Estimating the number of motor units using random sums with independently thinned terms

The problem of estimating the numbers of motor units N in a muscle is embedded in a general stochastic model using the notion of thinning from point process theory. In the paper a new moment type estimator for the numbers of motor units in a muscle is denned, which is derived using random sums with independently thinned terms. Asymptotic normality of the estimator is shown and its practical value is demonstrated with bootstrap and approximative confidence intervals for a data set from a 31-year-old healthy right-handed, female volunteer. Moreover simulation results are presented and Monte-Carlo based quantiles, means, and variances are calculated for N in{300,600,1000}.

The role of the number of uninvolved lymph nodes in predicting locoregional recurrence in breast cancer

PURPOSE: To identify groups of early breast cancer patients with substantial risk (10-year risk > 20%) for locoregional failure (LRF) who might benefit from postmastectomy radiotherapy (RT). PATIENTS AND METHODS: Prognostic factors for LRF were evaluated among 6,660 patients (2,588 node-negative patients, 4,072 node-positive patients) in International Breast Cancer Study Group Trials I to IX treated with chemotherapy and/or endocrine therapy, and observed for a median of 14 years. In total, 1,251 LRFs were detected. All patients were treated with mastectomy without RT. RESULTS: No group with 10-year LRF risk exceeding 20% was found among patients with node-negative disease. Among patients with node-positive breast cancer, increasing numbers of uninvolved nodes were significantly associated with decreased risk of LRF, even after adjustment for other prognostic factors. The highest quartile of uninvolved nodes was compared with the lowest quartile. Among premenopausal patients, LRF risk was decreased by 35% (P = .0010); among postmenopausal patients, LRF risk was decreased by 46% (P < .0001). The 10-year cumulative incidence of LRF was 20% among patients with one to three involved lymph nodes and fewer than 10 uninvolved nodes. Age younger than 40 years and vessel invasion were also associated significantly with increased risk. Among patients with node-positive disease, overall survival was significantly greater in those with higher numbers of uninvolved nodes examined (P < .0001). CONCLUSION: Patients with one to three involved nodes and a low number of uninvolved nodes, vessel invasion, or young age have an increased risk of LRF and may be candidates for a similar treatment as those with at least four lymph node metastases.

Effect of voluntary exercise on number and volume of cardiomyocytes and their mitochondria in the mouse left ventricle

Voluntary exercise (VE) has a beneficial influence on the heart and mean lifespan. The present study evaluates structural adaptations of cardiomyocytes and their mitochondria due to VE by new, unbiased stereological methods. Female, 7-9-week-old mice were randomly assigned to a control (CG, n = 7) or VE group (EG, n = 7). EG animals were housed in cages with free access to a running wheel and had a mean running distance of 6.7 (1.8) km per day. After 4 weeks, the hearts of all mice were processed for light and electron microscopy. We estimated the number and volume of cardiomyocytes by the disector method and the number and volume of mitochondria by estimation of the Euler number. In comparison to CG, VE did not have an effect on the myocardial volume of the left ventricle (CG: 93 (10), EG: 103 (17) (mm(3))), the number of cardiomyocytes (CG: 2.81 (0.27), EG: 2.82 (0.43) (x10(6))) and their number-weighted mean volume. However, the composition of the cardiomyocytes changed due to VE. The total volume of mitochondria (CG: 21.8 (4.9), EG: 32.2 (4.3) (mm(3)), P < 0.01) and the total number (CG: 3.76 (0.44), EG: 7.02 (1.13) (x10(10)), P < 0.001) were significantly higher in EG than in CG. The mean number-weighted mitochondrial volume was smaller in EG than in CG (P < 0.05). In summary, VE does not alter ventricular volume nor cardiomyocyte volume or number but the oxidative capacity of cardiomyocytes by an increased mitochondrial number and total volume in the left ventricle. These structural changes may participate in the beneficial effects of VE.

Mothers adjust egg size to helper number in a cooperatively breeding cichlid

Mothers should adjust the size of propagules to the selective forces to which these offspring will be exposed. Usually, a larger propagule size is favored when young are exposed to high mortality risk or conspecific competition. Here we test 2 predictions on how egg size should vary with these selective agents. When offspring are cared for by parents and/or alloparents, protection may reduce the predation risk to young, which may allow mothers to invest less per single offspring. In the cooperatively breeding cichlid Neolamprologus pulcher, brood care helpers protect group offspring and reduce the latters' mortality rate. Therefore, females are expected to reduce their investment per egg when more helpers are present. In a first experiment, we tested this prediction by manipulating the helper number. In N. pulcher, helpers compete for dispersal opportunities with similar-sized individuals of neighboring groups. If the expected future competition pressure on young is high, females should increase their investment per offspring to give them a head start. In a second experiment, we tested whether females produce larger eggs when perceived neighbor density is high. Females indeed reduced egg size with increasing helper number. However, we did not detect an effect of local density on egg size, although females took longer to produce the next clutch when local density was high. We argue that females can use the energy saved by adjusting egg size to reduced predation risk to enhance future reproductive output. Adaptive adjustment of offspring size to helper number may be an important, as yet unrecognized, strategy of cooperative breeders.