mouse-parameterized two-compartment model of 5-fluorouracil, we show that schedule viability depends on initial tumor volume. Finally, we illustrate the trade-off between tumor response and lean mass preservation. Mathematical modeling indicates that high variance dose schedules provide a potential path forward in mitigating the risk of chemotherapy-associated cachexia by preserving lean mass without sacrificing tumor response.

Spatial interactions modulate tumor growth and immune infiltration.

Direct observation of immune cell trafficking patterns and tumor-immune interactions is unlikely in human tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen formation evolve as a mechanism of immune escape, but the exact nature of the interaction between immune cells and collagen is poorly understood. Spatial data quantifying the degree of collagen fiber alignment in squamous cell carcinomas indicates that late stage disease is associated with highly aligned fibers. Here, we introduce a computational modeling framework (called Lenia) to discriminate between two hypotheses: immune cell migration that moves 1) parallel or 2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-ECM interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. We also illustrate the capabilities of Lenia to model the evolution of tumor progression and immune predation. Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining a kernel cell-cell interaction function that governs tumor growth dynamics under immune predation with immune cell migration. Mathematical modeling provides important mechanistic insights into cell interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interactions drives tumor growth and infiltration.

Pilot Study of Donor-Engrafted Clonal Hematopoiesis Evolution and Clinical Outcomes in Allogeneic Hematopoietic Cell Transplantation Recipients Using a National Registry.

Improved treatment options, such as reduced-intensity conditioning (RIC), enable older patients to receive potentially curative allogeneic hematopoietic cell transplantation (HCT). This progress has led to increased use of older HLA-matched sibling donors. An unintended potential risk associated with older donors is transplantation of donor cells with clonal hematopoiesis (CH) into patients. We aimed to determine the prevalence of CH in older HLA-matched sibling donors pretransplantation and to assess the clinical impact of donor-engrafted CH on HCT outcomes. This was an observational study using donor peripheral blood samples from the Center for International Blood and Marrow Transplant Research repository, linked with corresponding recipient outcomes. To explore engraftment efficiency and evolution of CH mutations following HCT, recipient follow-up samples available through the Bone Marrow Transplant Clinical Trials Network (Protocol 1202) were included. Older donors and patients (both ≥55 years) receiving first RIC HCT for myeloid malignancies were eligible. DNA from archived donor blood samples was used for targeted deep sequencing to identify CH. The associations between donor CH status and recipient outcomes, including acute graft-versus-host disease (aGVHD), chronic GVHD (cGVHD), overall survival, relapse, nonrelapse mortality, disease-free survival, composite GVHD-free and relapse-free survival, and cGVHD-free and relapse-free survival, were analyzed. A total of 299 donors were successfully sequenced to detect CH. At a variant allele frequency (VAF) ≥2%, there were 44 CH mutations in 13.7% (41 of 299) of HLA-matched sibling donors. CH mostly involved DNMT3A (n = 27; 61.4%) and TET2 (n= 9; 20.5%). Post-HCT samples from 13 recipients were also sequenced, of whom 7 had CH+ donors. All of the donor CH mutations (n = 7/7; 100%) were detected in recipients at day 56 or day 90 post-HCT. Overall, mutation VAFs remained relatively constant up to day 90 post-HCT (median change, .005; range, -.008 to .024). Doubling time analysis of recipient day 56 and day 90 data showed that donor-engrafted CH mutations initially expand then decrease to a stable VAF; germline mutations had longer doubling times than CH mutations. The cumulative incidence of grade II-IV aGVHD at day 100 was higher in HCT recipients with CH+ donors (37.5% versus 25.1%); however, the risk for aGVHD by donor CH status did not reach statistical significance (hazard ratio, 1.35; 95% confidence interval, .61 to 3.01; P = .47). There were no statistically significant differences in the cumulative incidence of cGVHD or any secondary outcomes by donor CH status. In subset analysis, the incidence of cGVHD was lower in recipients of grafts from DNMT3A CH+ donors versus donors without DNMT3A CH (34.4% versus 57%; P = .035). Donor cell leukemia was not reported in any donor-recipient pairs. CH in older HLA-matched sibling donors is relatively common and successfully engrafts and persists in recipients. In a homogenous population (myeloid malignancies, older donors and recipients, RICr, non-cyclophosphamide-containing GVHD prophylaxis), we did not detect a difference in cGVHD risk or other secondary outcomes by donor CH status. Subgroup analyses suggest potential differential effects by clinical characteristics and CH mutations. Larger prospective studies are needed to robustly determine which subsets of patients and CH mutations elicit meaningful impacts on clinical outcomes.

Intermetastatic and Intrametastatic Heterogeneity Shapes Adaptive Therapy Cycling Dynamics.

Adaptive therapies that alternate between drug applications and drug-free vacations can exploit competition between sensitive and resistant cells to maximize the time to progression. However, optimal dosing schedules depend on the properties of metastases, which are often not directly measurable in clinical practice. Here, we proposed a framework for estimating features of metastases through tumor response dynamics during the first adaptive therapy treatment cycle. Longitudinal prostate-specific antigen (PSA) levels in 16 patients with metastatic castration-resistant prostate cancer undergoing adaptive androgen deprivation treatment were analyzed to investigate relationships between cycle dynamics and clinical variables such as Gleason score, the change in the number of metastases over a cycle, and the total number of cycles over the course of treatment. The first cycle of adaptive therapy, which consists of a response period (applying therapy until 50% PSA reduction), and a regrowth period (removing treatment until reaching initial PSA levels), delineated several features of the computational metastatic system: larger metastases had longer cycles; a higher proportion of drug-resistant cells slowed the cycles; and a faster cell turnover rate sped up drug response time and slowed regrowth time. The number of metastases did not affect cycle times, as response dynamics were dominated by the largest tumors rather than the aggregate. In addition, systems with higher intermetastasis heterogeneity responded better to continuous therapy and correlated with dynamics from patients with high or low Gleason scores. Conversely, systems with higher intrametastasis heterogeneity responded better to adaptive therapy and correlated with dynamics from patients with intermediate Gleason scores. SIGNIFICANCE: Multiscale mathematical modeling combined with biomarker dynamics during adaptive therapy helps identify underlying features of metastatic cancer to inform treatment decisions.

Adaptive therapy for ovarian cancer: An integrated approach to PARP inhibitor scheduling.

Toxicity and emerging drug resistance are important challenges in PARP inhibitor (PARPi) treatment of ovarian cancer. Recent research has shown that evolutionary-inspired treatment algorithms which adapt treatment to the tumor's treatment response (adaptive therapy) can help to mitigate both. Here, we present a first step in developing an adaptive therapy protocol for PARPi treatment by combining mathematical modelling and wet-lab experiments to characterize the cell population dynamics under different PARPi schedules. Using data from in vitro Incucyte Zoom time-lapse microscopy experiments and a step-wise model selection process we derive a calibrated and validated ordinary differential equation model, which we then use to test different plausible adaptive treatment schedules. Our model can accurately predict the in vitro treatment dynamics, even to new schedules, and suggests that treatment modifications need to be carefully timed, or one risks losing control over tumour growth, even in the absence of any resistance. This is because our model predicts that multiple rounds of cell division are required for cells to acquire sufficient DNA damage to induce apoptosis. As a result, adaptive therapy algorithms that modulate treatment but never completely withdraw it are predicted to perform better in this setting than strategies based on treatment interruptions. Pilot experiments in vivo confirm this conclusion. Overall, this study contributes to a better understanding of the impact of scheduling on treatment outcome for PARPis and showcases some of the challenges involved in developing adaptive therapies for new treatment settings.

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation.

Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

Working with Convex Responses: Antifragility from Finance to Oncology.

We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology, where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis for medical problems, through the properties of nonlinear responses (convex or concave). We (1) link the convexity/concavity of the dose-response function to the statistical properties of the results; (2) define "antifragility" as a mathematical property for local beneficial convex responses and the generalization of "fragility" as its opposite, locally concave in the tails of the statistical distribution; (3) propose mathematically tractable relations between dosage, severity of conditions, and iatrogenics. In short, we propose a framework to integrate the necessary consequences of nonlinearities in evidence-based oncology and more general clinical risk management.

Agent-based methods facilitate integrative science in cancer.

In this opinion, we highlight agent-based modeling as a key tool for exploration of cell-cell and cell-environment interactions that drive cancer progression, therapeutic resistance, and metastasis. These biological phenomena are particularly suited to be captured at the cell-scale resolution possible only within agent-based or individual-based mathematical models. These modeling approaches complement experimental work (in vitro and in vivo systems) through parameterization and data extrapolation but also feed forward to drive new experiments that test model-generated predictions.

Antifragility as a complex system's response to perturbations, volatility, and time.

Antifragility characterizes the benefit of a dynamical system derived from the variability in environmental perturbations. Antifragility carries a precise definition that quantifies a system's output response to input variability. Systems may respond poorly to perturbations (fragile) or benefit from perturbations (antifragile). In this manuscript, we review a range of applications of antifragility theory in technical systems (e.g., traffic control, robotics) and natural systems (e.g., cancer therapy, antibiotics). While there is a broad overlap in methods used to quantify and apply antifragility across disciplines, there is a need for precisely defining the scales at which antifragility operates. Thus, we provide a brief general introduction to the properties of antifragility in applied systems and review relevant literature for both natural and technical systems' antifragility. We frame this review within three scales common to technical systems: intrinsic (input-output nonlinearity), inherited (extrinsic environmental signals), and interventional (feedback control), with associated counterparts in biological systems: ecological (homogeneous systems), evolutionary (heterogeneous systems), and interventional (control). We use the common noun in designing systems that exhibit antifragile behavior across scales and guide the reader along the spectrum of fragility-adaptiveness-resilience-robustness-antifragility, the principles behind it, and its practical implications.

Homeostasis limits keratinocyte evolution.

Recent studies have revealed that normal human tissues accumulate many somatic mutations. In particular, human skin is riddled with mutations, with multiple subclones of variable sizes. Driver mutations are frequent and tend to have larger subclone sizes, suggesting selection. To begin to understand the histories encoded by these complex somatic mutations, we incorporated genomes into a simple agent-based skin-cell model whose prime directive is homeostasis. In this model, stem-cell survival is random and dependent on proximity to the basement membrane. This simple homeostatic skin model recapitulates the observed log-linear distributions of somatic mutations, where most mutations are found in increasingly smaller subclones that are typically lost with time. Hence, neutral mutations are "passengers" whose fates depend on the random survival of their stem cells, where a rarer larger subclone reflects the survival and spread of mutations acquired earlier in life. The model can also maintain homeostasis and accumulate more frequent and larger driver subclones if these mutations (NOTCH1 and TP53) confer relatively higher persistence in normal skin or during tissue damage (sunlight). Therefore, a relatively simple model of epithelial turnover indicates how observed passenger and driver somatic mutations could accumulate without violating the prime directive of homeostasis in normal human tissues.

Mistic: An open-source multiplexed image t-SNE viewer.

Understanding the complex ecology of a tumor tissue and the spatiotemporal relationships between its cellular and microenvironment components is becoming a key component of translational research, especially in immuno-oncology. The generation and analysis of multiplexed images from patient samples is of paramount importance to facilitate this understanding. Here, we present Mistic, an open-source multiplexed image t-SNE viewer that enables the simultaneous viewing of multiple 2D images rendered using multiple layout options to provide an overall visual preview of the entire dataset. In particular, the positions of the images can be t-SNE or UMAP coordinates. This grouped view of all images allows an exploratory understanding of the specific expression pattern of a given biomarker or collection of biomarkers across all images, helps to identify images expressing a particular phenotype, and can help select images for subsequent downstream analysis. Currently, there is no freely available tool to generate such image t-SNEs.

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition.

Background: Adaptive therapy aims to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Here, we present a theoretical study of intra-tumoral competition during adaptive therapy, to investigate under which circumstances it will be superior to aggressive treatment. Methods: We develop and analyse a simple, 2-D, on-lattice, agent-based tumour model in which cells are classified as fully drug-sensitive or resistant. Subsequently, we compare this model to its corresponding non-spatial ordinary differential equation model, and fit it to longitudinal prostate-specific antigen data from 65 prostate cancer patients undergoing intermittent androgen deprivation therapy following biochemical recurrence. Results: Leveraging the individual-based nature of our model, we explicitly demonstrate competitive suppression of resistance during adaptive therapy, and examine how different factors, such as the initial resistance fraction or resistance costs, alter competition. This not only corroborates our theoretical understanding of adaptive therapy, but also reveals that competition of resistant cells with each other may play a more important role in adaptive therapy in solid tumours than was previously thought. To conclude, we present two case studies, which demonstrate the implications of our work for: (i) mathematical modelling of adaptive therapy, and (ii) the intra-tumoral dynamics in prostate cancer patients during intermittent androgen deprivation treatment, a precursor of adaptive therapy. Conclusion: Our work shows that the tumour's spatial architecture is an important factor in adaptive therapy and provides insights into how adaptive therapy leverages both inter- and intra-specific competition to control resistance.

Immunosuppressive niche engineering at the onset of human colorectal cancer.

The evolutionary dynamics of tumor initiation remain undetermined, and the interplay between neoplastic cells and the immune system is hypothesized to be critical in transformation. Colorectal cancer (CRC) presents a unique opportunity to study the transition to malignancy as pre-cancers (adenomas) and early-stage cancers are frequently resected. Here, we examine tumor-immune eco-evolutionary dynamics from pre-cancer to carcinoma using a computational model, ecological analysis of digital pathology data, and neoantigen prediction in 62 patient samples. Modeling predicted recruitment of immunosuppressive cells would be the most common driver of transformation. As predicted, ecological analysis reveals that progressed adenomas co-localized with immunosuppressive cells and cytokines, while benign adenomas co-localized with a mixed immune response. Carcinomas converge to a common immune "cold" ecology, relaxing selection against immunogenicity and high neoantigen burdens, with little evidence for PD-L1 overexpression driving tumor initiation. These findings suggest re-engineering the immunosuppressive niche may prove an effective immunotherapy in CRC.

Gattaca: Base-Pair Resolution Mutation Tracking for Somatic Evolution Studies using Agent-based Models.

Research over the past two decades has made substantial inroads into our understanding of somatic mutations. Recently, these studies have focused on understanding their presence in homeostatic tissue. In parallel, agent-based mechanistic models have emerged as an important tool for understanding somatic mutation in tissue; yet no common methodology currently exists to provide base-pair resolution data for these models. Here, we present Gattaca as the first method for introducing and tracking somatic mutations at the base-pair resolution within agent-based models that typically lack nuclei. With nuclei that incorporate human reference genomes, mutational context, and sequence coverage/error information, Gattaca is able to realistically evolve sequence data, facilitating comparisons between in silico cell tissue modeling with experimental human somatic mutation data. This user-friendly method, incorporated into each in silico cell, allows us to fully capture somatic mutation spectra and evolution.

Aberrant anterior cingulate processing of anticipated threat as a mechanism for psychosis.

Stress and abnormal stress response are associated with schizophrenia spectrum disorder (SSD), but the brain mechanisms linking stress to symptomatology remain unclear. In this study, we used a stress-based functional neuroimaging task, reverse-translated from preclinical studies, to test the hypothesis that abnormal corticolimbic processing of stressful threat anticipation is associated with psychosis and affective symptoms in SSD. Participants underwent an MRI-compatible ankle-shock task (AST) in which the threat of mild electrical shock was anticipated. We compared functional brain activations during anticipatory threat periods from N = 18 participants with SSD (10 M/8F) to those from N = 12 community controls (9 M/3F). After family-wise error correction, only one region, the ventral anterior cingulate cortex (vACC), showed significantly reduced activation compared with controls. vACC activation significantly correlated with clinical symptoms measured by the Brief Psychiatric Rating Scale total score (r = 0.54) and the psychosis subscale (r = 0.71), and inversely correlated with trait depression measured by the Maryland Trait and State Depression scale (r=-0.48). Deficient activation in vACC under stress of anticipated threat may lead to aberrant interpretation of such threat, contributing to psychosis and mood symptoms in SSD. This experimental paradigm has translational potential and may identify circuitry-level mechanisms of stress-related mental illness, leading to more targeted treatment.

Multimodal Neuroimaging Study of Visual Plasticity in Schizophrenia.

Schizophrenia is a severe mental illness with visual learning and memory deficits, and reduced long term potentiation (LTP) may underlie these impairments. Recent human fMRI and EEG studies have assessed visual plasticity that was induced with high frequency visual stimulation, which is thought to mimic an LTP-like phenomenon. This study investigated the differences in visual plasticity in participants with schizophrenia and healthy controls. An fMRI visual plasticity paradigm was implemented, and proton magnetic resonance spectroscopy data were acquired to determine whether baseline resting levels of glutamatergic and GABA metabolites were related to visual plasticity response. Adults with schizophrenia did not demonstrate visual plasticity after family-wise error correction; whereas, the healthy control group did. There was a significant regional difference in visual plasticity in the left visual cortical area V2 when assessing group differences, and baseline GABA levels were associated with this specific ROI in the SZ group only. Overall, this study suggests that visual plasticity is altered in schizophrenia and related to basal GABA levels.

Normal tissue architecture determines the evolutionary course of cancer.

Cancer growth can be described as a caricature of the renewal process of the tissue of origin, where the tissue architecture has a strong influence on the evolutionary dynamics within the tumor. Using a classic, well-studied model of tumor evolution (a passenger-driver mutation model) we systematically alter spatial constraints and cell mixing rates to show how tissue structure influences functional (driver) mutations and genetic heterogeneity over time. This approach explores a key mechanism behind both inter-patient and intratumoral tumor heterogeneity: competition for space. Time-varying competition leads to an emergent transition from Darwinian premalignant growth to subsequent invasive neutral tumor growth. Initial spatial constraints determine the emergent mode of evolution (Darwinian to neutral) without a change in cell-specific mutation rate or fitness effects. Driver acquisition during the Darwinian precancerous stage may be modulated en route to neutral evolution by the combination of two factors: spatial constraints and limited cellular mixing. These two factors occur naturally in ductal carcinomas, where the branching topology of the ductal network dictates spatial constraints and mixing rates.