Designing and interpreting 4D tumour spheroid experiments

Multimaterial 3D and 4D Bioprinting of Heterogenous Constructs for Tissue Engineering

Additive manufacturing (AM), which is based on the principle of layer-by-layer shaping and stacking of discrete materials, has shown significant benefits in the fabrication of complicated implants for tissue engineering (TE). However, many native tissues exhibit anisotropic heterogenous constructs with diverse components and functions. Consequently, the replication of complicated biomimetic constructs using conventional AM processes based on a single material is challenging. Multimaterial 3D and 4D bioprinting (with time as the fourth dimension) has emerged as a promising solution for constructing multifunctional implants with heterogenous constructs that can mimic the host microenvironment better than single-material alternatives. Notably, 4D-printed multimaterial implants with biomimetic heterogenous architectures can provide a time-dependent programmable dynamic microenvironment that can promote cell activity and tissue regeneration in response to external stimuli. This paper first presents the typical design strategies of biomimetic heterogenous constructs in TE applications. Subsequently, the latest processes in the multimaterial 3D and 4D bioprinting of heterogenous tissue constructs are discussed, along with their advantages and challenges. In particular, the potential of multimaterial 4D bioprinting of smart multifunctional tissue constructs is highlighted. Furthermore, this review provides insights into how multimaterial 3D and 4D bioprinting can facilitate the realization of next-generation TE applications.

Patient-derived melanoma models

Melanoma is a very aggressive, rapidly metastasizing tumor that has been studied intensively in the past regarding the underlying genetic and molecular mechanisms. More recently developed treatment modalities have improved response rates and overall survival of patients. However, the majority of patients suffer from secondary treatment resistance, which requires in depth analyses of the underlying mechanisms. Here, melanoma models based on patients-derived material may play an important role. Consequently, a plethora of different experimental techniques have been developed in the past years. Among these are 3D and 4D culture techniques, organotypic skin reconstructs, melanoma-on-chip models and patient-derived xenografts, Every technique has its own strengths but also weaknesses regarding throughput, reproducibility, and reflection of the human situation. Here, we provide a comprehensive overview of currently used techniques and discuss their use in different experimental settings.

Making Predictions Using Poorly Identified Mathematical Models

Many commonly used mathematical models in the field of mathematical biology involve challenges of parameter non-identifiability. Practical non-identifiability, where the quality and quantity of data does not provide sufficiently precise parameter estimates is often encountered, even with relatively simple models. In particular, the situation where some parameters are identifiable and others are not is often encountered. In this work we apply a recent likelihood-based workflow, called Profile-Wise Analysis (PWA), to non-identifiable models for the first time. The PWA workflow addresses identifiability, parameter estimation, and prediction in a unified framework that is simple to implement and interpret. Previous implementations of the workflow have dealt with idealised identifiable problems only. In this study we illustrate how the PWA workflow can be applied to both structurally non-identifiable and practically non-identifiable models in the context of simple population growth models. Dealing with simple mathematical models allows us to present the PWA workflow in a didactic, self-contained document that can be studied together with relatively straightforward Julia code provided on GitHub . Working with simple mathematical models allows the PWA workflow prediction intervals to be compared with gold standard full likelihood prediction intervals. Together, our examples illustrate how the PWA workflow provides us with a systematic way of dealing with non-identifiability, especially compared to other approaches, such as seeking ad hoc parameter combinations, or simply setting parameter values to some arbitrary default value. Importantly, we show that the PWA workflow provides insight into the commonly-encountered situation where some parameters are identifiable and others are not, allowing us to explore how uncertainty in some parameters, and combinations of parameters, regardless of their identifiability status, influences model predictions in a way that is insightful and interpretable.

Real-Time Cell Cycle Imaging in a 3D Cell Culture Model of Melanoma, Quantitative Analysis, Optical Clearing, and Mathematical Modeling

Aberrant cell cycle progression is a hallmark of solid tumors. Therefore, cell cycle analysis is an invaluable technique to study cancer cell biology. However, cell cycle progression has been most commonly assessed by methods that are limited to temporal snapshots or that lack spatial information. In this chapter, we describe a technique that allows spatiotemporal real-time tracking of cell cycle progression of individual cells in a multicellular context. The power of this system lies in the use of 3D melanoma spheroids generated from melanoma cells engineered with the fluorescent ubiquitination-based cell cycle indicator (FUCCI). This technique, combined with mathematical modeling, allows us to gain further and more detailed insight into several relevant aspects of solid cancer cell biology, such as tumor growth, proliferation, invasion, and drug sensitivity.

Prediction of Spheroid Cell Death Using Fluorescence Staining and Convolutional Neural Networks

Three-dimensional (3D) cell culture is emerging for drug design and drug screening. Skin toxicity is one of the most important assays for determining the toxicity of a compound before being used in skin application. Much work has been done to find an alternative assay without animal experiments. 3D cell culture is one of the methods that provides clinically relevant models with superior clinical translation compared to that of 2D cell culture. In this study, we developed a spheroid toxicity assay using keratinocyte HaCaT cells with propidium iodide and calcein AM. We also applied the transfer learning-containing convolutional neural network (CNN) to further determine spheroid cell death with fluorescence labeling. Our result shows that the morphologies of the spheroid are the key features in determining the apoptosis cell death of the HaCaT spheroid. Our CNN model provided good statistical measurement in terms of accuracy, precision, and recall in both validation and external test data sets. One can predict keratinocyte spheroid cell death if that spheroid image contains the fluorescence signals from propidium iodide and calcein AM. The CNN model can be accessed in the web application at https://qsarlabs.com/#spheroiddeath.

Formation and Growth of Co-Culture Tumour Spheroids: New Compartment-Based Mathematical Models and Experiments

Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. Therefore, methods to quantitatively characterise and interpret co-culture spheroid growth are of great interest. However, co-culture spheroid growth is complex. Multiple biological processes occur on overlapping timescales and different cell types within the spheroid may have different characteristics, such as differing proliferation rates or responses to nutrient availability. At present there is no standard, widely-accepted mathematical model of such complex spatio-temporal growth processes. Typical approaches to analyse these experiments focus on the late-time temporal evolution of spheroid size and overlook early-time spheroid formation, spheroid structure and geometry. Here, using a range of ordinary differential equation-based mathematical models and parameter estimation, we interpret new co-culture experimental data. We provide new biological insights about spheroid formation, growth, and structure. As part of this analysis we connect Greenspan's seminal mathematical model to co-culture data for the first time. Furthermore, we generalise a class of compartment-based spheroid mathematical models that have previously been restricted to one population so they can be applied to multiple populations. As special cases of the general model, we explore multiple natural two population extensions to Greenspan's seminal model and reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types and the new class of mathematical models provide opportunities for further mathematical and biological insights.

Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Tumor Organoid and Spheroid Models for Cervical Cancer

Cervical cancer is one of the most common malignant diseases in women worldwide. Despite the global introduction of a preventive vaccine against the leading cause of cervical cancer, human papillomavirus (HPV) infection, the incidence of this malignant disease is still very high, especially in economically challenged areas. New advances in cancer therapy, especially the rapid development and application of different immunotherapy strategies, have shown promising pre-clinical and clinical results. However, mortality from advanced stages of cervical cancer remains a significant concern. Precise and thorough evaluation of potential novel anti-cancer therapies in pre-clinical phases is indispensable for efficient development of new, more successful treatment options for cancer patients. Recently, 3D tumor models have become the gold standard in pre-clinical cancer research due to their capacity to better mimic the architecture and microenvironment of tumor tissue as compared to standard two-dimensional (2D) cell cultures. This review will focus on the application of spheroids and patient-derived organoids (PDOs) as tumor models to develop novel therapies against cervical cancer, with an emphasis on the immunotherapies that specifically target cancer cells and modulate the tumor microenvironment (TME).

Tumour growth: An approach to calibrate parameters of a multiphase porous media model based on in vitro observations of Neuroblastoma spheroid growth in a hydrogel microenvironment

To unravel processes that lead to the growth of solid tumours, it is necessary to link knowledge of cancer biology with the physical properties of the tumour and its interaction with the surrounding microenvironment. Our understanding of the underlying mechanisms is however still imprecise. We therefore developed computational physics-based models, which incorporate the interaction of the tumour with its surroundings based on the theory of porous media. However, the experimental validation of such models represents a challenge to its clinical use as a prognostic tool. This study combines a physics-based model with in vitro experiments based on microfluidic devices used to mimic a three-dimensional tumour microenvironment. By conducting a global sensitivity analysis, we identify the most influential input parameters and infer their posterior distribution based on Bayesian calibration. The resulting probability density is in agreement with the scattering of the experimental data and thus validates the proposed workflow. This study demonstrates the huge challenges associated with determining precise parameters with usually only limited data for such complex processes and models, but also demonstrates in general how to indirectly characterise the mechanical properties of neuroblastoma spheroids that cannot feasibly be measured experimentally.

Applications and Advances of Multicellular Tumor Spheroids: Challenges in Their Development and Analysis

Biomedical research requires both in vitro and in vivo studies in order to explore disease processes or drug interactions. Foundational investigations have been performed at the cellular level using two-dimensional cultures as the gold-standard method since the early 20th century. However, three-dimensional (3D) cultures have emerged as a new tool for tissue modeling over the last few years, bridging the gap between in vitro and animal model studies. Cancer has been a worldwide challenge for the biomedical community due to its high morbidity and mortality rates. Various methods have been developed to produce multicellular tumor spheroids (MCTSs), including scaffold-free and scaffold-based structures, which usually depend on the demands of the cells used and the related biological question. MCTSs are increasingly utilized in studies involving cancer cell metabolism and cell cycle defects. These studies produce massive amounts of data, which demand elaborate and complex tools for thorough analysis. In this review, we discuss the advantages and disadvantages of several up-to-date methods used to construct MCTSs. In addition, we also present advanced methods for analyzing MCTS features. As MCTSs more closely mimic the in vivo tumor environment, compared to 2D monolayers, they can evolve to be an appealing model for in vitro tumor biology studies.

Replacement, Reduction, and Refinement of Animal Experiments in Anticancer Drug Development: The Contribution of 3D In Vitro Cancer Models in the Drug Efficacy Assessment

In the last decades three-dimensional (3D) in vitro cancer models have been proposed as a bridge between bidimensional (2D) cell cultures and in vivo animal models, the gold standards in the preclinical assessment of anticancer drug efficacy. 3D in vitro cancer models can be generated through a multitude of techniques, from both immortalized cancer cell lines and primary patient-derived tumor tissue. Among them, spheroids and organoids represent the most versatile and promising models, as they faithfully recapitulate the complexity and heterogeneity of human cancers. Although their recent applications include drug screening programs and personalized medicine, 3D in vitro cancer models have not yet been established as preclinical tools for studying anticancer drug efficacy and supporting preclinical-to-clinical translation, which remains mainly based on animal experimentation. In this review, we describe the state-of-the-art of 3D in vitro cancer models for the efficacy evaluation of anticancer agents, focusing on their potential contribution to replace, reduce and refine animal experimentations, highlighting their strength and weakness, and discussing possible perspectives to overcome current challenges.

Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970 s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry has established their significance to tumour growth dynamics. In this tutorial, we formulate a hierarchy of mathematical models of increasing complexity to explore the role of mechanics in spheroid growth, all the while seeking to retain desirable simplicity and analytical tractability. Beginning with the theory of morphoelasticity, which combines solid mechanics and growth, we successively refine our assumptions to develop a somewhat minimal model of mechanically regulated spheroid growth that is free from many unphysical and undesirable behaviours. In doing so, we will see how iterating upon simple models can provide rigorous guarantees of emergent behaviour, which are often precluded by existing, more complex modelling approaches. Perhaps surprisingly, we also demonstrate that the final model considered in this tutorial agrees favourably with classical experimental results, highlighting the potential for simple models to provide mechanistic insight whilst also serving as mathematical examples.

Hybrid computational models of multicellular tumour growth considering glucose metabolism

Cancer cells metabolize glucose through metabolic pathways that differ from those used by healthy and differentiated cells. In particular, tumours have been shown to consume more glucose than their healthy counterparts and to use anaerobic metabolic pathways, even under aerobic conditions. Nevertheless, scientists have still not been able to explain why cancer cells evolved to present an altered metabolism and what evolutionary advantage this might provide them. Experimental and computational models have been increasingly used in recent years to understand some of these biological questions. Multicellular tumour spheroids are effective experimental models as they replicate the initial stages of avascular solid tumour growth. Furthermore, these experiments generate data which can be used to calibrate and validate computational studies that aim to simulate tumour growth. Hybrid models are of particular relevance in this field of research because they model cells as individual agents while also incorporating continuum representations of the substances present in the surrounding microenvironment that may participate in intracellular metabolic networks as concentration or density distributions. Henceforth, in this review, we explore the potential of computational modelling to reveal the role of metabolic reprogramming in tumour growth.

Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability

Tumours are subject to external environmental variability. However, in vitro tumour spheroid experiments, used to understand cancer progression and develop cancer therapies, have been routinely performed for the past fifty years in constant external environments. Furthermore, spheroids are typically grown in ambient atmospheric oxygen (normoxia), whereas most in vivo tumours exist in hypoxic environments. Therefore, there are clear discrepancies between in vitro and in vivo conditions. We explore these discrepancies by combining tools from experimental biology, mathematical modelling, and statistical uncertainty quantification. Focusing on oxygen variability to develop our framework, we reveal key biological mechanisms governing tumour spheroid growth. Growing spheroids in time-dependent conditions, we identify and quantify novel biological adaptation mechanisms, including unexpected necrotic core removal, and transient reversal of the tumour spheroid growth phases.

Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates

An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot always resolve the mismatch between available data and the granularity required in mathematical models to answer important biological questions. Often, it is only simple phenomenological models, such as the logistic and Gompertz growth models, that are identifiable from standard experimental measurements. To draw insights from complex, non-identifiable models that incorporate key biological mechanisms of interest, we study the geometry of a map in parameter space from the complex model to a simple, identifiable, surrogate model. By studying how non-identifiable parameters in the complex model quantitatively relate to identifiable parameters in surrogate, we introduce and exploit a layer of interpretation between the set of non-identifiable parameters and the goodness-of-fit metric or likelihood studied in typical identifiability analysis. We demonstrate our approach by analysing a hierarchy of mathematical models for multicellular tumour spheroid growth experiments. Typical data from tumour spheroid experiments are limited and noisy, and corresponding mathematical models are very often made arbitrarily complex. Our geometric approach is able to predict non-identifiabilities, classify non-identifiable parameter spaces into identifiable parameter combinations that relate to features in the data characterised by parameters in a surrogate model, and overall provide additional biological insight from complex non-identifiable models.

Computationally efficient framework for diagnosing, understanding and predicting biphasic population growth

Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as biphasic growth for the commonly encountered situation involving two phases. Biphasic population growth occurs over a massive range of spatial and temporal scales, ranging from microscopic growth of tumours over several days, to decades-long regrowth of corals in coral reefs that can extend for hundreds of kilometres. Different mathematical models and statistical methods are used to diagnose, understand and predict biphasic growth. Common approaches can lead to inaccurate predictions of future growth that may result in inappropriate management and intervention strategies being implemented. Here, we develop a very general computationally efficient framework, based on profile likelihood analysis, for diagnosing, understanding and predicting biphasic population growth. The two key components of the framework are as follows: (i) an efficient method to form approximate confidence intervals for the change point of the growth dynamics and model parameters and (ii) parameter-wise profile predictions that systematically reveal the influence of individual model parameters on predictions. To illustrate our framework we explore real-world case studies across the life sciences.

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling

In vitro tumour spheroids have been used to study avascular tumour growth and drug design for over 50 years. Tumour spheroids exhibit heterogeneity within the growing population that is thought to be related to spatial and temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us to identify the position and cell cycle status of individual cells within the growing spheroid, giving rise to the notion of a four-dimensional (4D) tumour spheroid. We develop the first stochastic individual-based model (IBM) of a 4D tumour spheroid and show that IBM simulation data compares well with experimental data using a primary human melanoma cell line. The IBM provides quantitative information about nutrient availability within the spheroid, which is important because it is difficult to measure these data experimentally.