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PubMed1993

Evaluation of reconstruction algorithms in SPECT neuroimaging: II. Computation of deterministic and statistical error components.

For the reconstruction of a series of computer simulations of statistically-independent noisy realizations of projection data, the total error of the ith reconstructed voxel in the rth realization, Er,i, is composed of the statistical error, Sr,i, and the (deterministic) inaccuracy in the presence of noise, Di+. Di+ is composed of the (deterministic) inaccuracy in the absence of noise, Di-, and the (deterministic) additional inaccuracy in the presence of noise, Di delta. E(Er,i), the theoretical expected value of Er,i, is given by E(Er,i) = E(Di+) + E(Sr,i). Similarly, E(Di+) = E(Di-) + E(Di delta). The corresponding theoretical variances are given by sigma 2(Er,i) = sigma 2(Di+)+2C(Di+, Sr,i)+ sigma 2(Sr,i) and sigma 2(Di+) = sigma 2(Di-)+2C(Di-, Di delta)+ sigma 2(Di delta), where C(.,.) is the covariance. We have utilized these relationships to evaluate three reconstruction algorithms: standard filtered back projection (FBP), an iterative reconstruction algorithm (IRA), and a version of the IRA which incorporates a linear transformation (TIRA). For simulated brain images in which the projection data (500,000 events detected) were degraded as the result of convolution of the true radioactivity distribution with a realistic distance-dependent detector response function, for FBP the major contribution to both E(Er,i) and sigma 2(Er,i) was Di-. For the IRA and TIRA, the major contributions to E(Er,i) were Di- and Di delta, and the major contribution to sigma 2(Er,i) was Sr,i, although in some cases Di delta was also a contributing factor. Furthermore, the errors due to sigma 2(Er,i) (that is, [sigma 2(Er,i)]0.5) were more severe than those due to E(Er,i). We conclude that, in contrast to FBP, the effects of statistical noise are an important limiting factor for the IRA and TIRA, and that the future development of tomographic devices with higher sensitivity would expand the quantitative potential of the IRA and TIRA.

Algorithms↗

PubMed1991

Use of a simulation model to evaluate the influence of reproductive performance and management decisions on net income in beef production.

A stochastic dynamic model of reproduction and a deterministic cow-herd economic simulation model were used to evaluate how management decisions and reproductive performance interact to influence net income in a cow-calf operation (1,000 cows) for 1 yr of production. The stochastic model was used to determine herd performance when length of breeding season (45, 70, or 120 d) interacted with three postpartum intervals of anestrus (48, 65, or 90 d) and three conception rates at first service (60, 70, or 80%). Short, moderate, and long postpartum intervals were used to reflect differences in reproductive performance. In addition, replacement heifers were bred beginning either 3 wk ahead of the cow herd or at the same time as the cow herd. Fifty-four simulations were generated. Inputs into the economic model were herd performance, livestock and feed prices, nonfeed costs, and feed requirements for 1 yr of production. Feed requirements were calculated separately for each postpartum interval to reflect three different body condition scores, thin, moderate, and good, to correspond with long, moderate, and short postpartum intervals. Net income was greatest with 70-d breeding seasons when the postpartum interval was short or moderate. When the postpartum interval was long, net income was greatest with 120-d breeding seasons because pregnancy rates, as a result of the long breeding season, were highest and feed costs were lowest for thin cows. Overall, net income was greatest when cows were managed to have postpartum intervals of moderate length. Breeding heifers 3 wk before the cows provided the most economic benefit with long postpartum intervals.

Age Factors↗

PubMed2003

Dynamics of deterministic and stochastic paired excitatory-inhibitory delayed feedback.

We examine the effects of paired delayed excitatory and inhibitory feedback on a single integrate-and-fire neuron with reversal potentials embedded within a feedback network. These effects are studied using bifurcation theory and numerical analysis. The feedback occurs through modulation of the excitatory and inhibitory conductances by the previous firing history of the neuron; as a consequence, the feedback also modifies the membrane time constant. Such paired feedback is ubiquitous in the nervous system. We assume that the feedback dynamics are slower than the membrane time constant, which leads to a rate model formulation. Our article provides an extensive analysis of the possible dynamical behaviors of such simple yet realistic neural loops as a function of the balance between positive and negative feedback, with and without noise, and offers insight into the potential behaviors such loops can exhibit in response to time-varying external inputs. With excitatory feedback, the system can be quiescent, can be periodically firing, or can exhibit bistability between these two states. With inhibitory feedback, quiescence, oscillatory firing rates, and bistability between constant and oscillatory firing-rate solutions are possible. The general case of paired feedback exhibits a blend of the behaviors seen in the extreme cases and can produce chaotic firing. We further derive a condition for a dynamically balanced paired feedback in which there is neither bistability nor oscillations. We also show how a biophysically plausible smoothing of the firing function by noise can modify the existence and stability of fixed points and oscillations of the system. We take advantage in our mathematical analysis of the existence of an invariant manifold, which reduces the dimensionality of the dynamics, and prove the stability of this manifold. The novel computational challenges involved in analyzing such dynamics with and without noise are also described. Our results demonstrate that a paired delayed feedback loop can act as a sophisticated computational unit, capable of switching between a variety of behaviors depending on the input current, the relative strengths and asymmetry of the two parallel feedback pathways, and the delay distributions and noise level.

Action Potentials↗

PubMed1994

Noise properties of the EM algorithm: I. Theory.

The expectation-maximization (EM) algorithm is an important tool for maximum-likelihood (ML) estimation and image reconstruction, especially in medical imaging. It is a non-linear iterative algorithm that attempts to find the ML estimate of the object that produced a data set. The convergence of the algorithm and other deterministic properties are well established, but relatively little is known about how noise in the data influences noise in the final reconstructed image. In this paper we present a detailed treatment of these statistical properties. The specific application we have in mind is image reconstruction in emission tomography, but the results are valid for any application of the EM algorithm in which the data set can be described by Poisson statistics. We show that the probability density function for the grey level at a pixel in the image is well approximated by a log-normal law. An expression is derived for the variance of the grey level and for pixel-to-pixel covariance. The variance increases rapidly with iteration number at first, but eventually saturates as the ML estimate is approached. Moreover, the variance at any iteration number has a factor proportional to the square of the mean image (though other factors may also depend on the mean image), so a map of the standard deviation resembles the object itself. Thus low-intensity regions of the image tend to have low noise. By contrast, linear reconstruction methods, such as filtered back-projection in tomography, show a much more global noise pattern, with high-intensity regions of the object contributing to noise at rather distant low-intensity regions. The theoretical results of this paper depend on two approximations, but in the second paper in this series we demonstrate through Monte Carlo simulation that the approximations are justified over a wide range of conditions in emission tomography. The theory can, therefore, be used as a basis for calculation of objective figures of merit for image quality.

Algorithms↗

PubMed2004

Estimation of patient dose and associated radiogenic risks from fluoroscopically guided pedicle screw insertion.

STUDY DESIGN: An experimental model for the assessment of patient dose and associated radiogenic risks associated with pedicle screw internal fixation surgical procedures. OBJECTIVES: To provide data for the accurate determination of patient effective dose, gonadal dose, and entrance skin dose from fluoroscopically assisted pedicle screw insertion procedures and to investigate the potential of both stochastic and deterministic radiogenic effects to occur following such procedures. SUMMARY OF BACKGROUND DATA: There is increased concern on radiation exposure of patients undergoing fluoroscopically guided interventional procedures. METHODS: The cumulative screening time and dose area product, for each fluoroscopic projection used, were monitored in 20 patients undergoing pedicle screw internal fixation. The dose absorbed by each radiosensitive organ/tissue was determined from direct measurements obtained using an anthropomorphic phantom appropriately loaded with thermoluminescence dosimeters. RESULTS: An average pedicle screw insertion procedure requires 1.2 minutes and 2.1 minutes of fluoroscopic exposure along anteroposterior and lateral projections, respectively, resulting in a dose area product of 232 cGy cm and 568 cGy cm, correspondingly. Gender-specific normalized data for the determination of effective, gonadal, and entrance skin dose to patients undergoing fluoroscopically guided pedicle screw internal fixation procedures were derived. The effective dose from an average procedure was 1.52 and 1.40 mSv and the gonadal dose 0.67 and 0.12 mGy for female and male patients, respectively. The average radiogenic risks for fatal cancer and genetic defects were 115 and 4 per million of patients treated, respectively. Induction of skin injuries might be induced when fluoroscopy along the lateral projection is highly extended and the source to skin distance is kept low. CONCLUSIONS: Patient dose and radiogenic risks associated with an average pedicle screw internal fixation procedure are tolerable. However, for young patients with complex spinal disorders requiring extended fluoroscopy, radiogenic risks may be considerable. Present data may beused for estimation of effective dose, gonadal dose, and entrance skin exposure and associated radiogenic risks to patients undergoing fluoroscopically guided pedicle screw insertion in any institution.

Adult↗

PubMed2006

Climate and spatio-temporal variation in the population dynamics of a long distance migrant, the white stork.

1. A central question in ecology is to separate the relative contribution of density dependence and stochastic influences to annual fluctuations in population size. Here we estimate the deterministic and stochastic components of the dynamics of different European populations of white stork Ciconia ciconia. We then examined whether annual changes in population size was related to the climate during the breeding period (the 'tap hypothesis' sensu Saether, Sutherland & Engen (2004, Advances in Ecological Research, 35, 185 209) or during the nonbreeding period, especially in the winter areas in Africa (the 'tube hypothesis'). 2. A general characteristic of the population dynamics of this long-distance migrant is small environmental stochasticity and strong density regulation around the carrying capacity with short return times to equilibrium. 3. Annual changes in the size of the eastern European populations were correlated by rainfall in the wintering areas in Africa as well as local weather in the breeding areas just before arrival and in the later part of the breeding season and regional climate variation (North Atlantic Oscillation). This indicates that weather influences the population fluctuations of white storks through losses of sexually mature individuals as well as through an effect on the number of individuals that manages to establish themselves in the breeding population. Thus, both the tap and tube hypothesis explains climate influences on white stork population dynamics. 4. The spatial scale of environmental noise after accounting for the local dynamics was 67 km, suggesting that the strong density dependence reduces the synchronizing effects of climate variation on the population dynamics of white stork. 5. Several climate variables reduced the synchrony of the residual variation in population size after accounting for density dependence and demographic stochasticity, indicating that these climate variables had a synchronizing effect on the population fluctuations. In contrast, other climatic variables acted as desynchronizing agents. 6. Our results illustrate that evaluating the effects of common environmental variables on the spatio-temporal variation in population dynamics require estimates and modelling of their influence on the local dynamics.

Animal Migration↗

PubMed1999

Temporal difference between testis and ovary determinations with possible involvement of testosterone and aromatase in gonadal differentiation in TSD lacking lizard, Calotes versicolor.

In the garden lizard, Calotes versicolor, which lacks identifiable sex chromosomes, incubation temperature also does not have a deterministic effect on the gender. However, the embryos reared at high temperature (33-35 degrees C) have a shorter duration of incubation as well as gonadal differentiation. In contrast, exogenous application of the male hormone testosterone to embryos at ambient temperature (28 degrees C) results in almost all individuals with only testis. Thus the testosterone treatment reverts genic females to males and accelerates the differentiation of testis, a feature similar to the high-temperature treatment. Treatment of eggs with estradiol shows no difference from that seen in the untreated eggs. The present series of experiments was done to establish the "window" of testosterone sensitivity and to understand the interaction between sex hormones and high temperature on gonadal differentiation. The period between day 5 and 15 of embryonic development was the window period of testosterone sensitivity for sex reversal. This period coincided with the formation of the genital ridge and its differentiation into cortex and medulla. Treatment of the 33 degrees C-reared embryos with testosterone resulted in hatchlings of both the sexes, in contrast to only males at the ambient temperature. In contrast, at the same temperature (33 degrees C), all the dihydrotestosterone (nonaromatisable testosterone)-treated embryos hatched into males. However, those given estradiol showed no sex bias regardless of the day of application and the concentration of drug. Eggs were also treated with aromatase inhibitor, CGS 16949 A, at ambient temperature and at 33 degrees C. All the 33 degrees C eggs to which the drug was given on day 25 hatched into males. These results suggest that though high temperature has no direct effect on sex determination in this species, it may have a stimulatory effect on aromatase activity, leading to the conversion of the exogenously applied testosterone into estradiol and permitting ovarian differentiation in the genic females. It also follows from the present report that the pathway of testis formation in Calotes versicolor is triggered much earlier, and irreversibly, than that for the ovary.

Animals↗

PubMed2005

Monte Carlo treatment planning for molecular targeted radiotherapy within the MINERVA system.

The aim of this project is to extend accurate and patient-specific treatment planning to new treatment modalities, such as molecular targeted radiation therapy, incorporating previously crafted and proven Monte Carlo and deterministic computation methods. A flexible software environment is being created that allows planning radiation treatment for these new modalities and combining different forms of radiation treatment with consideration of biological effects. The system uses common input interfaces, medical image sets for definition of patient geometry and dose reporting protocols. Previously, the Idaho National Engineering and Environmental Laboratory (INEEL), Montana State University (MSU) and Lawrence Livermore National Laboratory (LLNL) had accrued experience in the development and application of Monte Carlo based, three-dimensional, computational dosimetry and treatment planning tools for radiotherapy in several specialized areas. In particular, INEEL and MSU have developed computational dosimetry systems for neutron radiotherapy and neutron capture therapy, while LLNL has developed the PEREGRINE computational system for external beam photon-electron therapy. Building on that experience, the INEEL and MSU are developing the MINERVA (modality inclusive environment for radiotherapeutic variable analysis) software system as a general framework for computational dosimetry and treatment planning for a variety of emerging forms of radiotherapy. In collaboration with this development, LLNL has extended its PEREGRINE code to accommodate internal sources for molecular targeted radiotherapy (MTR), and has interfaced it with the plugin architecture of MINERVA. Results from the extended PEREGRINE code have been compared to published data from other codes, and found to be in general agreement (EGS4-2%, MCNP-10%) (Descalle et al 2003 Cancer Biother. Radiopharm. 18 71-9). The code is currently being benchmarked against experimental data. The interpatient variability of the drug pharmacokinetics in MTR can only be properly accounted for by image-based, patient-specific treatment planning, as has been common in external beam radiation therapy for many years. MINERVA offers 3D Monte Carlo-based MTR treatment planning as its first integrated operational capability. The new MINERVA system will ultimately incorporate capabilities for a comprehensive list of radiation therapies. In progress are modules for external beam photon-electron therapy and boron neutron capture therapy (BNCT). Brachytherapy and proton therapy are planned. Through the open application programming interface (API), other groups can add their own modules and share them with the community.

Boron Neutron Capture Therapy↗