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Results for “Problem Formulation”

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At least 433 records · Page 24Linked to original sources

PubMed1980

Fully three-dimensional positron emission tomography.

Fully three-dimensional positron emission tomography is considered and a reconstruction algorithm derived. The reconstruction problem is formulated mathematically as a three-dimensional convolution integral of a point spread function with an unknown positron activity distribution and is solved by Fourier transform methods. Performance of the algorithm is evaluated using both simulated phantom data produced by a Monte Carlo computer program and phantom data obtained from the University of Chicago/Searle Positron Camera. It is concluded that the method is computationally feasible and results in accurate reconstructions.

Mathematics↗

PubMed2004

Algebraic reconstruction for 3D magnetic resonance-electrical impedance tomography (MREIT) using one component of magnetic flux density.

Magnetic resonance-electrical impedance tomography (MREIT) algorithms fall into two categories: those utilizing internal current density and those utilizing only one component of measured magnetic flux density. The latter group of algorithms have the advantage that the object does not have to be rotated in the magnetic resonance imaging (MRI) system. A new algorithm which uses only one component of measured magnetic flux density is developed. In this method, the imaging problem is formulated as the solution of a non-linear matrix equation which is solved iteratively to reconstruct resistivity. Numerical simulations are performed to test the algorithm both for noise-free and noisy cases. The uniqueness of the solution is monitored by looking at the singular value behavior of the matrix and it is shown that at least two current injection profiles are necessary. The method is also modified to handle region-of-interest reconstructions. In particular it is shown that, if the image of a certain xy-slice is sought for, then it suffices to measure the z-component of magnetic flux density up to a distance above and below that slice. The method is robust and has good convergence behavior for the simulation phantoms used.

Electric Impedance↗

PubMed2006

Imaging of conductivity changes and electrode movement in EIT.

Electrical impedance tomography (EIT) attempts to reconstruct the internal impedance distribution in a medium from electrical measurements at electrodes on the medium surface. One key difficulty with EIT measurements is due to the position uncertainty of the electrodes, especially for medical applications, in which the body surface moves during breathing and posture change. In this paper, we develop a new approach which directly reconstructs both electrode movements and internal conductivity changes for difference EIT. The reconstruction problem is formulated in terms of a regularized inverse, using an augmented Jacobian, sensitive to impedance change and electrode movement. A reconstruction prior term is computed to impose a smoothness constraint on both the spatial distribution of impedance change and electrode movement. A one-step regularized imaging algorithm is then implemented based on the augmented Jacobian and smoothness constraint. Images were reconstructed using the algorithm of this paper with data from simulated 2D and 3D conductivity changes and electrode movements, and from saline phantom measurements. Results showed good reconstruction of the actual electrode movements, as well as a dramatic reduction in image artefacts compared to images from the standard algorithm, which did not account for electrode movement.

Algorithms↗

PubMed2006

Hypothesis generation in signaling networks.

Biological signaling networks comprise the chemical processes by which cells detect and respond to changes in their environment. Such networks have been implicated in the regulation of important cellular activities, including cellular reproduction, mobility, and death. Though technological and scientific advances have facilitated the rapid accumulation of information about signaling networks, utilizing these massive information resources has become infeasible except through computational methods and computer-based tools. To date, visualization and simulation tools have received significant emphasis. In this paper, we present a graph-theoretic formalization of biological signaling network models that are in wide but informal use, and formulate two problems on the graph: the Constrained Downstream and Minimum Knockout Problems. Solutions to these problems yield qualitative tools for generating hypotheses about the networks, which can then be experimentally tested in a laboratory setting. Using established graph algorithms, we provide a solution to the Constrained Downstream Problem. We also show that the Minimum Knockout Problem is NP-Hard, propose a heuristic, and assess its performance. In tests on the Epidermal Growth Factor Receptor (EGFR) network, we find that our heuristic reports the correct solution to the problem in seconds. Source code for the implementations of both solutions is available from the authors upon request.

Algorithms↗

PubMed1997

Mathematical modeling of pharmacy systems.

Mathematical modeling and its potential applications in pharmacy are discussed. A model is a simplified representation of the real world. As an experimental approach, modeling minimizes expense, risk, and disruption, but its validity can be hard to ascertain. Mathematical models describe numerically the relationships among elements of a system and are a powerful tool in making decisions affecting that system. There are two types of mathematical models: analytical models, which directly describe the relationships between system inputs and outputs using mathematical equations (such as pharmacokinetic models), and simulation models, which involve the replication, usually with a computer, of events as they occur in the real world. Analytical models are easier to develop but are not appropriate for describing highly complex systems. In continuous-time simulation, the system is represented as an uninterrupted flow of material; in discrete-event simulation, it is assumed that events occur only at distinct times. Various simulation programs are commercially available. The stages of a mathematical modeling study are (1) formulate the problem, (2) determine the model's structure, (3) collect and analyze initial data, (4) develop the model further, (5) validate the model, (6) experiment using the model, and (7) use the results. There have been many applications of modeling in health care, but relatively few have involved the study of pharmacy systems. Mathematical modeling offers pharmacists a low-risk, low-cost tool for aiding decisions about pharmacy systems by predicting alternative futures.

Models, Organizational↗

PubMed2004

Sample size for gene expression microarray experiments.

MOTIVATION: Microarray experiments often involve hundreds or thousands of genes. In a typical experiment, only a fraction of genes are expected to be differentially expressed; in addition, the measured intensities among different genes may be correlated. Depending on the experimental objectives, sample size calculations can be based on one of the three specified measures: sensitivity, true discovery and accuracy rates. The sample size problem is formulated as: the number of arrays needed in order to achieve the desired fraction of the specified measure at the desired family-wise power at the given type I error and (standardized) effect size. RESULTS: We present a general approach for estimating sample size under independent and equally correlated models using binomial and beta-binomial models, respectively. The sample sizes needed for a two-sample z-test are computed; the computed theoretical numbers agree well with the Monte Carlo simulation results. But, under more general correlation structures, the beta-binomial model can underestimate the needed samples by about 1-5 arrays. CONTACT: jchen@nctr.fda.gov.

Algorithms↗

PubMed2005

On the relation between initial value and slope.

Suppose measurements of a particular feature are collected at baseline and at a number of subsequent time points and that for each individual there is a roughly linear trend in time. This paper takes three approaches to testing whether there is a relation between the initial value and the slope. It also considers whether the initial value for an individual is a useful predictor of the slope for that individual. The problems are formulated in terms of regression models with random coefficients. The solutions are illustrated using data from an observational study of clinical correlates of disability and progression in Huntington's disease.

Biometry↗

PubMed1993

Estimation of mitotic stability in conidial fungi: a theoretical framework.

Mitotic stability refers to the probability that genetic elements are transmitted to both daughters during mitosis. This is of practical importance in molecular genetics because autonomous cloning vectors should be transmitted at high frequency during mitosis. In filamentous coencytic fungi it is difficult to quantify mitotic stability because a fluctuation test is not feasible. We show how to get around this problem by formulating a general model of the transmission of nuclear genetic elements through the course of conidiogenesis. We derive formulas by two different methods for the expected proportion of conidiospores that retain the element as a function of its mitotic stability and the number of generations of spore production. An important by-product yields the exact probability distributions for the number of conidiospores retaining elements at each stage of conidiophore development. We outline, and illustrate through specific numerical examples, how to use these formulas to estimate mitotic stability. Although we use Aspergillus nidulans as our biological paradigm, the same general framework can be extended to other fungal species, and possibly to less closely related systems as well.

Aspergillus nidulans↗

PubMed1993

A class of population genetic questions formulated as the generalized occupancy problem.

In categorical genetic data analysis when the sampling units are classified into an arbitrary number of distinct classes, sometimes the sample size may not be large enough to apply large sample approximations for hypothesis testing purposes. Exact sampling distributions of several statistics are derived here, using combinatorial approaches parallel to the classical occupancy problem to help overcome this difficulty. Since the multinomial probabilities can be unequal, this situation is described as a generalized occupancy problem. The sampling properties derived are used to examine nonrandomness of occurrence of mutagen-induced mutations across loci, to devise tests of Hardy-Weinberg proportions of genotype frequencies in the presence of a large number of alleles, and to provide a global test of gametic phase disequilibrium of several restriction site polymorphisms.

Genetics, Population↗

PubMed1989

A two-type population epidemic problem.

We consider a two-type population such that the birth rate of the second type depends on the size of the population of the first type. This problem was formulated by Kendall (1949) and Goodman (1953), then solved for constant parameters by Tapaswi & Roychoudhury (1984) and Gani & Tin (1984) (where the first type was female, and the second type, male). We generalize the known results to cases where the parameters are time dependent. Analytic expressions for the first two moments are found. For constant parameters, we derive the asymptotic law for the process.

Epidemiology↗

PubMed1991

A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue.

Unless they are furnished with an adequate blood supply and a means of disposing of their waste products by a mechanism other than diffusion, solid tumours cannot grow beyond a few millimetres in diameter. It is now a well-established fact that, in order to accomplish this neovascularization, solid tumours secrete a diffusable chemical compound known as tumour angiogenesis factor (TAF) into the surrounding tissue. This stimulates nearby blood vessels to migrate towards and finally penetrate the tumour. Once provided with the new supply of nutrient, rapid growth takes place. In this paper, a mathematical model is presented for the diffusion of TAF into the surrounding tissue. The complete process of angiogenesis is made up of a sequence of several distinct events and the model is an attempt to take into account as many of these as possible. In the diffusion equation for the TAF, a decay term is included which models the loss of the chemical into the surrounding tissue itself. A threshold distance for the TAF is incorporated in an attempt to reflect the results from experiments on corneal implants in test animals. By formulating the problems in terms of a free boundary problem, the extent of the diffusion of TAF into the surrounding tissue can be monitored. Finally, by introducing a sink term representing the action of proliferating endothelial cells, the boundary of the TAF is seen to recede, and hence the position and movement of the capillaries can be indirectly followed. The changing concentration gradient observed as the boundary recedes may offer a possible explanation for the initiation of anastomosis. Several functions are considered as possible sink terms and numerical results are presented. The situation where the tumour (i.e. the source of TAF) is removed is also considered.

Angiogenesis Inducing Agents↗

PubMed2005

Resting shape and spontaneous membrane curvature of red blood cells.

A boundary-value problem is formulated describing the biconcave resting shape of normal red blood cells, based on local constitutive equations for the membrane tensions and bending moments. The fundamental physical assumption is that curvature-dependent anisotropic membrane stress resultants accompanied by isotropic bending moments arise from isotropic tensions developing in each leaflet of the lipid bilayer, while the cytoskeleton is unstressed in the resting configuration. Families of equilibrium resting shapes parametrized by the spontaneous bilayer curvature and cell sphericity compare favourably with the average shape of normal red blood cells. The successful comparison supports Helfrich's notion of a non-zero spontaneous curvature whose magnitude is nearly equal to the negative of the equivalent cell radius defined with respect to the membrane surface area. The structure of the solution space suggests a minimum spontaneous curvature below which the cell sphericity is lower than that of the red blood cell, independent of the transmural pressure. The computed cell shapes also compare favourably with the shapes of swollen red blood cells, though for a different value of the spontaneous curvature. The dependence of the spontaneous curvature on the cell volume is attributed to in-plane elastic tensions developing due to the deformation of the cytoskeleton. An alternative formulation based on a non-local model for the monolayer tensions is found to be incapable of predicting non-spherical shapes.

Cell Shape↗

PubMed2005

Making sense of itraconazole pharmacokinetics.

The triazole, itraconazole, has a wide spectrum of antifungal activity in vitro. Confirming this activity in vivo has been a long and difficult task because of problems with formulation, delivery and uncertainty about effective bioavailability. The physicochemical properties of the drug make it insoluble in water but strongly protein bound. The absorption and blood levels of the original capsular formulation were predictable with non-linear, saturation kinetics in normal volunteers. Tissue penetration was high and sustained. In neutropenic patients with haematological malignancies, levels were very variable and the doses required to achieve effective antifungal levels were higher than predicted from normal subjects' results. The solubility of the drug and predictability of blood levels were improved by the formulation of an oral solution with cyclodextrin. Wash-out times were prolonged in patients with this new formulation implying that tissue penetration was maintained. A high volume of distribution suggests that loading may be necessary. An intravenous cyclodextrin solution is also now available allowing rapid loading and avoidance of the well-known gut side effects of the oral solution. Clinical studies have suggested minimum bioavailable dosage and minimum trough blood levels for effective prophylaxis against systemic fungal infection. Interactions are also now well documented and manageable. The drug can be measured reliably, quickly and comparatively cheaply by HPLC in serum and plasma. The frequency of such testing in clinical practice depends on the need to ensure adequate levels and to avoid unwanted toxicity.

Animals↗

PubMed1991

American moralism and the origin of bioethics in the United States.

The theology of John Calvin has deeply affected the American mentality through two streams of thought, Puritanism and Jansenism. These traditions formulate moral problems in terms of absolute, clear principles and avoid casuistic analysis of moral problems. This approach is designated American moralism. This article suggests that the bioethics movement in the United States was stimulated by the moralistic mentality but that the work of the bioethics has departed from this viewpoint.

Advisory Committees↗

PubMed2004

Outcome monitoring to facilitate clinical governance; experience from a national programme in the independent sector.

BACKGROUND: Since 1998 BUPA has used the Short-Form 36 (SF-36) questionnaire to monitor changes in health status after adult elective surgery. Over 70 independent hospitals across the United Kingdom have collected data on over 100000 patient episodes. SF-36 is one of a number of tools that support clinical governance in the sector. Results are reported confidentially, putting the emphasis on supporting a learning culture. FORMULATION OF PROBLEMS APPARENT AT 3 YEARS: Feedback was sub-optimal: discussions with hospital staff and consultants revealed that the league tables were hard to interpret, and there was uncertainty about the definition of outlier results. The number of patients recruited to the survey was variable across the hospitals. No grouping of low-volume procedures met with agreement. ACTION PLAN FOR YEAR 4: Use 'Shewhart' control charts to distinguish common and special cause variation in results; substitute a condition-specific tool in one instance; adoption of an 'alert' process to prompt local audit of unusual results; use of a reminder letter to improve return rate of follow-up questionnaires; and focus programme on a list of 20 common procedures. Discuss these changes with the managerial and clinical leaders of each of BUPA's hospitals. CURRENT POSITION AT YEAR 5 : The use of Shewhart charts has been welcomed by managers and clinicians at BUPA's hospitals. The renewed confidence in the programme has encouraged constructive debate into allowing wider access to previously confidential results. Some changes in clinical practice have occurred.

Attitude of Health Personnel↗

PubMed1990

Factors influencing the development of area health education centers with Texas-Mexico border populations.

Area Health Education Centers (AHECs) have been viewed as an appropriate vehicle for implementing new initiatives for training health professionals who will work along the U.S.-Mexico border. Perceptions about this program in Texas were evaluated from July 1988 to June 1989 to identify problems and formulate suggestions that might be of use to academic health science centers (HSCs)--and in particular medical schools--working with Hispanic populations. Interviews were conducted with 116 people: the presidents and/or deans of all eight Texas HSCs and/or medical schools, other deans and faculty, community leaders in five border counties, and state officials. The school and community perspectives about past and present AHEC activities were compared. Some of the barriers were: insufficient components of the health care delivery system to support medical education in severely underserved areas; differing school and community priorities; cultural differences between the school faculty and the community; and feeling among community physicians and dentists that AHECs were a source of competition. The school and community respondents agreed that the AHEC program needs more cooperative planning and training that emphasizes public health education for future AHEC-like activities with border populations.

Academic Medical Centers↗

PubMed2001

Oral contraceptives: current status.

During the past four decades, oral contraceptives have remained a safe and effective method of birth control. Reductions in the estrogen and progestin dosages have significantly decreased the incidence of cardiovascular complications. The association between oral contraceptives and breast cancer appears to be primarily because of detection bias or possibly a promotional effect. Despite the changes in formulation, the problems related to side effects have not been totally solved. Because compliance and successful use is strongly affected by side effects, improvement in this area is probably the biggest challenge faced by developers of oral contraceptives. It is also clear that there are a growing number of significant noncontraceptive benefits that accrue in oral contraceptive users. Unfortunately, many women do not know about these benefits. Thus, one of the issues that providers need to continue to address is how to provide better information about oral contraceptives and contraception in general to patients.

Acne Vulgaris↗

PubMed2006

Simultaneous surface registration of ictal and interictal SPECT and magnetic resonance images for epilepsy studies.

BACKGROUND: Subtraction of ictal and interictal single photon emission computed tomography (SPECT) images is known to be successful in localizing the seizure focus in the pre-surgical evaluation of patients with partial epilepsy. A computer-aided methods for producing subtraction ictal SPECT co-registered to the magnetic resonance image (MRI) (the SISCOM method) is commonly used. The two registrations involved in SISCOM are (1) between the ictal-interictal SPECT images, which was shown to be the more critical, and (2) between the ictal image and MRI. OBJECTIVE: To improve the accuracy of ictal-interictal registration in SISCOM by registering all three images (ictal, interictal SPECT, MRI) simultaneously. METHODS: The registration problem is formulated as the minimization of a cost function between three surfaces. Then, to achieve a global minimum of this cost function, the Powell algorithm with randomly distributed initial configurations is used. This technique is tested by a realistic simulation study, a phantom study and a patient study. RESULTS: The results of the simulation study demonstrate that, in surface-based registration, the triple-registration method results in a smaller ictal-interictal SPECT registration error than the pair-wise registration method (P<0.05) for a range of values of the cost-function parameter. However, the improved registration error is still larger than that obtained by the normalized mutual information method (P<0.001), which is a voxel-based registration algorithm. The phantom and patient studies reveal no observable difference between registration results. CONCLUSIONS: Although the improved accuracy of triple registration is slightly worse than voxel-based registration, it will soon be possible to apply the results of this study in research utilizing the triple-registration principle to improving voxel-based results of ictal-interictal registration.

Algorithms↗