Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Klassifizierung von pflanzlichen Produkten aus ökologischem und konventionellem Anbau durch Messung sekundärer Pflanzenstoffe

The content of secondary plant compounds in plants is influenced by various environmental factors. Cultivation and fertilization are factors which are characteristic for the farming system organic or conventional. Within a german governmental funded project (BÖL02OE170/F) carrot, maize and wheat samples from different farming systems (defined trials and farm pairs) are differentiated and classified using their polyphenolic and carotenoid contents and profiles, respectively. The samples from organic farming could be differentiated from samples which were conventionally grown as statistical significant for carrot and wheat samples in a two year repetition. The samples could be classified by both, polyphenolic as well as carotenoid profiles. The sum parameters only can not be applied for the differentiation and classification of the samples. Factors like cultivar and site have a strong influence on the classification. Therefore for the classification of the carrot samples according to the farming systems land site must be included

Gas hydrate systems respond slowly to seafloor warming

In a marine environment, gas hydrates are stable at certain pressure (sea level) and temperature (bottom water temperature) conditions. Changes in these conditions may result in the destabilization of the gas hydrates. In this study we investigate the temporal response of a continental margin gas hydrate reservoir to changes in the pressure and/or temperature regime, considering the latent heat of hydrate dissociation and the long response times to conductive heat transport in submarine sediments. Gas hydrates and the surrounding sediments do not instantly respond to changing environmental conditions. A vertical subsoil column without gas hydrates needs more than 5,000 years to adapt its temperature profile to an increase in seafloor temperature. A vertical subsoil column containing gas hydrates has the same response time if the stability of the hydrates is not affected. Although, when gas hydrates stability is affected due to changes in their environment, the response time to these changes is extended. Destabilized gas hydrates will dissociate into methane gas and water. The dissociation process happens at a constant temperature and requires a lot of energy (heat). Dissociation of gas hydrates thus delays the response time of the surrounding subsoil; up to 100,000 years may pass before the temperature profile completely adapted to the changed environmental parameters. Because of this slow response to changes in environmental parameters, gas hydrate dissociation cannot be regarded as the trigger to global warming at the end of glacial and stadial periods and gas hydrate dissociation cannot be responsible for the high observed atmospheric methane concentrations in ice core records, as has been postulated in a number of high-profile publications