Maria Teresa Giraudo

A Monte Carlo Method for the Simulation of First Passage Times of Diffusion Processes

A reliable Monte Carlo method for the evaluation of first passage times of diffusion processes through boundaries is proposed. A nested algorithm that simulates the first passage time of a suitable tied-down process is introduced to account for undetected crossings that may occur inside each discretization interval of the stochastic differential equation associated to the diffusion. A detailed analysis of the performances of the algorithm is then carried on both via analytical proofs and by means of some numerical examples. The advantages of the new method with respect to a previously proposed numerical-simulative method for the evaluation of first passage times are discussed. Analytical results on the distribution of tied-down diffusion processes are proved in order to provide a theoretical justification of the Monte Carlo method.

An improved technique for the simulation of first passage times for diffusion processes

Improved simulation schemes for the evaluation of first passage times through boundaries for one dimensional diffusion processes can be obtained taking into account possible crossings that occur inside each simulation interval. Approximated evaluations for the probabilities of such events are proposed and the error connected with their use in a simulation algorithm is discussed. Two examples are finally given to illustrate the features of the method.

Stochastic Integrate and Fire Models: a review on mathematical methods and their applications

Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved and numerical and simulation methods have been developed for their study. Reviews appeared recently collect the main features of these models but do not focus on the methodologies employed to obtain them. Aim of this paper is to fill this gap by upgrading old reviews on this topic. The idea is to collect the existing methods and the available analytical results for the most common one dimensional stochastic Integrate and Fire models to make them available for studies on networks. An effort to unify the mathematical notations is also made. This review is divided in two parts: Derivation of the models with the list of the available closed forms expressions for their characterization; Presentation of the existing mathematical and statistical methods for the study of these models.

Risk of second primary malignancies in women with breast cancer: Results from the European prospective investigation into cancer and nutrition (EPIC).

Women with a diagnosis of breast cancer are at increased risk of second primary cancers, and the identification of risk factors for the latter may have clinical implications. We have followed‐up for 11 years 10,045 women with invasive breast cancer from a European cohort, and identified 492 second primary cancers, including 140 contralateral breast cancers. Expected and observed cases and Standardized Incidence Ratios (SIR) were estimated using Aalen‐Johansen Markovian methods. Information on various risk factors was obtained from detailed questionnaires and anthropometric measurements. Cox proportional hazards regression models were used to estimate the role of risk factors. Women with breast cancer had a 30% excess risk for second malignancies (95% confidence interval—CI 18–42) after excluding contralateral breast cancers. Risk was particularly elevated for colorectal cancer (SIR, 1.71, 95% CI 1.43–2.00), lymphoma (SIR 1.80, 95% CI 1.31–2.40), melanoma (2.12; 1.63–2.70), endometrium (2.18; 1.75–2.70) and kidney cancers (2.40; 1.57–3.52). Risk of second malignancies was positively associated with age at first cancer, body mass index and smoking status, while it was inversely associated with education, post‐menopausal status and a history of full‐term pregnancy. We describe in a large cohort of women with breast cancer a 30% excess of second primaries. Among risk factors for breast cancer, a history of full‐term pregnancy was inversely associated with the risk of second primary cancer.

Chemical-shift and diffusion-weighted magnetic resonance imaging of thymus in myasthenia gravis: usefulness of quantitative assessment.

ObjectivesThe objective of this study was to prospectively investigate the usefulness of chemical-shift and diffusion-weighted (DW) magnetic resonance imaging (MRI) in patients with myasthenia gravis (MG) for distinguishing thymic lymphoid hyperplasia (TLH), normal thymus (NT), and thymoma (THY) by using the signal intensity index (SII) and the apparent diffusion coefficient (ADC). Materials and MethodsWe examined 87 subjects (44 males, 43 females; range, 15–71 years) with generalized MG and antibodies to the acetylcholine receptor seropositivity who underwent surgery. They were divided into a TLH/NT group (A, 64 patients; TLH, 49; NT, 15) and a THY group (B, 24 patients; nonadvanced THY, 15; advanced THY, 9) on the basis of histological findings. One patient with contemporary findings of TLH and nonadvanced THY at histology was listed in both groups (87 subjects, 88 findings). Chemical-shift MRI (CS-MRI) was performed with dual-echo acquisition, and the SII was measured for each subject. Diffusion-weighted MRI was performed at b values of 0, 150, 500, and 800 s/mm2, and the ADC value was obtained on the ADC map after excluding the 0-s/mm2 b value diffusion weighting. All measures were performed independently by 2 radiologists, and interreader agreement was assessed by calculating the intraclass correlation coefficient. Differences on SII and ADC levels between the groups and subgroups were tested using the Student t test. Logistic regression models were estimated, and discrimination abilities were individuated according to the area under the receiver operating characteristic curve (AUROC). The optimal cut points for the differentiation of the groups and subgroups were obtained by using the Youden index. ResultsThe interreader agreement was excellent (intraclass correlation coefficient: SII, 0.998; ADC, 0.944). For CS-MRI, the mean (SD) SII value was significantly different between the groups (A, 36.37% [12.60%]; B, −0.06% [3.85%]; P < 0.001). No overlap in indexes was found with sensitivity, specificity, and cut point of 100%, 100%, and 6.37%, respectively. Conversely, the mean SII value was not different between the subgroups of each group (A, P = 0.607; B, P = 0.252). For DW-MRI, the mean (SD) ADC values were significantly different between the groups (A, 1.92 [0.21] × 10−3·mm2/s; B, 1.36 [0.33] × 10−3 mm2/s; P < 0.001) and between the subgroups of group A (TLH, 1.86 [0.17] × 10−3 mm2/s; NT, 2.10 [0.23] × 10−3 mm2/s; P = 0.002), although overlapped values were found. The AUROC of ADC in discriminating TLH/NT from THY was 0.931 (95% confidence interval, 0.863–0.998), and the optimal cut point for this distinction was 1.625 × 10−3 mm2/s (Youden index, J = 0.760) with sensitivity of 96.8% and specificity of 79.2%. For the subgroups of group A, the AUROC of ADC in discriminating NT from TLH was 0.794 (95% confidence interval, 0.666–0.923), and the optimal cut point for this distinction was 2.01 × 10−3 mm2/s (Youden index, J = 0.458) with sensitivity of 66.7% and specificity of 79.2%. ConclusionsCS-MRI and DW-MRI are both useful tools for examining patients with MG. The SII is more accurate than the ADC to differentiate TLH and NT from THY (AUROC, 1.000 and 0.931, respectively). Furthermore, the ADC is a noninvasive parameter that could be used for distinguishing TLH from NT, which is useful in selecting patients for surgery because, for nonthymomatous MG, acceptable rates of complete stable remission after thymectomy are found in TLH but not in NT.

Jump-diffusion processes as models for neuronal activity☆

Aiming at an improvement of the existing neuronal models, we consider a mixed process ensuing from the superposition of continuous diffusions and of Poisson time-distributed sequence of impulses and focus our attention on the moments of the firing time. In particular, we consider three different instances: the large jumps model in which each jump causes the neuron firing, the reset model characterized by jumps towards the resting potential and a more general model where constant amplitude excitatory and inhibitory jumps are superimposed on diffusion. By resorting to analytical arguments and to numerical computations, the main behavioral differences of the considered models are outlined.

Simulation methods in neuronal modelling

The interspike distribution can be modelled as the first-passage-time distribution of suitable diffusion processes with biologically meaningful boundaries. Since various mathematical difficulties arise when one attempts to obtain closed form solutions for first-passage-time problems, one can resort to simulation methods in order to study the problem. In this paper we pinpoint possible overestimations connected with simulations of first-passage-times for diffusion processes and propose a suitable simulation technique to determine the moments and the distribution of the firing times. After checking the validity of the proposed method in some instances where numerical evaluations for such quantities are available, we apply the simulation algorithm to model the spiking activity by means of a particular diffusion process constrained by a suitable time varying threshold.

Effects of random jumps on a very simple neuronal diffusion model.

The effects of taking into account in a perfect integrate and fire model of neuronal activity the spatial localization of the synapses are studied by superposing to the diffusion a simple discrete jump component. Different criteria are employed to assess the role of excitatory and inhibitory discrete contributions. Comparisons are performed with respect to the case where contributions coming from synapses more distal from the trigger zone are summed up in a continuous model. A systematic study of the output frequency and of the inter spike interval coefficient of variation (CV) is performed by means of examples as the model parameters are varied.

How sample paths of leaky integrate-and-fire models are influenced by the presence of a firing threshold

Neural membrane potential data are necessarily conditional on observation being prior to a firing time. In a stochastic leaky integrate-and-fire model, this corresponds to conditioning the process on not crossing a boundary. In the literature, simulation and estimation have almost always been done using unconditioned processes. In this letter, we determine the stochastic differential equations of a diffusion process conditioned to stay below a level S up to a fixed time t1 and of a diffusion process conditioned to cross the boundary for the first time at t1. This allows simulation of sample paths and identification of the corresponding mean process. Differences between the mean of free and conditioned processes are illustrated, as well as the role of noise in increasing these differences.

Reticulocyte parameters: Markers of early response to oral treatment in children with severe iron-deficiency anemia

The aim of the present study was to determine the effects of exclusive oral iron supplementation (iron sulphate 2 mg/kg/die) in asymptomatic children with severe iron-deficiency anemia [median hemoglobin (Hb) level before treatment 6.3 g/dL; range 4.5 to 7 g/dL] and to investigate the accuracy of Hb, reticulocyte hemoglobin content (CHr), and absolute reticulocyte count (ARC) as markers for monitoring early response to treatment. The increase in ARC and CHr was statistically significant at day +3. There was a significant association between suitable logarithmic functions of the percentage increase in CHr and ARC at day +3 and the fraction of required Hb increase compared with baseline to reach the mean reference value for age and sex at day +14. If these results are confirmed in a larger population, ARC and CHr could be considered affordable and widely available markers to detect early responders to oral iron therapy, and to switch unresponsive children to parenteral iron supplementation or transfusion.