A superstatistical model of metastasis and cancer survival

Chen, L. Leon; Beck, Christian

doi:10.1016/j.physa.2008.01.116

Cited by 53 publications

(10 citation statements)

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“…The concept has also been useful to analyse hydroclimatic fluctuations [22] as well as the statistics of train delays on the British railway network [38]. There are also medical applications [39].…”

Section: Reminder: What Is Superstatistics?mentioning

confidence: 99%

“…A superstatistical model of the progression of metastasis and the corresponding survival statistics of cancer patients has been developed by Leon Chen & Beck [39]. The final result that comes out of that model is the following prediction for the probability density function of survival time t of a randomly chosen patient who is diagnosed with cancer at t = 0: This can also be written as…”

Section: Survival Statistics Of Cancer Patientsmentioning

confidence: 99%

“…In general, the superstatistical parameter b need not be an inverse temperature but can be an effective parameter in a stochastic differential equation, a volatility in finance or just a local variance parameter extracted from some experimental time series. There are interesting applications in hydrodynamic turbulence [2,19,29,30], defect turbulence [17], cosmic rays [25] and other scattering processes in high-energy physics [31,32], solar flares [18], share price fluctuations [26,27,33,34], random matrix theory [20,21,35], random networks [36], multiplicative-noise stochastic processes [37], wind velocity fluctuations [23,24], hydroclimatic fluctuations [22], the statistics of train departure delays [38] and survival statistics of cancer patients [39]. Maximum entropy principles can be generalized in a suitable way to yield the relevant probability distributions that characterize the various important universality classes in superstatistics [5,[40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

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Generalized statistical mechanics for superstatistical systems

Beck

2011

Phil. Trans. R. Soc. A.

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Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex system onto a system of ordinary statistical mechanics with modified energy levels. We also briefly review recent examples of applications of the superstatistics concept for three very different subject areas, namely train delay statistics, turbulent tracer dynamics and cancer survival statistics.

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Section: Reminder: What Is Superstatistics?mentioning

confidence: 99%

Section: Survival Statistics Of Cancer Patientsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalized statistical mechanics for superstatistical systems

Beck

2011

Phil. Trans. R. Soc. A.

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“…There are numerous applications of superstatistical theory on data analyses, such as sea-level fluctuations [14], high energy physics [15], modeling train delays [16], environmental atmospheric turbulence [17], temperature fluctuations [18], metastasis and cancer survival [19], currents in complex polymers [20], and headway distributions [21].…”

Section: Introductionmentioning

confidence: 99%

A superstatistical model of vehicular traffic flow

Koşun

Ozdemir

2016

Physica A: Statistical Mechanics and its Applications

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In the analysis of vehicular traffic flow, a myriad of techniques have been implemented. In this study, superstatistics is used in modeling the traffic flow on a highway segment. Traffic variables such as vehicular speeds, volume, and headway were collected for three days. For the superstatistical approach, at least two distinct time scales must exist, so that a superposition of nonequilibrium systems assumption could hold. When the slow dynamics of the vehicle speeds exhibit a Gaussian distribution in between the fluctuations of the system at large, one speaks of a relaxation to a local equilibrium. These Gaussian distributions are found with corresponding standard deviations 1/β. This translates into a series of fluctuating beta values, hence the statistics of statistics, superstatistics. The traffic flow model has generated an inverse temperature parameter (beta) distribution as well as the speed distribution. This beta distribution has shown that the fluctuations in beta are distributed with respect to a chi-square distribution. It must be mentioned that two distinct Tsallis q values are specified: one is time-dependent and the other is independent. A ramification of these q values is that the highway segment and the traffic flow generate separate characteristics. This highway segment in question is not only nonadditive in nature, but a nonequilibrium driven system, with frequent relaxations to a Gaussian

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“…A great variety of mathematical models have been developed, ranging from very fine-grained ones that consider very detailed biological and molecular or even genetic characteristics of individual tumour cells [14] to more descriptive models that concentrate on the whole process, like number of cells, size or number of metastases [15] – [17] . All these so far published models only describe a specific aspect of malignant progression, e. g. to model the untreated course [15] , to estimate the survival time [16] , to predict drug pharmacokinetics [18] , [19] or to estimate the effective radiation dose [20] .…”

Section: Introductionmentioning

confidence: 99%

Are Metastases from Metastases Clinical Relevant? Computer Modelling of Cancer Spread in a Case of Hepatocellular Carcinoma

et al. 2012

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BackgroundMetastasis formation remains an enigmatic process and one of the main questions recently asked is whether metastases are able to generate further metastases. Different models have been proposed to answer this question; however, their clinical significance remains unclear. Therefore a computer model was developed that permits comparison of the different models quantitatively with clinical data and that additionally predicts the outcome of treatment interventions.MethodsThe computer model is based on discrete events simulation approach. On the basis of a case from an untreated patient with hepatocellular carcinoma and its multiple metastases in the liver, it was evaluated whether metastases are able to metastasise and in particular if late disseminated tumour cells are still capable to form metastases. Additionally, the resection of the primary tumour was simulated. The simulation results were compared with clinical data.ResultsThe simulation results reveal that the number of metastases varies significantly between scenarios where metastases metastasise and scenarios where they do not. In contrast, the total tumour mass is nearly unaffected by the two different modes of metastasis formation. Furthermore, the results provide evidence that metastasis formation is an early event and that late disseminated tumour cells are still capable of forming metastases. Simulations also allow estimating how the resection of the primary tumour delays the patient's death.ConclusionThe simulation results indicate that for this particular case of a hepatocellular carcinoma late metastases, i.e., metastases from metastases, are irrelevant in terms of total tumour mass. Hence metastases seeded from metastases are clinically irrelevant in our model system. Only the first metastases seeded from the primary tumour contribute significantly to the tumour burden and thus cause the patient's death.

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A superstatistical model of metastasis and cancer survival

Cited by 53 publications

References 35 publications

Generalized statistical mechanics for superstatistical systems

Generalized statistical mechanics for superstatistical systems

A superstatistical model of vehicular traffic flow

Are Metastases from Metastases Clinical Relevant? Computer Modelling of Cancer Spread in a Case of Hepatocellular Carcinoma

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