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Sample size estimation for comparing two or more treatment groups in clinical trials.

Methods for estimating required sample size for comparing two population means have been published. Most involve the use of complicated formulae and tables. These methods are limited to comparing two groups. Although techniques exist to determine sample sizes for comparing more than two groups, they are intrinsically far more complicated. A simple linear nomogram is proposed as a solution to these problems, and its use is illustrated with examples of parallel group, ordered parallel group and factorial designs.

Algorithms

Asymmetric Boltzmann machines.

We study asymmetric stochastic networks from two points of view: combinatorial optimization and learning algorithms based on relative entropy minimization. We show that there are non trivial classes of asymmetric networks which admit a Lyapunov function L under deterministic parallel evolution and prove that the stochastic augmentation of such networks amounts to a stochastic search for global minima of L. The problem of minimizing L for a totally antisymmetric parallel network is shown to be associated to an NP-complete decision problem. The study of entropic learning for general asymmetric networks, performed in the non equilibrium, time dependent formalism, leads to a Hebbian rule based on time averages over the past history of the system. The general algorithm for asymmetric networks is tested on a feed-forward architecture.

Algorithms

A two-dimensional pencil-beam algorithm for calculation of arc electron dose distributions.

A two-dimensional pencil-beam algorithm is presented for the calculation of arc electron dose distributions in any plane that is perpendicular to the axis of rotation. The dose distributions are calculated by modelling the arced beam as a single broad beam defined by the irradiated surface of the patient. The algorithm is two-dimensional in that the anatomical cross section of the patient and the skin collimators are assumed identical in parallel planes outside the plane of calculation. The broad beam is modelled as a collection of strip beams, each strip beam being characterised by its planar fluence, mean projected angular direction and a root-mean-square spread about the mean direction. Using these parameters, the dose distribution is calculated using pencil-beam theory. Examples of strip-beam parameters and resulting dose distributions for patient geometries are presented. Features of the algorithm, which include (1) incorporation of pencil-beam theory for the calculation of dose in heterogeneous tissue, (2) run times of only about twice that of comparable-sized fixed electron fields and (3) the input requirement of only a single depth dose and four off-axis dose profiles of measured data, make the algorithm practical for clinical use.

Algorithms

High-resolution CT of the wrist: initial experience with scaphoid disorders and surgical fusions.

We performed high-resolution CT scans on 30 wrists in 27 patients with either previous surgical intercarpal fusion or known or suspected scaphoid abnormalities. Most examinations used the same protocol: contiguous 1.5-mm axial sections parallel to the long axis of the body of the scaphoid, small reconstruction circle, and bone reconstruction algorithm. Fifteen patients were evaluated for union of previous surgical carpal fusions; eight patients were evaluated for healing of scaphoid fractures; and the other four patients had miscellaneous disorders, including a midcarpal dislocation with a scaphoid fracture. High-resolution CT clearly showed whether the carpal fusions were united. In addition, metallic fixation devices were easy to locate and did not significantly degrade image quality. Osseous union of healing scaphoid fractures was reliably assessed. We conclude that high-resolution CT of the wrist is a useful method for evaluating surgical carpal fusions and various disorders of the scaphoid.

Arthrodesis

Deblurring of 3-dimensional patterns of evoked rat cerebellar cortical activity: a study using voltage-sensitive dyes and optical sectioning.

One of the benefits of imaging neuronal activity is the capability of resolving spatial patterns in the x-y plane. With optical sectioning microscopy, the 3-dimensional (3-D) structure may also be studied without physical deformation by serially moving the focal plane of the microscope through the volume of interest along the focal axis. However, each image is blurred by contributions from neighboring planes. This degradation is most severe for low numerical aperture lenses and large amounts of defocus. In this study, an image restoration method using the optical properties of an aberration-free, defocused optical system has been developed for improving optical signals from voltage-sensitive dyes. Deblurring based on the optical transfer function (OTF) of the system was applied on two test sets of serially sectioned images: (1) fluorescent beads and (2) in vivo rat cerebellar cortex stained with the voltage-sensitive dye RH795. This method was shown to reduce significantly the out-of-focus contribution to the images, improving the spatial resolution not only in the x-y plane, but also the z axis. The algorithms were then applied to optical signals obtained by stimulation of the cerebellar surface. Optical signals having a distinct beam-like pattern were evoked and recorded over depths ranging from 0 to 300 microns prior to deblurring. Application of the deblurring algorithm reduced the depth of cerebellar cortex over which the optical signals were observed. In agreement, field potential recordings of the evoked parallel fiber volley and post-synaptic components were restricted to a narrow range of depths similar to the deblurred optical images. Removal of out-of-focus information is an essential step in the serial sectioning of central nervous system structures for neuronal imaging and 3-D reconstruction.

Algorithms

PR interval behavior during exercise: implications for physiological pacemakers.

The relationship between heart rate response and the dynamic changes in the PR interval was assessed in 631 patients undergoing routine cardiac exercise tests for a variety of clinical indications. Patients were stratified into four subsets: nonmedicated normals (n = 437), patients on beta-antagonist agents (n = 118), those on antiarrhythmic agents alone (n = 61) and those with a clinical diagnosis of advanced (New York Heart Association [NYHA] Class III or IV) congestive heart failure. All patients were in stable sinus rhythm throughout the test. PR intervals were measured at rest, at mid-exercise and at peak exercise. Mean PR intervals shortened to a statistically significant degree in most subgroups. This effect was predominantly observed in the earlier stages of exercise. In patients with advanced heart failure, there was no statistically significant shortening of exercise PR intervals later in exercise, demonstrating a parallel with their relatively blunted heart rate response. These changes in exercise PR intervals suggest that implanted pacemaker algorithms may be constructed to maximize hemodynamic benefit in patients requiring physiological pacemakers.

Adolescent

Rapid three-dimensional treatment planning: I. Ray-tracing approach to primary component dose calculations.

Algorithms for fully three-dimensional divergent-beam radiotherapy treatment planning have been developed to achieve very high sampling of dose in heterogeneous (inhomogeneous density) tissue throughout an arbitrarily oriented patient volume, in clinically acceptable times of calculation. Dose is calculated at points along numerous rays which sample each beam. To display the dose distribution, the calculated dose values for each beam are interpolated onto rectilinear grids of (arbitrary) parallel planes, scaled for beam weight and finally merged with the weighted dose contributions of other beams. In this paper we describe and demonstrate the algorithm for the primary component of the three-dimensional photon dose distribution delivered to a patient.

Clinical Trials as Topic

A multiple projection method for digital tomosynthesis.

A new method of optimized efficiency for the retrospective reconstruction of tomograms is presented. The method has been developed for use with isocentric fluoroscopic units and is capable of performing digital tomosynthesis of anatomical planes of user selected orientation and distance from the isocenter. Optimization of efficiency has been achieved by segmenting the reconstruction process into discrete transformations that are specific to groups of pixels, rather than performing pixel by pixel operations. These involve a number of projections of the acquired image matrices as well as parallel translations and summing. Application of this method has resulted in a significant reduction of computing time. The proposed algorithm has been experimentally tested on a radiotherapy simulator unit with the use of a phantom and the obtained results are reported and discussed.

Algorithms

A reflectance photometer with a square photodiode array detector for use on multilayer dry-film slides.

This semiautomated prototype reflectance photometer measures reflected light from multilayer dry-film slides. The instrument makes use of a square photodiode array detector, a Hewlett-Packard desktop computer, and a modified mechanical transport mechanism from an Ektachem DT60 analyzer. When 2 microL of serum is placed on a dry-film slide, a colored spot is formed. The slide is automatically transported to an incubation area and then to the photometer area. There the spot is illuminated with dual tungsten lamps, and the reflected light passes through an interference filter, where it is focused on a square photodiode array containing 10,000 individual detectors. The analog signal from each detector is digitized and transmitted to a computer for calculation of the percentage of reflectance. I used a series of algorithms to locate the spot, estimate spot area, correct for minor variations in sample volume, and compute the average reflectance from a central spot area. To evaluate the instrument's performance, I ran parallel glucose determinations in the Beckman Astra; results correlated well. The small sample size along with no dead sample volume makes the system useful for small sample volumes.

Algorithms

Sequencing of megabase plus DNA by hybridization: theory of the method.

A mismatch-free hybridization of oligonucleotides containing from 11 to 20 monomers to unknown DNA represents, in essence, a sequencing of a complementary target. Realizing this, we have used probability calculations and, in part, computer simulations to estimate the types and numbers of oligonucleotides that would have to be synthesized in order to sequence a megabase plus segment of DNA. We estimate that 95,000 specific mixes of 11-mers, mainly of the 5'(A,T,C,G)(A,T,C,G)N8(A,T,C,G)3' type, hybridized consecutively to dot blots of cloned genomic DNA fragments would provide primary data for the sequence assembly. An optimal mixture of representative libraries in M13 vector, having inserts of (i) 7 kb, (ii) 0.5 kb genomic fragments randomly ligated in up to 10-kb inserts, and (iii) tandem "jumping" fragments 100 kb apart in the genome, will be needed. To sequence each million base pairs of DNA, one would need hybridization data from about 2100 separate hybridization sample dots. Inevitable gaps and uncertainties in alignment of sequenced fragments arising from nonrandom or repetitive sequence organization of complex genomes and difficulties in cloning "poisonous" sequences in Escherichia coli, inherent to large sequencing by any method, have been considered and minimized by choice of libraries and number of subclones used for hybridization. Because it is based on simpler biochemical procedures, our method is inherently easier to automate than existing sequencing methods. The sequence can be derived from simple primary data only by extensive computing. Phased experimental tests and computer simulations increasing in complexity are needed before accurate estimates can be made in terms of cost and speed of sequencing by the new approach. Nevertheless, sequencing by hybridization should show advantages over existing methods because of the inherent redundancy and parallelism in its data gathering.

Algorithms

A software-controlled EKG simulator.

This design allows generation of a wide range of waveforms from subaudio to ultrasonic directly via software. Waveforms may be calculated on the fly by suitable algorithms or produced from previously created lookup tables. The heart of the design is a fast 16-bit processor which directly executes the Forth programming language. A simple R/2R digital-to-analog converter is coupled to a parallel output port to produce the desired waveforms. This device has been used to generate realistic-appearing normal and abnormal EKG tracings in the lab.

Algorithms

Standard forms of dentition and mandible for applications in rotational panoramic radiography.

Mathematical expressions describing the average form and size of the dentition and the mandible are presented. These expressions should be of value in applications of panoramic radiography when reference to an average standard jaw form is of interest. Data were collected from axial radiographs of 35 males and 35 females of three ethnic groups: Mexican-Americans, black Americans and American and Scandinavian Caucasians. Curves were traced on the axial radiographs representing the dentition and the mandible and points along these curves digitized. Mathematical expressions were established using advanced algorithms for orthogonal polynomial curve fitting, i.e. perpendicular distances to the curved dentition and mandible were minimized rather than distances parallel to the y-axis in an arbitrarily chosen coordinate system. The standard deviations around the polynomials defining the average curves are demonstrated and expressions for calculating the continuously varying standard deviations are given.

Dentition

Fully automated measurements by light microscopy of tissue sections using a cellular array computer.

Software was developed for the acquisition, segmentation and analysis of microscopic OD-images on a VICOM digital image processor, extended with a VISIOMORPH morphoprocessor board. The delineation algorithms for peroxisomes, lysosomes, and nuclei in liver, kidney, and adrenal gland sections start by thresholding the difference between the original image and a low pass filtered version. The resulting binary mask is then processed by morphological operations in order to produce an object overlay. The efficiency of the programs is evaluated by comparing delineated objects at different OD-levels, created by varying the stain or by multiplying the original pixel values with constant factors. Manual delineation on some images is also used as a reference. More complex algorithms are used for the delineation of muscle fibres in ATP-ase-stained sections and immunocytochemically labelled cells in monolayer preparations. Muscle images from parallel sections with different stainings are matched with a coordinate transform, enabling the transfer of the object mask from a single delineated image to the unprocessed images and thus obtain all necessary information for fibre classification. After segmentation, the OD-images and their object overlays are fed into a data extraction program, measuring for each delineated object user-selected features. Data are sent to a VAX for statistical interpretation.

Adrenal Cortex

Eye-hand-coordination: a model for computing reaction times in a visually guided reach task.

A model is described which provides a simple algorithm to compute the reaction times of saccadic eye movements and reach movements aimed at a single visual target. It is assumed, that the two movements are prepared in parallel and initiated independently unless the preparation of the saccade for some reason takes longer than the preparation of the reach movement. In the latter case the final command to execute the reach movement is synchronized with that to execute the eye movement and therefore the corresponding reaction times are highly correlated in a one-to-one relationship. Random variables are used to predict sets of data that are directly comparable with the experimental results. The algorithm includes the effects of daily practice (learning). The structure of the model and its computational results will be compared with the physiological data from monkey and man.

Algorithms

Combined therapy for obese type 2 diabetes: suppertime mixed insulin with daytime sulfonylurea.

Combined insulin and sulfonylurea therapy for type 2 diabetes may improve the effectiveness of a single injection of insulin, thereby postponing the need for multiple injections. This concept was tested in 21 obese subjects imperfectly controlled by 20 mg of glyburide daily in a double masked, placebo-controlled, parallel design, 16-week protocol. Premixed 70% NPH/30% Regular insulin was taken before supper, and the dosage was adjusted weekly by an algorithm seeking nearly normal fasting glycemia. Eleven subjects using insulin plus 10 mg glyburide before breakfast had lower mean fasting glucose at 10-16 weeks than 10 subjects using insulin with placebo (mean +/- SEM; 5.9 +/- 0.3 versus 7.5 +/- 0.7 mmol/L; p less than 0.05), and had a greater decrement of glycosylated hemoglobin from baseline values (1.3 +/- 0.1 versus 0.8 +/- 0.2% A1, p less than 0.05). After 16 weeks the combined therapy group used half as much insulin as the insulin-only group (50 +/- 5 versus 101 +/- 13 units/d; p less than 0.01). Fasting serum free insulin values increased 58% from baseline after insulin therapy in the insulin-only group (p less than 0.05) but did not increase with combined therapy. Weight gain was similar in the two groups. These data support this form of combined therapy as one option for treating obese persons with type 2 diabetes no longer responsive to oral therapy alone.

Adult

Parallel computation for biological sequence comparison: comparing a portable model to the native model for the Intel Hypercube.

A parallel program for inter-database sequence comparison was developed on the Intel Hypercube using two models of parallel programming. One version was built using machine-specific Hypercube parallel programming commands. The other version was built using Linda, a machine-independent parallel programming language. The two versions of the program provide a case study comparing these two approaches to parallelization in an important biological application area. Benchmark tests with both programs gave comparable results with a small number of processors. As the number of processors was increased, the Linda version was somewhat less efficient. The Linda version was also run without change on Network Linda, a virtual parallel machine running on a network of desktop workstations.

Algorithms

An algorithm for protein engineering: simulations of recursive ensemble mutagenesis.

An algorithm for protein engineering, termed recursive ensemble mutagenesis, has been developed to produce diverse populations of phenotypically related mutants whose members differ in amino acid sequence. This method uses a feedback mechanism to control successive rounds of combinatorial cassette mutagenesis. Starting from partially randomized "wild-type" DNA sequences, a highly parallel search of sequence space for peptides fitting an experimenter's criteria is performed. Each iteration uses information gained from the previous rounds to search the space more efficiently. Simulations of the technique indicate that, under a variety of conditions, the algorithm can rapidly produce a diverse population of proteins fitting specific criteria. In the experimental analog, genetic selection or screening applied during recursive ensemble mutagenesis should force the evolution of an ensemble of mutants to a targeted cluster of related phenotypes.

Algorithms