Oxygen transport in a three-dimensional microvascular network incorporated with early tumour growth and preexisting vessel cooption: Numerical simulation study

We propose a dynamic mathematical model of tissue oxygen transport by a preexisting three-dimensional microvascular network which provides nutrients for an in situ cancer at the very early stage of primary microtumour growth. The expanding tumour consumes oxygen during its invasion to the surrounding tissues and cooption of host vessels. The preexisting vessel cooption, remodelling and collapse are modelled by the changes of haemodynamic conditions due to the growing tumour. A detailed computational model of oxygen transport in tumour tissue is developed by considering (a) the time-varying oxygen advection diffusion equation within the microvessel segments, (b) the oxygen flux across the vessel walls, and (c) the oxygen diffusion and consumption with in the tumour and surrounding healthy tissue. The results show the oxygen concentration distribution at different time points of early tumour growth. In addition, the influence of preexisting vessel density on the oxygen transport has been discussed. The proposed model not only provides a quantitative approach for investigating the interactions between tumour growth and oxygen delivery, but also is extendable to model other molecules or chemotherapeutic drug transport in the future study.

Fatigue crack growth under pulsatile pressure and plaque rupture

Identification of vulnerable plaque pre-rupture is extremely important for patient risk stratification. The mechanism of plaque rupture is still not entirely clear, but it is thought to be a process involving multiple factors. From a biomechanical viewpoint, plaque rupture is usually seen as a structural failure when the plaque cannot resist the hemodynamic blood pressure and shear stress exerted on it. However, the cardiovascular system is naturally a cyclical hemodynamic environment, and myocardial infarction can be a symptomatically quiescent but potentially progressive process when plaque ruptures at stresses much lower than its strength. Therefore, fatigue accumulation is a possible mechanism for plaque rupture. In this study, a crack growth model was developed, and the previously-mentioned hypothesis was tested by conducting a comparative study between 18 symptomatic and 16 asymptomatic patients with carotid stenosis.

A hybrid cellular automata model of multicellular tumour spheroid growth in hypoxic microenvironment

A three-dimensional hybrid cellular automata (CA) model is developed to study the dynamic process of multicellular tumour spheroid (MTS) growth by introducing hypoxia as an important microenvironment factor which influences cell migration and cell phenotype expression. The model enables us to examine the effects of different hypoxic environments on the growth history of the MTS and to study the dynamic interactions between MTS growth and chemical environments. The results include the spatial distribution of different phenotypes of tumour cells and associated oxygen concentration distributions under hypoxic conditions. The discussion of the model system responses to the varied hypoxic conditions reveals that the improvement of the resistance of tumour cells to a hypoxic environment may be important in the tumour normalization therapy.

3D numerical simulation of avascular tumour growth: effect of hypoxic micro-environment in host tissue

A three-dimensional (3D) mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors (VEGFs), and the discrete part of tumour cells (TCs) and blood vessel networks. The simulation shows the dynamic process of avascular tumour growth from a few initial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of the TCs, more and more host vessels collapse due to the stress caused by the growing tumour. In addition, the consumption of oxygen expands with the enlarged tumour region. The study also discusses the effects of certain factors on tumour growth, including the density and configuration of preexisting vessel networks and the blood oxygen content. The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumour metastasis and the initialization of tumour angiogenesis.

Computed wall stress may predict the growth of abdominal aortic aneurysm

Growth rate of abdominal aortic aneurysm (AAA) is thought to be an important indicator of the potential risk of rupture. Wall stress is also thought to be a trigger for its rupture. However, stress change during the expansion of an AAA is unclear. Forty-four patients with AAAs were included in this longitudinal follow-up study. They were assessed by serial abdominal ultrasonography and computerized tomography (CT) scans if a critical size was reached or a rapid expansion occurred. Patient-specific 3-dimensional AAA geometries were reconstructed from the follow-up CT images. Structural analysis was performed to calculate the wall stresses of the AAA models at both baseline and final visit. A non-linear large-strain finite element method was used to compute the wall stress distribution. The average growth rate was 0.66cm/year (range 0-1.32 cm/year). A significantly positive correlation between shoulder tress at baseline and growth rate was found (r=0.342; p=0.02). A higher shoulder stress is associated with a rapidly expanding AAA. Therefore, it may be useful for estimating the growth expansion of AAAs and further risk stratification of patients with AAAs.

Comparative proteomics of uropathogenic Escherichia coli during growth in human urine identify UCA-like (UCL) fimbriae as an adherence factor involved in biofilm formation and binding to uroepithelial cells

Uropathogenic Escherichia coli (UPEC) are the primary cause of urinary tract infection (UTI) in humans. For the successful colonisation of the human urinary tract, UPEC employ a diverse collection of secreted or surface-exposed virulence factors including toxins, iron acquisition systems and adhesins. In this study, a comparative proteomic approach was utilised to define the UPEC pan and core surface proteome following growth in pooled human urine. Identified proteins were investigated for subcellular origin, prevalence and homology to characterised virulence factors. Fourteen core surface proteins were identified, as well as eleven iron uptake receptor proteins and four distinct fimbrial types, including type 1, P, F1C/S and a previously uncharacterised fimbrial type, designated UCA-like (UCL) fimbriae in this study. These pathogenicity island (PAI)-associated fimbriae are related to UCA fimbriae of Proteus mirabilis, associated with UPEC and exclusively found in members of the E. coli B2 and D phylogroup. We further demonstrated that UCL fimbriae promote significant biofilm formation on abiotic surfaces and mediate specific attachment to exfoliated human uroepithelial cells. Combined, this study has defined the surface proteomic profiles and core surface proteome of UPEC during growth in human urine and identified a new type of fimbriae that may contribute to UTI.

Rapid assessment of genotype-by-environment interactions and heritability for growth rate in aquaculture species using in vitro fertilisation and DNA tagging

Commercial environments may receive only a fraction of expected genetic gains for growth rate as predicted from the selection environment This fraction is the result of undesirable genotype-by-environment interactions (G x E) and measured by the genetic correlation (r(g)) of growth between environments. Rapid estimates of genetic correlation achieved in one generation are notoriously difficult to estimate with precision. A new design is proposed where genetic correlations can be estimated by utilising artificial mating from cryopreserved semen and unfertilised eggs stripped from a single female. We compare a traditional phenotype analysis of growth to a threshold model where only the largest fish are genotyped for sire identification. The threshold model was robust to differences in family mortality differing up to 30%. The design is unique as it negates potential re-ranking of families caused by an interaction between common maternal environmental effects and growing environment. The design is suitable for rapid assessment of G x E over one generation with a true 0.70 genetic correlation yielding standard errors as low as 0.07. Different design scenarios were tested for bias and accuracy with a range of heritability values, number of half-sib families created, number of progeny within each full-sib family, number of fish genotyped, number of fish stocked, differing family survival rates and at various simulated genetic correlation levels

Stochastic growth models for analyzing crustacean data

The contemporary methodology for growth models of organisms is based on continuous trajectories and thus it hinders us from modelling stepwise growth in crustacean populations. Growth models for fish are normally assumed to follow a continuous function, but a different type of model is needed for crustacean growth. Crustaceans must moult in order for them to grow. The growth of crustaceans is a discontinuous process due to the periodical shedding of the exoskeleton in moulting. The stepwise growth of crustaceans through the moulting process makes the growth estimation more complex. Stochastic approaches can be used to model discontinuous growth or what are commonly known as "jumps" (Figure 1). However, in stochastic growth model we need to ensure that the stochastic growth model results in only positive jumps. In view of this, we will introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that will assist in modelling crustacean growth for better understanding of the individual variability and stochasticity in moulting periods and increments. We develop the estimation methods for parameter estimation and illustrate them with the help of a dataset from laboratory experiments. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, which can be found between Australia and Papua New Guinea. Due to the presence of sex effects on the growth (Munday et al., 2004), we estimate the growth parameters separately for each sex. Since all hard parts are shed too often, the exact age determination of a lobster can be challenging. However, the growth parameters for the aforementioned moult processes from tank data being able to estimate through: (i) inter-moult periods, and (ii) moult increment. We will attempt to derive a joint density, which is made up of two functions: one for moult increments and the other for time intervals between moults. We claim these functions are conditionally independent given pre-moult length and the inter-moult periods. The variables moult increments and inter-moult periods are said to be independent because of the Markov property or conditional probability. Hence, the parameters in each function can be estimated separately. Subsequently, we integrate both of the functions through a Monte Carlo method. We can therefore obtain a population mean for crustacean growth (e. g. red curve in Figure 1). [GRAPHICS]

Study of Pinna nobilis growth from inner record: How biased are posterior adductor muscle scars estimates?

Previous studies have shown that the external growth records of the posterior adductor muscle scar (PAMS) of the bivalve Pinna nobilis are incomplete and do not produce accurate age estimations. We have developed a new methodology to study age and growth using the inner record of the PAMS, which avoids the necessity of costly in situ shell measurements or isotopic studies. Using the inner record we identified the positions of PAMS previously obscured by nacre and estimated the number of missing records in adult specimens with strong abrasion of the calcite layer in the anterior portion of the shell. The study of the PAMS and inner record of two shells that were 6 years old when collected showed that only 2 and 3 PAMS were observed, while 6 inner records could be counted, thus confirming our working methodology. Growth parameters of a P. nobilis population located in Moraira, Spain (western Mediterranean) were estimated with the new methodology and compared to those obtained using PAMS data and in situ measurements. For the comparisons, we applied different models considering the data alternatively as length-at-age (LA) and tag-recapture (TR). Among every method we tested to fit the Von Bertalanffy growth model, we observed that LA data from inner record fitted to the model using non-linear mixed effects and the estimation of missing records using the calcite width was the most appropriate. The equation obtained with this method, L = 573*(1 - e(-0.16(t-0.02))), is very similar to that calculated previously from in situ measurements for the same population.

A maximum likelihood approach for estimating growth from tag–recapture data

The Fabens method is commonly used to estimate growth parameters k and l infinity in the von Bertalanffy model from tag-recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use nf thp measurements at tno and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag-recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.

Accounting for individual variability in the von Bertalanffy growth model

Estimation of von Bertalanffy growth parameters has received considerable attention in fisheries research. Since Sainsbury (1980, Can. J. Fish. Aquat. Sci. 37: 241-247) much of this research effort has centered on accounting for individual variability in the growth parameters. In this paper we demonstrate that, in analysis of tagging data, Sainsbury's method and its derivatives do not, in general, satisfactorily account for individual variability in growth, leading to inconsistent parameter estimates (the bias does not tend to zero as sample size increases to infinity). The bias arises because these methods do not use appropriate conditional expectations as a basis for estimation. This bias is found to be similar to that of the Fabens method. Such methods would be appropriate only under the assumption that the individual growth parameters that generate the growth increment were independent of the growth parameters that generated the initial length. However, such an assumption would be unrealistic. The results are derived analytically, and illustrated with a simulation study. Until techniques that take full account of the appropriate conditioning have been developed, the effect of individual variability on growth has yet to be fully understood.

Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L-infinity. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Population structure, mortality and growth of Pinna nobilis Linnaeus, 1758 (Mollusca, Bivalvia) at different depths in Moraira bay (Alicante, Western Mediterranean)

An investigation to characterize the causes of Pinna nobilis population structure in Moraira bay (Western Mediterranean) was developed. Individuals of two areas of the same Posidonia meadow, located at different depths (A1, -13 and A2, -6 m), were inventoried, tagged, their positions accurately recorded and monitored from July 1997 to July 2002. On each area, different aspects of population demography were studied (i.e. spatial distribution, size structure, displacement evidences, mortality, growth and shell orientation). A comparison between both groups of individuals was carried out, finding important differences between them. In A1, the individuals were more aggregated and mean and maximum size were higher (A1, 10.3 and A2, 6 individuals/100 m(2); A1, x = 47.2 +/- 9.9; A2, x = 29.8 +/- 7.4 cm, P < 0.001, respectively). In A2, growth rate and mortality were higher, the latter concentrated on the largest individuals, in contrast to A1, where the smallest individuals had the higher mortality rate [A1, L = 56.03(1 - e(-0.17t)); A2, L = 37.59(1 - e(-0.40t)), P < 0.001; mean annual mortality A1: 32 dead individuals out of 135, 23.7% and A2: 16 dead individuals out of 36, 44.4%, and total mortality coefficients (z), z(A1(-30)) = 0.28, z(A1(31-45)) = 0.05, z(A1(46-)) = 0.08; z(A2(-30)) = 0.15, z(A2(31-45)) = 0.25]. A common shell orientation N-S, coincident with the maximum shore exposure, was observed in A2. Spatial distribution in both areas showed not enough evidence to discard a random distribution of the individuals, despite the greater aggregation on the deeper area (A1) (A1, chi(2) = 0.41, df = 3, P > 0.5, A2, chi(2)= 0.98, df = 2 and 0.3 < P < 0.5). The obtained results have demonstrated that the depth-related size segregation usually shown by P. nobilis is mainly caused by differences in mortality and growth among individuals located at different depths, rather than by the active displacement of individuals previously reported in the literature. Furthermore, dwarf individuals are observed in shallower levels and as a consequence, the relationship between size and age are not comparable even among groups of individuals inhabiting the same meadow at different depths. The final causes of the differences on mortality and growth are also discussed.

Evaluation of growth and changes in body composition following neonatal diagnosis of cystic fibrosis

Early deficits in nutritional status that might require specific treatment and early response to nutritional therapy were studied longitudinally in 25 infants with cystic fibrosis (CF) diagnosed by neonatal screening, using anthropometric and research body composition methodology, and evaluation of pancreatic function. At the time of confirmed diagnosis (mean 5.4 weeks), body mass, length, total body fat (TBF), and total body potassium (TBK) were all significantly reduced. Following diagnosis and commencement of therapy there was a normalization of weight, length, and TBK by 6-12 months of age, indicating catch-up growth. But in some individuals the response was incomplete, and as a group, mean total body fat remained significantly lower than normal at 1 year of age. Seven of 25 (28%) were pancreatic sufficient at diagnosis, and all but one had evidence of declining pancreatic function requiring the institution of pancreatic enzyme therapy during the next 1-9 months. The median age of commencement of enzyme therapy was 10 weeks (range 5 weeks to 11 months). These longitudinal assessments emphasize the dynamic changes occurring in absorptive function, body composition, and nutritional status following neonatal diagnosis of cystic fibrosis and may reflect previously described abnormalities of energy metabolism in this age group. Abnormal body composition is evident in most CF infants following diagnosis by neonatal screening but pancreatic damage may still be evolving. We suggest that early active nutritional therapy and surveillance for changes in pancreatic function are warranted in CF infants diagnosed by neonatal screening.