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

Background: Metastasis 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. Methods: The 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. Results: The 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. Conclusion: The simulation results indicate that for this particular case of a hepatocellular carcinoma late metastases, i.e.

The proportion of cancer-related entries in PubMed has increased considerably; is cancer truly "The Emperor of All Maladies"?

In this work, the public database of biomedical literature PubMed was mined using queries with combinations of keywords and year restrictions. It was found that the proportion of Cancer-related entries per year in PubMed has risen from around 6% in 1950 to more than 16% in 2016. This increase is not shared by other conditions such as AIDS, Malaria, Tuberculosis, Diabetes, Cardiovascular, Stroke and Infection some of which have, on the contrary, decreased as a proportion of the total entries per year. Organ-related queries were performed to analyse the variation of some specific cancers. A series of queries related to incidence, funding, and relationship with DNA, Computing and Mathematics, were performed to test correlation between the keywords, with the hope of elucidating the cause behind the rise of Cancer in PubMed. Interestingly, the proportion of Cancer-related entries that contain "DNA", "Computational" or "Mathematical" have increased, which suggests that the impact of these scientific advances on Cancer has been stronger than in other conditions. It is important to highlight that the results obtained with the data mining approach here presented are limited to the presence or absence of the keywords on a single, yet extensive, database. Therefore, results should be observed with caution. All the data used for this work is publicly available through PubMed and the UK's Office for National Statistics. All queries and figures were generated with the software platform Matlab and the files are available as supplementary material

Une application du théorème ergodique sous-additif à la théorie métrique des fractions continues

RésuméFor any irrationalx∈[0,1] we denote bypn(x)/qn(x),n=1,2,… the sequence of its continued fraction convergents and defineθn(x) ≔qn|qnx−pn|. Also letT: [0,1]→[0,1] be defined byT(0)=0 andT(x)=1/x−[1/x] ifx≠0. For some random variablesX1,X2,…, which are connected with the regular continued fraction expansion, the subadditive ergodic theorem yields to the existence of a functionωsatisfying: for allz∈R,limn→+∞1n#{1⩽i⩽n/Xi(z)⩽z}=ω(z) for almost everyx.In particular, forXn=θn, using this study and a result of Knuth, we give another proof of the following conjecture of Lenstra (the first proof of this conjecture has been given by Bosma, Jager, and Wiedijk): for allz∈[0,1],[formula]for almost everyx. Furthermore, forXn=θn∘TnandXn=(qn−1/qn)∘Tn, the functionsωare explicitly determined. The above results show that the subadditive ergodic theorem can be useful in the metric theory of continued fraction

Metrical properties of some random variables connected with the continued fraction expansion

AbstractFor certain random variables X1,X2,… which can be expressed by means of the natural extension of the Gauss transformation of a continued fraction, we prove that for all z ϵ R and for all probability measures on [0, 1] absolutely continuous with respect to the Lebesgue measure, the probabilities P(Xn ≤ z) converge when n → ∞. The limit can be determined explicitly

Sur les grands quotients partiels du développement en fraction continue

AbstractIn this paper we obtain some metrics results about large partial quotients in the continued fraction expansion

Mathematical optimisation of the cisplatin plus etoposide combination for managing extensive-stage small-cell lung cancer patients

BACKGROUND: Small-cell lung cancer (SCLC) represents one of the most aggressive forms of lung cancer. Despite the fair sensitivity of SCLC to chemotherapy and radiotherapy, the current standard treatment regimens have modest survival rates and are associated with potential life-threatening adverse events. Therefore, research into new optimised regimens that increase drug efficacy while respecting toxicity constraints is of primary importance. METHODS: A PK/PD model for the combination of cisplatin and etoposide to treat extensive-stage SCLC patients was generated. The model takes into consideration both the efficacy of the drugs and their haematological toxicity. Using optimisation techniques, the model can be used to propose new regimens. RESULTS: Three new regimens with varying timing for combining cisplatin and etoposide have been generated that respect haematological toxicity constraints and achieve better or similar tumour regression. The proposed regimens are: (1) Protocol OP1: etoposide 80 mg m(−2) over 1 h D1, followed by a long infusion 12 h later (over 3 days) of 160 mg m(−2) plus cisplatin 80 mg m(−2) over 1 h D1, D1–D1 21 days; (2) Protocol OP2: etoposide 80 mg m(−2) over 1 h D1, followed by a long infusion 12 h later (over 4 days) of 300 mg m(−2) plus cisplatin 100 mg m(−2) over 1 h D1, D1–D1 21 days; and (3) Protocol OP3: etoposide 40 mg m(−2) over 1 h, followed by a long infusion 6 h later (3 days) of 105 mg m(−2) plus cisplatin 50 mg m(−2) over 1 h, D1–D1 14 days. CONCLUSIONS: Mathematical modelling can help optimise the design of new cisplatin plus etoposide regimens for managing extensive-stage SCLC patients