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.

Modelling count data with partial differential equation models in biology.

Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is often bounded above by some carrying capacity that arises through biological competition for space or nutrients. Parameter estimation, parameter identifiability, and making model predictions usually involves working with a measurement error model that explicitly relating experimental measurements with the solution of a mathematical model. In many biological applications, a typical approach is to assume the data are normally distributed about the solution of the mathematical model. Despite the widespread use of the standard additive Gaussian measurement error model, the assumptions inherent in this approach are rarely explicitly considered or compared with other options. Here, we interpret scratch assay data, involving migration, proliferation and delays in a population of cancer cells using a reaction-diffusion PDE model. We consider relating experimental measurements to the PDE solution using a standard additive Gaussian measurement error model alongside a comparison to a more biologically realistic binomial measurement error model. While estimates of model parameters are relatively insensitive to the choice of measurement error model, model predictions for data realisations are very sensitive. The standard additive Gaussian measurement error model leads to biologically inconsistent predictions, such as negative counts and counts that exceed the carrying capacity across a relatively large spatial region within the experiment. Furthermore, the standard additive Gaussian measurement error model requires estimating an additional parameter compared to the binomial measurement error model. In contrast, the binomial measurement error model leads to biologically plausible predictions and is simpler to implement. We provide open source Julia software on GitHub to replicate all calculations in this work, and we explain how to generalise our approach to deal with coupled PDE models with several dependent variables through a multinomial measurement error model, as well as pointing out other potential generalisations by linking our work with established practices in the field of generalised linear models.

Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences.

Throughout the life sciences, we routinely seek to interpret measurements and observations using parametrized mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis and prediction, called profile-wise analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.

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.

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.

Profile likelihood-based parameter and predictive interval analysis guides model choice for ecological population dynamics.

Calibrating mathematical models to describe ecological data provides important insight via parameter estimation that is not possible from analysing data alone. When we undertake a mathematical modelling study of ecological or biological data, we must deal with the trade-off between data availability and model complexity. Dealing with the nexus between data availability and model complexity is an ongoing challenge in mathematical modelling, particularly in mathematical biology and mathematical ecology where data collection is often not standardised, and more broad questions about model selection remain relatively open. Therefore, choosing an appropriate model almost always requires case-by-case consideration. In this work we present a straightforward approach to quantitatively explore this trade-off using a case study exploring mathematical models of coral reef regrowth after some ecological disturbance, such as damage caused by a tropical cyclone. In particular, we compare a simple single species ordinary differential equation (ODE) model approach with a more complicated two-species coupled ODE model. Univariate profile likelihood analysis suggests that the both models are practically identifiable. To provide additional insight we construct and compare approximate prediction intervals using a new parameter-wise prediction approximation, confirming both the simple and complex models perform similarly with regard to making predictions. Our approximate parameter-wise prediction interval analysis provides explicit information about how each parameter affects the predictions of each model. Comparing our approximate prediction intervals with a more rigorous and computationally expensive evaluation of the full likelihood shows that the new approximations are reasonable in this case. All algorithms and software to support this work are freely available as jupyter notebooks on GitHub so that they can be adapted to deal with any other ODE-based 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.

Designing and interpreting 4D tumour spheroid experiments.

Tumour spheroid experiments are routinely used to study cancer progression and treatment. Various and inconsistent experimental designs are used, leading to challenges in interpretation and reproducibility. Using multiple experimental designs, live-dead cell staining, and real-time cell cycle imaging, we measure necrotic and proliferation-inhibited regions in over 1000 4D tumour spheroids (3D space plus cell cycle status). By intentionally varying the initial spheroid size and temporal sampling frequencies across multiple cell lines, we collect an abundance of measurements of internal spheroid structure. These data are difficult to compare and interpret. However, using an objective mathematical modelling framework and statistical identifiability analysis we quantitatively compare experimental designs and identify design choices that produce reliable biological insight. Measurements of internal spheroid structure provide the most insight, whereas varying initial spheroid size and temporal measurement frequency is less important. Our general framework applies to spheroids grown in different conditions and with different cell types.

Measuring and Modelling the Epithelial- Mesenchymal Hybrid State in Cancer: Clinical Implications.

The epithelial-mesenchymal (E/M) hybrid state has emerged as an important mediator of elements of cancer progression, facilitated by epithelial mesenchymal plasticity (EMP). We review here evidence for the presence, prognostic significance, and therapeutic potential of the E/M hybrid state in carcinoma. We further assess modelling predictions and validation studies to demonstrate stabilised E/M hybrid states along the spectrum of EMP, as well as computational approaches for characterising and quantifying EMP phenotypes, with particular attention to the emerging realm of single-cell approaches through RNA sequencing and protein-based techniques.

Quantitative analysis of tumour spheroid structure.

Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, tumour spheroids more closely mimic the avascular tumour microenvironment where spatial differences in nutrient availability strongly influence growth. We show that spheroids initiated using significantly different numbers of cells grow to similar limiting sizes, suggesting that avascular tumours have a limiting structure; in agreement with untested predictions of classical mathematical models of tumour spheroids. We develop a novel mathematical and statistical framework to study the structure of tumour spheroids seeded from cells transduced with fluorescent cell cycle indicators, enabling us to discriminate between arrested and cycling cells and identify an arrested region. Our analysis shows that transient spheroid structure is independent of initial spheroid size, and the limiting structure can be independent of seeding density. Standard experimental protocols compare spheroid size as a function of time; however, our analysis suggests that comparing spheroid structure as a function of overall size produces results that are relatively insensitive to variability in spheroid size. Our experimental observations are made using two melanoma cell lines, but our modelling framework applies across a wide range of spheroid culture conditions and cell lines.

In Vitro Biofilm Formation on Aryl Ketone Polymer (AKP), A New Denture Material, Compared with That on Three Traditional Dental Denture Materials.

Control of denture plaque biofilms is a practical approach to preventing persistent oral infections such as denture stomatitis. Objectives. This study compared in vitro biofilm attachment and growth on a new denture material, Ultaire® AKP, with that on traditional denture materials including cobalt chrome (CoCr), polymethyl methacrylate (PMMA), and polyoxymethylene (POM). Methods. Microbial biofilms were grown with cultures of Candida albicans, Streptococcus mutans UA159, or a mixed Streptococcus spp. (S. mutans 700610/Streptococcus sanguinis BAA-1455) for 6 hours in a static protocol or 24 hours in a dynamic protocol for each material. Adherent biofilm cells were removed, and viable colony-forming units (CFUs) were enumerated. Confocal microscopy of the 24-hour Streptococcus spp. biofilms was used to determine biofilm mass and roughness coefficients. Results. The rank order of C. albicans attachment after 6 hours was CoCr > PMMA ∗ > Ultaire® AKP ∗ ( ∗ vs CoCr, p ≤ 0.05), and that for 24-hour biofilm growth was CoCr > Ultaire® AKP ∗ > PMMA ∗ ( ∗ vs CoCr, p ≤ 0.05). The rank order of S. mutans biofilm attachment was CoCr > POM > Ultaire® AKP ∗ > PMMA ∗ ( ∗ vs CoCr, p ≤ 0.05), and that for the 24-hour Streptococcus spp. biofilm growth was POM > Ultaire® AKP > PMMA > CoCr ∗ ( ∗ vs POM, p ≤ 0.05). Confocal images revealed structural differences in Streptococcus spp. biofilms on CoCr compared with the other test materials. Significantly lower roughness coefficients of Streptococcus spp. biofilms on Ultaire® AKP were noted, suggesting that these biofilms were less differentiated. Ultaire® AKP promoted significantly less C. albicans and S. mutans biofilm attachment than CoCr at 6 hours and C. albicans growth at 24 hours. Streptococcus spp. biofilms on Ultaire® AKP were less differentiated than those on other test materials. Conclusion. In addition to its material strength, Ultaire® AKP represents an attractive option for denture material in removable partial dentures.

Mechanical Pressure Driving Proteoglycan Expression in Mammographic Density: a Self-perpetuating Cycle?

Regions of high mammographic density (MD) in the breast are characterised by a proteoglycan (PG)-rich fibrous stroma, where PGs mediate aligned collagen fibrils to control tissue stiffness and hence the response to mechanical forces. Literature is accumulating to support the notion that mechanical stiffness may drive PG synthesis in the breast contributing to MD. We review emerging patterns in MD and other biological settings, of a positive feedback cycle of force promoting PG synthesis, such as in articular cartilage, due to increased pressure on weight bearing joints. Furthermore, we present evidence to suggest a pro-tumorigenic effect of increased mechanical force on epithelial cells in contexts where PG-mediated, aligned collagen fibrous tissue abounds, with implications for breast cancer development attributable to high MD. Finally, we summarise means through which this positive feedback mechanism of PG synthesis may be intercepted to reduce mechanical force within tissues and thus reduce disease burden.

A biomechanically-guided planning and execution paradigm for osteoporotic hip augmentation: Experimental evaluation of the biomechanics and temperature-rise.

BACKGROUND: Augmentation of the proximal femur with bone cement (femoroplasty) has been identified as a potential preventive approach to reduce the risk of fracture. Femoroplasty, however, is associated with a risk of thermal damage as well as the leakage of bone cement or blockage of blood supply when large volumes of cement are introduced inside the bone. METHODS: Six pairs of cadaveric femora were augmented using a newly proposed planning paradigm and an in-house navigation system to control the location and volume of the injected cement. To evaluate the risk of thermal damage, we recorded the peak temperature of bone at three regions of interest as well as the exposure time for temperature rise of 8 °C, 10 °C, and 12 °C in these regions. Augmentation was followed by mechanical testing to failure resembling a sideway fall on the greater trochanter. FINDINGS: Results of the fracture tests correlated with those of simulations for the yield load (R2 = 0.77) and showed that femoroplasty can significantly improve the yield load (42%, P < 0.001) and yield energy (139%, P = 0.062) of the specimens. Meanwhile, temperature recordings of the bone surface showed that the areas close to the greater trochanter will be exposed to more critical temperature rise than the trochanteric crest and femoral neck areas. INTERPRETATION: The new planning paradigm offers a more efficient injection strategy with injection volume of 9.1 ml on average. Meanwhile, temperature recordings of bone surfaces suggest that risk of thermal necrosis remains as a concern with femoroplasty using Polymethylmethacrylate.

The role of mechanical interactions in EMT.

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-ß, produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.

A free boundary mechanobiological model of epithelial tissues.

In this study, we couple intracellular signalling and cell-based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in a discrete modelling framework, and new reaction-diffusion equations are derived to describe tissue-level outcomes. The free boundary evolves as a result of the underlying biological mechanisms included in the discrete model. To demonstrate the accuracy of the continuum model, we compare numerical solutions of the discrete and continuum models for two different signalling pathways. First, we study the Rac-Rho pathway where cell- and tissue-level mechanics are directly related to intracellular signalling. Second, we study an activator-inhibitor system which gives rise to spatial and temporal patterning related to Turing patterns. In all cases, the continuum model and free boundary condition accurately reflect the cell-level processes included in the discrete model.

Mechanical Cell Competition in Heterogeneous Epithelial Tissues.

Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are incorporated into the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Using the new discrete model and continuum description, we explore several applications including the evolution of homogeneous tissues experiencing proliferation and death, and competition in a heterogeneous setting with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mechanisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than an intrinsic proliferative advantage. We advise when the continuum model is beneficial and demonstrate why naively adding source/sink terms to a continuum model without considering the underlying discrete model may lead to incorrect results.

Fracture Load of Veneered Telescopic Secondary Crowns Made of High-Performance Polymer on Zirconia Primary Crowns: Impact of Veneering Technique.

PURPOSE: To analyze the impact of different veneering techniques on the fracture load of telescopic secondary crowns made of a high-performance polymer (Ultaire aryl ketone polymer [UAKP]). MATERIALS AND METHODS: Zirconia primary crown models (taper of 0 degrees) were prepared (N = 48), polished, scanned, and divided into four veneering groups (n = 12 each): premanufactured, digital, full anatomical, and vestibular. For all groups except vestibular, a standardized telescopic secondary crown (thickness: 0.6 mm, circular margin: 1 mm) was constructed, adapted to the corresponding primary crown, milled from UAKP, and veneered. The veneered master crown was developed based on the premanufactured group. After surface polishing, all specimens were artificially aged in a chewing simulator (1.2 million cycles, 50 N, 1.1 Hz, between 5°C and 55°C). Fracture load was tested in a universal testing machine with a piston (Ø = 6 mm, 1 mm/minute). Fracture patterns were analyzed. For statistical analysis, Kolmogorov-Smirnov test and descriptive statistics followed by one-way ANOVA with post hoc Scheffé test were conducted (P < .05). RESULTS: Significant differences in fracture load were found between different veneering techniques (P < .001), with the highest values for the vestibular and digital groups, followed by the premanufactured group. Full anatomical veneering showed the significantly lowest fracture load (1,885 ± 397 N). For all specimens, cohesive brittle fractures with similar fracture patterns occurred, irrespective of the veneering technique. CONCLUSION: The veneering technique of telescopic secondary crowns made of high-performance polymer affects overall stability. All veneering techniques provided sufficient fracture load values for telescopic secondary crowns made of UAKP. Digital veneers seem the most recommendable.

Automatic annotation of hip anatomy in fluoroscopy for robust and efficient 2D/3D registration.

PURPOSE: Fluoroscopy is the standard imaging modality used to guide hip surgery and is therefore a natural sensor for computer-assisted navigation. In order to efficiently solve the complex registration problems presented during navigation, human-assisted annotations of the intraoperative image are typically required. This manual initialization interferes with the surgical workflow and diminishes any advantages gained from navigation. In this paper, we propose a method for fully automatic registration using anatomical annotations produced by a neural network. METHODS: Neural networks are trained to simultaneously segment anatomy and identify landmarks in fluoroscopy. Training data are obtained using a computationally intensive, intraoperatively incompatible, 2D/3D registration of the pelvis and each femur. Ground truth 2D segmentation labels and anatomical landmark locations are established using projected 3D annotations. Intraoperative registration couples a traditional intensity-based strategy with annotations inferred by the network and requires no human assistance. RESULTS: Ground truth segmentation labels and anatomical landmarks were obtained in 366 fluoroscopic images across 6 cadaveric specimens. In a leave-one-subject-out experiment, networks trained on these data obtained mean dice coefficients for left and right hemipelves, left and right femurs of 0.86, 0.87, 0.90, and 0.84, respectively. The mean 2D landmark localization error was 5.0 mm. The pelvis was registered within [Formula: see text] for 86% of the images when using the proposed intraoperative approach with an average runtime of 7 s. In comparison, an intensity-only approach without manual initialization registered the pelvis to [Formula: see text] in 18% of images. CONCLUSIONS: We have created the first accurately annotated, non-synthetic, dataset of hip fluoroscopy. By using these annotations as training data for neural networks, state-of-the-art performance in fluoroscopic segmentation and landmark localization was achieved. Integrating these annotations allows for a robust, fully automatic, and efficient intraoperative registration during fluoroscopic navigation of the hip.

Suitability of the new Aryl-Ketone-Polymer indicated for removable partial dentures: Analysis of elastic properties and bond strength to denture resin.

Elastic properties of Aryl-Ketone-Polymer (UAKP) and tensile bond strength (TBS) to denture resin (PalaXpress) were tested. Indentation modulus (EIT) and indentation hardness (HIT) were measured via Martens hardness (n=10 specimens) with 4.2±0.6 kN/mm2 and 261±8 N/mm2 respectively. TBS was tested in dependence of different adhesives (visio.link (VL), Adhese Universal (AU), All-Bond Universal (ABU), CLEARFIL UNIVERSAL BOND (CUB), G-Premio BOND (GPB), iBOND Universal (IBU), ONE COAT 7 UNIVERSAL (OCU), Scotchbond Universal (SBU) and without adhesive (CG), n=18/group) and the application of opaquer (n=9/group) after thermocycling (5°C/55°C, 10,000×). TBS was affected by the adhesive (η (P2=0.715, p<0.001) followed by the opaquer (ηP2=0.335, p<0.001). VL and CG showed highest TBS followed by AU and ABU. IBU and GPB resulted in lowest TBS. Opaquer increased TBS for all adhesives (p<0.05), except VL and CG (p<0.258). Elastic properties are well-suited for the indication of removable partial dentures. Bonding to denture resin is no limiting factor.