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Experimental measurements of fluence distribution in a UV reactor using fluorescent microspheres.

One concern with current techniques of UV reactor validation is that they provide only a measure of the mean UV fluence. In this research, the actual fluence distribution of a UV reactor is measured through the use of photochemically active fluorescent microspheres. Experimental tests were performed in a pilot-scale monochromatic UV 254 nm reactor operated at two flow rates. Analysis of the fluorescence intensity decay was performed using collimated beam experiments for determination of decay rate kinetics. A stochastic hierarchal process involving Bayesian statistics, and the Markov chain Monte Carlo integration technique was used to correlate the microsphere fluorescence intensity distribution to the UV fluence distribution. The experimental UV fluence distribution was compared with the fluence distribution predicted using a computational fluid dynamics model. The results showed that the fluorescent microspheres measured a wider distribution of UV fluences with a flow rate of 3 gpm than with 7.5 gpm. The principal differences between the modeled and the measured distribution were in the low UV fluences where the microspheres predicted lower fluence levels than the model. The use of microspheres is demonstrated as a novel technique for measurement of the fluence distribution in UV reactors. This technique has both fundamental and practical implications for reactor evaluation and testing and could improve confidence in the future use of mathematical models for UV reactor characterization. It also serves as a complement to biodosimetry testing by providing greater insights regarding reactor behavior and validation.

Bacillus subtilis↗

On the number of founding germ cells in humans.

BACKGROUND: The number of founding germ cells (FGCs) in mammals is of fundamental significance to the fidelity of gene transmission between generations, but estimates from various methods vary widely. In this paper we obtain a new estimate for the value in humans by using a mathematical model of germ cell development that depends on available oocyte counts for adult women. RESULTS: The germline-development model derives from the assumption that oogonial proliferation in the embryonic stage starts with a founding cells at t = 0 and that the subsequent proliferation can be defined as a simple stochastic birth process. It follows that the population size X(t) at the end of germline expansion (around the 5th month of pregnancy in humans; t = 0.42 years) is a random variable with a negative binomial distribution. A formula based on the expectation and variance of this random variable yields a moment-based estimate of a that is insensitive to the progressive reduction in oocyte numbers due to their utilization and apoptosis at later stages of life. In addition, we describe an algorithm for computing the maximum likelihood estimation of the FGC population size (a), as well as the rates of oogonial division and loss to apoptosis. Utilizing both of these approaches to evaluate available oocyte-counting data, we have obtained an estimate of a = 2 - 3 for Homo sapiens. CONCLUSION: The estimated number of founding germ cells in humans corresponds well with values previously derived from chimerical or mosaic mouse data. These findings suggest that the large variation in oocyte numbers between individual women is consistent with a smaller founding germ cell population size than has been estimated by cytological analyses.

Algorithms↗

A biomathematical model of time-delayed feedback in the human male hypothalamic-pituitary-Leydig cell axis.

We develop, implement, and test a feedback and feedforward biomathematical construct of the male hypothalamic [gonadotropin-releasing hormone (GnRH)]-pituitary [luteinizing hormone (LH)]-gonadal [testosterone (Te)] axis. This stochastic differential equation formulation consists of a nonstationary stochastic point process responsible for generating episodic release of GnRH, which is modulated negatively by short-loop (GnRH) and long-loop (Te) feedback. Pulsatile GnRH release in turn drives bursts of LH secretion via an agonistic dose-response curve that is partially damped by Te negative feedback. Circulating LH stimulates (feedforward) Te synthesis and release by a second dose response. Te acts via negative dose-responsive feedback on GnRH and LH output, thus fulfilling conditions of a closed-loop control system. Four computer simulations document expected feedback performance, as published earlier for the human male GnRH-LH-Te axis. Six other simulations test distinct within-model coupling mechanisms to link a circadian modulatory input to a pulsatile control node so as to explicate the known 24-h variations in Te and, to a lesser extent, LH. We conclude that relevant dynamic function, internodal dose-dependent regulatory connections, and within-system time-delayed coupling together provide a biomathematical basis for a nonlinear feedback-feedforward control model with combined pulsatile and circadian features that closely emulate the measurable output activities of the male hypothalamic-pituitary-Leydig cell axis.

Circadian Rhythm↗

On the formulation and computer implementation of an age-dependent two-sex demographic model.

A two-sex age-dependent demographic model is formulated within the framework of a stochastic population process, including both time-homogeneous and time-inhomogeneous laws of evolution. An outline of the parametric components of the system, which expedite computer implementation and experimentation, is also given. New features of the model include a component for couple formation, using the class of Farlie-Morgenstern bivariate distributions to accommodate age preferences in selecting marriage partners, a component for couple dissolution due to separation or divorce, and an outline of techniques for initializing a two-sex projection given scanty information. For the case of time-homogeneous laws of evolution, stability properties of two-sex models that are analogs of those for one-sex models are difficult to prove mathematically due to nonlinearities. But computer experiments in this case suggest that these properties continue to hold for two-sex models for such widely used demographic indicators as period crude birth rates, period rates of natural increase, and period age distributions, which converge to constant forms in long-term projections. The values of the stable crude birth rate, rate of natural increase, and quantiles of the stable age distribution differ markedly among projections that differ only in selected values of parameters governing couple formation and dissolution. Such experimental results demonstrate that two-sex models are not merely intellectual curiosities but exist in their own right and lead to insights not attainable in simpler one-sex formulations.

Age Factors↗

Stochastic signal inputs for chemotactic response in Dictyostelium cells revealed by single molecule imaging techniques.

Chemotactic cells can exhibit extreme sensitivity to chemical gradients. Theoretical estimations of the signal inputs required for chemotaxis suggest that the response can be achieved under the strong influence of stochastic input noise generated by the receptors during the transmembrane signaling. This arises a fundamental question regarding the mechanisms for directional sensing: how do cells obtain reliable information regarding gradient direction by using stochastically operating receptors and the downstream molecules? To address this question, we have developed single molecule imaging techniques to visualize signaling molecules responsible for chemotaxis in living Dictyostelium cells, allowing us to monitor the stochastic signaling processes directly. Single molecule imaging of a chemoattractant bound to a receptor demonstrates that signal inputs fluctuate with time and space. Downstream signaling molecules, such as PTEN and a PH domain-containing protein that are constituent parts of chemotactic signaling system, can also be followed at single molecule level in living cells, illuminating the stochastic nature of chemotactic signaling processes. In this report, we start with a brief introduction of chemotactic response of the eukaryotic cells, followed by an explanation for single molecule imaging techniques, and finally discuss these applications to chemotactic signaling system of Dictyostelium cells.

Animals↗

Image reconstruction in SNR units: a general method for SNR measurement.

The method for phased array image reconstruction of uniform noise images may be used in conjunction with proper image scaling as a means of reconstructing images directly in SNR units. This facilitates accurate and precise SNR measurement on a per pixel basis. This method is applicable to root-sum-of-squares magnitude combining, B(1)-weighted combining, and parallel imaging such as SENSE. A procedure for image reconstruction and scaling is presented, and the method for SNR measurement is validated with phantom data. Alternative methods that rely on noise only regions are not appropriate for parallel imaging where the noise level is highly variable across the field-of-view. The purpose of this article is to provide a nuts and bolts procedure for calculating scale factors used for reconstructing images directly in SNR units. The procedure includes scaling for noise equivalent bandwidth of digital receivers, FFTs and associated window functions (raw data filters), and array combining.

Algorithms↗

Riemannian elasticity: a statistical regularization framework for non-linear registration.

In inter-subject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the re-introduction in a registration algorithm is not easy. In this paper, we interpret the elastic energy as the distance of the Green-St Venant strain tensor to the identity, which reflects the deviation of the local deformation from a rigid transformation. By changing the Euclidean metric for a more suitable Riemannian one, we define a consistent statistical framework to quantify the amount of deformation. In particular, the mean and the covariance matrix of the strain tensor can be consistently and efficiently computed from a population of non-linear transformations. These statistics are then used as parameters in a Mahalanobis distance to measure the statistical deviation from the observed variability, giving a new regularization criterion that we called the statistical Riemannian elasticity. This new criterion is able to handle anisotropic deformations and is inverse-consistent. Preliminary results show that it can be quite easily implemented in a non-rigid registration algorithms.

Algorithms↗

Probabilistic Monte Carlo based mapping of cerebral connections utilising whole-brain crossing fibre information.

A methodology is presented for estimation of a probability density function of cerebral fibre orientations when one or two fibres are present in a voxel. All data are acquired on a clinical MR scanner, using widely available acquisition techniques. The method models measurements of water diffusion in a single fibre by a Gaussian density function and in multiple fibres by a mixture of Gaussian densities. The effects of noise on complex MR diffusion weighted data are explicitly simluated and parameterised. This information is used for standard and Monte Carlo streamline methods. Deterministic and probabilistic maps of anatomical voxel scale connectivity between brain regions are generated.

Algorithms↗

Usefulness of noise adaptive non-linear gaussian filter in FDG-PET study.

OBJECTIVE: In positron emission tomography (PET) studies, shortening transmission (TR) scan time can improve patient comfort and increase scanner throughput. However, PET images from short TR scans may be degraded due to the statistical noise included in the TR image. The purpose of this study was to apply non-linear Gaussian (NLG) and noise adaptive NLG (ANLG) filters to TR images, and to evaluate the extent of noise reduction by the ANLG filter in comparison with that by the NLG filter using phantom and clinical studies. METHODS: In phantom studies, pool phantoms of various diameters and injected doses of 2-deoxy-2-[18F]fluoro-D-glucose (FDG) were used and the coefficients of variation (CVs) of the counts in the TR images processed with the NLG and ANLG filters were compared. In clinical studies, two normal volunteers and 13 patients with tumors were studied. In volunteer studies, the CV values in the liver were compared. In patient studies, the standardized uptake values (SUVs) of tumors in the emission images were obtained after processing the TR images using the NLG and ANLG filters. RESULTS: In phantom studies, the CV values in the TR images processed with the ANLG filter were smaller than those in the images processed with the NLG filter. When using the ANLG filter, their dependency on the phantom size, injected dose of FDG and TR scan time was smaller than when using the NLG filter. In volunteer studies, the CV values in the images processed with the ANLG filter were smaller than those in the images processed with the NLG filter, and were almost constant regardless of the TR scan time. In patient studies, there was an excellent correlation between the SUVs obtained from the images with a TR scan time of 7 min processed with the NLG filter (x) and those obtained from the images with a TR scan time of 4 min processed with the ANLG filter (y) (r = 0.995, y = 1.034x - 0.075). CONCLUSIONS: Our results suggest that the ANLG filter is effective and useful for noise reduction in TR images and shortening TR scan time while maintaining the quantitative accuracy of FDG-PET studies.

Adult↗

Similarity of interspike interval distributions and information gain in a stationary neuronal firing.

The Kullback-Leibler (KL) information distance is proposed for judging similarity between two different interspike interval (ISI) distributions. The method is applied by a comparison of four common ISI descriptors with an exponential model which is characterized by the highest entropy. Under the condition of equal mean ISI values, the KL distance corresponds to information gain coming from the state described by the exponential distribution to the state described by the chosen ISI model. It has been shown that information can be transmitted changing neither the spike rate nor coefficient of variation (CV). Furthermore the KL distance offer an indication of the exponentiality of the chosen ISI descriptor (or data): the distance is zero if, and only if, the ISIs are distributed exponentially. Finally an application on experimental data coming from the olfactory sensory neurons of rats is shown.

Action Potentials↗

Optimum signal in a simple neuronal model with signal-dependent noise.

How does the information about a signal in neural threshold crossings depend on the noise acting upon it? Two models are explored, a binary McCulloch and Pitts (threshold exceedance) model and a model of waiting time to exceedance--a discrete-time version of interspike intervals. If noise grows linearly with the signal, we find the best identification of the signal in terms of the Fisher information is for signals that do not reach the threshold in the absence of noise. Identification attains the same precision under weak and strong signals, but the coding range decreases at both extremes of signal level. We compare the results obtained for Fisher information with those using related first and second moment measures. The maximum obtainable information is plotted as a function of the ratio of noise to signal.

Action Potentials↗

Solution for nonuniformities and spatial noise in medical LCD displays by using pixel-based correction.

Liquid crystal displays (LCD) are rapidly replacing cathode ray tube displays (CRT) for medical imaging. LCD technology has improved significantly in the last few years and has important advantages over CRT. However, there are still some aspects of LCD that raise questions as to the usefulness of liquid crystal displays for very subtle clinical diagnosis such as mammography. One drawback of modern LCD displays is the existence of spatial noise expressed as measurable stationary differences in the behavior of individual pixels. This type of noise can be described as a random stationary image superposed on top of the medical image being displayed. It is obvious that this noise image can make subtle structures invisible or add nonexistent patterns to the medical image. In the first case, subtle abnormalities in the medical image could remain undetected, whereas in the second case, it could result into a false positive. This paper describes a method to characterize the spatial noise present in high-resolution medical displays and a technique to solve the problem. A medical display with built-in compensation for the spatial noise at pixel level was developed and improved image quality is demonstrated.

Algorithms↗

Computer analysis of ENG spectral features from patients with congenital nystagmus.

Power spectral estimation from electromystagmographic recording of eye position is proposed as a simple digital processing method to quantify both the amplitude and the frequency features of eye motion in patients affected by the oculomotor disorder of congenital nystagmus (CN). Different basic wave shapes clinically identified and studied in the literature are shown to have slightly different power spectra, which can be used to characterize the CN disorder from nystagmus waveforms. This treatment, statistical in nature, does not depend strongly on the detailed structure of each recorded wave shape, thus emphasizing that accurate descriptive analysis of all patient's waveforms characteristics adds little to the comprehension of CN. We show that the power spectral estimation also represents a useful tool in modelling both the CN defect and the non-defective oculomotor system, and in assessing the effect of the surgical treatment of CN through the differences in the power spectra before and after surgery.

Electronystagmography↗

Cascaded z-filters for efficient single-scan suppression of zero-quantum coherence.

A simple and robust method to suppress zero-quantum coherence (ZQC) in NMR experiments, in a single scan and with very high suppression ratio, is described. It is an appreciable improvement on a previous technique by Thrippleton and Keeler [Angew. Chem. Int. Ed. 42 (2003) 3938]. The method, called a z-filter cascade, preserves longitudinal, or z-magnetization, with high efficiency. Losses depend mostly on T1 relaxation but not T2 relaxation mechanisms. At the same time, suppression of ZQC can be essentially complete in a single scan. The time duration of the z-filter cascade scales inversely to representative chemical shift differences between the coupled spins, and is typically a few tens of milliseconds. The high efficiency of the zero-quantum suppression and excellent retention of the desired z-magnetization, in a single scan without resort to phase cycling or difference spectroscopy, makes the z-filter cascade a useful new pulse sequence building block for a whole range of NMR experiments. In cases where unwanted residual ZQC may have previously contributed to baseline " t1-noise" in two-dimensional NMR spectra, the z-filter cascade can deliver a noteworthy improvement in spectral quality.

Algorithms↗

Centric scan SPRITE magnetic resonance imaging: optimization of SNR, resolution, and relaxation time mapping.

Two strategies for the optimization of centric scan SPRITE (single point ramped imaging with T1 enhancement) magnetic resonance imaging techniques are presented. Point spread functions (PSF) for the centric scan SPRITE methodologies are numerically simulated, and the blurring manifested in a centric scan SPRITE image through PSF convolution is characterized. Optimal choices of imaging parameters and k-space sampling scheme are predicted to obtain maximum signal-to-noise ratio (SNR) while maintaining acceptable image resolution. The point spread function simulation predictions are verified experimentally. The acquisition of multiple FID points following each RF excitation is described and the use of the Chirp z-Transform algorithm for the scaling of field of view (FOV) of the reconstructed images is illustrated. Effective recombination of the rescaled images for SNR improvement and T*2 mapping is demonstrated.

Algorithms↗

A generalized Luria-Delbrück model.

We develop extensions of the Luria-Delbrück model that explicitly consider non-exponential growth of normal cells and a birth-death process with mean exponential or Gompertz growth of mutants. Death of mutant cells can be important in clones arising during cancer progression. The use of a birth-death process for growth of mutant cells, as opposed to a pure birth process as in previous work on the Luria-Delbrück model, leads to a large increase in the extra Poisson variation in the size of the mutant cell populations, which needs to be addressed in statistical analyses. We also discuss connections with previous work on carcinogenesis models.

Cell Growth Processes↗

A simple scheme for probehead background suppression in one-pulse 1H NMR.

A very simple method for reducing probehead background signal in one-pulse 1H nuclear magnetic resonance (NMR) spectra is presented. Two one-pulse spectra are recorded, the first with pulse length tp1, the second with an L-times longer pulse, e.g. with L = 2. The second spectrum scaled by 1/L is subtracted from the first. Since the weak pulses experienced by spins outside the coil are in the linear regime, the background from outside the coil is effectively subtracted out. The background suppression efficiency is approximately 1.5b2, where b is the ratio of the B1 field inside the coil relative to that outside the coil. Experimentally, background suppression by at least a factor of 10 was achieved. Examples of background suppression in 1H wideline as well as 1H fast magic-angle spinning (MAS) one-pulse spectra of clay and polymer samples are shown.

Algorithms↗

A statistically based filter.

A simple procedure is developed that uses concepts from statistical process control to filter noise from a process variable. Code is presented for the algorithm, and it is experimentally demonstrated on a pilot-scale process for which both noise and level change significantly and frequently.

Algorithms↗