Density-dependence as a size-independent regulatory mechanism

Measuring differences between phenomenological growth models applied to epidemiology

Phenomenological growth models (PGMs) provide a framework for characterizing epidemic trajectories, estimating key transmission parameters, gaining insight into the contribution of various transmission pathways, and providing long-term and short-term forecasts. Such models only require a small number of parameters to describe epidemic growth patterns. They can be expressed by an ordinary differential equation (ODE) of the type C^'(t)=f(t,C;Θ) for t>0, C(0)=C₀, where t is time, C(t) is the total size of the epidemic (the cumulative number of cases) at time t, C₀ is the initial number of cases, f is a model-specific incidence function, and Θ is a vector of parameters. The current COVID-19 pandemic is a scenario for which such models are of obvious importance. In Bürger et al. (2019) it is demonstrated that some PGMs are better at fitting data of specific epidemic outbreaks than others even when the models have the same number of parameters. This situation motivates the need to measure differences in the dynamics that two different models are capable of generating. The present work contributes to a systematic study of differences between PGMs and how these may explain the ability of certain models to provide a better fit to data than others. To this end a so-called empirical directed distance (EDD) is defined to describe the differences in the dynamics between different dynamic models. The EDD of one PGM from another one quantifies how well the former fits data generated by the latter. The concept of EDD is, however, not symmetric in the usual sense of metric spaces. The procedure of calculating EDDs is applied to synthetic data and real data from influenza, Ebola, and COVID-19 outbreaks.

Coupling ecological and social network models to assess "transmission" and "contagion" of an aquatic invasive species

Network analysis is used to address diverse ecological, social, economic, and epidemiological questions, but few efforts have been made to combine these field-specific analyses into interdisciplinary approaches that effectively address how complex systems are interdependent and connected to one another. Identifying and understanding these cross-boundary connections improves natural resource management and promotes proactive, rather than reactive, decisions. This research had two main objectives; first, adapt the framework and approach of infectious disease network modeling so that it may be applied to the socio-ecological problem of spreading aquatic invasive species, and second, use this new coupled model to simulate the spread of the invasive Chinese mystery snail (Bellamya chinensis) in a reservoir network in Southeastern Nebraska, USA. The coupled model integrates an existing social network model of how anglers move on the landscape with new reservoir-specific ecological network models. This approach allowed us to identify 1) how angler movement among reservoirs aids in the spread of B. chinensis, 2) how B. chinensis alters energy flows within individual-reservoir food webs, and 3) a new method for assessing the spread of any number of non-native or invasive species within complex, social-ecological systems.

Joint fitting reveals hidden interactions in tumor growth

Tumor growth is often the result of the simultaneous development of two or more cancer cell populations. Crucial to the system evolution are the interactions between these populations. To obtain information about these interactions we apply the recently developed vector universality (VUN) formalism to various instances of competition between tumor populations. The formalism allows us (a) to quantify the growth mechanisms of a HeLa cell colony, describing the phenotype switching responsible for its fast expansion, (b) to reliably reconstruct the evolution of the necrotic and viable fractions in both in vitro and in vivo tumors using data for the time dependences of the total masses alone, and (c) to show how the shedding of cells leading to subspheroid formation is beneficial to both the spheroid and subspheroid populations, suggesting that shedding is a strong positive influence on cancer dissemination.

Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, "Average Relative Growth Rate" is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.

A generalization of Gompertz law compatible with the Gyllenberg-Webb theory for tumour growth

We present a new extension of Gompertz law for tumour growth and anti-tumour therapy. After discussing its qualitative and analytical properties, we show, in the spirit of [16], that, like the standard Gompertz model, it is fully compatible with the two-population model of Gyllenberg and Webb, formulated in [14] in order to provide a theoretical basis to Gompertz law. Compatibility with the model proposed in [17] is also investigated. Comparisons with some experimental data confirm the practical applicability of the model. Numerical simulations about the method performance are presented.

Oscillations in growth of multicellular tumour spheroids: a revisited quantitative analysis

OBJECTIVES

Multicellular tumour spheroids (MTS) provide an important tool for study of the microscopic properties of solid tumours and their responses to therapy. Thus, observation of large-scale volume oscillations in MTS, reported several years ago by two independent groups (1,2), in our opinion represent a remarkable discovery, particularly if this could promote careful investigation of the possible occurrence of volume oscillations of tumours 'in vivo'.

MATERIALS AND METHODS

Because of high background noise, quantitative analysis of properties of observed oscillations has not been possible in previous studies. Such an analysis can be now performed, thanks to a recently proposed approach, based on formalism of phenomenological universalities (PUN).

RESULTS

Results have provided unambiguous confirmation of the existence of MTS volume oscillations, and quantitative evaluation of their properties, for two tumour cell lines. Proof is based not only on quality of fitting of the experimental datasets, but also on determination of well-defined values of frequency and amplitude of the oscillations for each line investigated, which would not be consistent with random fluctuation.

CONCLUSIONS

Biological mechanisms, which can be directly responsible for observed oscillations, are proposed, which relates also to recent work on related topics. Further investigations, both at experimental and at modelling levels, are also suggested. Finally, from a methodological point of view, results obtained represent further confirmation of applicability and usefulness of the PUN approach.

In vitro ovine articular chondrocyte proliferation: experiments and modelling

This study focuses on analysis of in vitro cultures of chondrocytes from ovine articular cartilage. Isolated cells were seeded in Petri dishes, then expanded to confluence and phenotypically characterized by flow cytometry. The sigmoidal temporal profile of total counts was obtained by classic haemocytometry and corresponding cell size distributions were measured electronically using a Coulter Counter. A mathematical model recently proposed (1) was adopted for quantitative interpretation of these experimental data. The model is based on a 1-D (that is, mass-structured), single-staged population balance approach capable of taking into account contact inhibition at confluence. The model's parameters were determined by fitting measured total cell counts and size distributions. Model reliability was verified by predicting cell proliferation counts and corresponding size distributions at culture times longer than those used when tuning the model's parameters. It was found that adoption of cell mass as the intrinsic characteristic of a growing chondrocyte population enables sigmoidal temporal profiles of total counts in the Petri dish, as well as cell size distributions at 'balanced growth', to be adequately predicted.

Experimental analysis and modelling of in vitro proliferation of mesenchymal stem cells

OBJECTIVES

Stem cell therapies based on differentiation of adult or embryonic stem cells into specialized ones appear to be effective for treating several human diseases. This work addresses the mathematical simulation of proliferation kinetics of stem cells.

MATERIALS AND METHODS

Sheep bone marrow mesenchymal stem cells (phenotype characterized by flow cytometry analysis) seeded at different initial concentrations in Petri dishes were expanded to confluence. Sigmoid temporal profiles of total counts obtained through classic haemocytometry were quantitatively interpreted by both a phenomenological logistic equation and a novel model based on a one-dimensional, single-staged population balance approach capable of taking into account contact inhibition at confluence. The models' parameters were determined by comparison with experimental data on population expansion starting from single seeding concentration. Reliability of the models was tested by predicting cell proliferation carried out starting from different seeding concentrations.

RESULTS AND DISCUSSION

It was found that the proposed population balance modelling approach was successful in predicting the experimental data over the whole range of initial cell numbers investigated, while prediction capability of phenomenological logistic equation was more limited.

Phenomenological approach to mechanical damage growth analysis

The problem of characterizing damage evolution in a generic material is addressed with the aim of tracing it back to existing growth models in other fields of research. Based on energetic considerations, a system evolution equation is derived for a generic damage indicator describing a material system subjected to an increasing external stress. The latter is found to fit into the framework of a recently developed phenomenological universality (PUN) approach and, more specifically, the so-called U2 class. Analytical results are confirmed by numerical simulations based on a fiber-bundle model and statistically assigned local strengths at the microscale. The fits with numerical data prove, with an excellent degree of reliability, that the typical evolution of the damage indicator belongs to the aforementioned PUN class. Applications of this result are briefly discussed and suggested.

Scaling, growth and cyclicity in biology: a new computational approach

Background

The Phenomenological Universalities approach has been developed by P.P. Delsanto and collaborators during the past 2–3 years. It represents a new tool for the analysis of experimental datasets and cross-fertilization among different fields, from physics/engineering to medicine and social sciences. In fact, it allows similarities to be detected among datasets in totally different fields and acts upon them as a magnifying glass, enabling all the available information to be extracted in a simple way. In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.

Results

The main goal of the present contribution is to extend the applicability of the new approach to the study of problems of growth with cyclicity, which are of particular relevance in the fields of biology and medicine.

Conclusion

As an example of its implementation, the method is applied to the analysis of human growth curves. The excellent quality of the results (R² = 0.988) demonstrates the usefulness and reliability of the approach.

A unified model of sigmoid tumour growth based on cell proliferation and quiescence

OBJECTIVES

A class of sigmoid functions designated generalized von Bertalanffy, Gompertzian and generalized Logistic has been used to fit tumour growth data. Various models have been proposed to explain the biological significance and foundations of these functions. However, no model has been found to fully explain all three or the relationships between them.

MATERIALS AND METHODS

We propose a simple cancer cell population dynamics model that provides a biological interpretation for these sigmoids' ability to represent tumour growth.

RESULTS AND CONCLUSIONS

We show that the three sigmoids can be derived from the model and are in fact a single solution subject to the continuous variation of parameters describing the decay of the proliferation fraction and/or cell quiescence. We use the model to generate proliferation fraction profiles for each sigmoid and comment on the significance of the differences relative to cell cycle-specific and non-cell cycle-specific therapies.

Classification scheme for phenomenological universalities in growth problems in physics and other sciences

A classification in universality classes of broad categories of phenomenologies, belonging to physics and other disciplines, may be very useful for a cross fertilization among them and for the purpose of pattern recognition and interpretation of experimental data. We present here a simple scheme for the classification of nonlinear growth problems. The success of the scheme in predicting and characterizing the well known Gompertz, West, and logistic models, suggests to us the study of a hitherto unexplored class of nonlinear growth problems.