Random sampling for evaluating treatment plans

We analyze the influence of sampling technique on the accuracy of estimating irradiated volumes, dose-volume histograms and tumor control and normal tissue complication probabilities. The sampling techniques we consider are uniform distribution of points on a regular Cartesian grid and random selection of points. For three-dimensional treatment planning, random sampling leads to a significant reduction in estimation error and/or in the number of calculation points necessary to achieve a required accuracy. We discuss advantages and drawbacks of random sampling, as compared to sampling on a regular grid. It is suggested that, in practical situations, at least 50 times fewer randomly sampled points per organ/volume of interest are needed for fast estimation of complication probability with the same accuracy, i.e., not exceeding 5% (within 95% confidence limits) in the worst case.     

Three-dimensional computer-automated threshold Amsler grid test

We describe a novel method for testing a visual field that employs a computer monitor with displays of varying contrast that permits unprecedented resolution and characterization of the structure of scotomas in three dimensions. Patients are placed in front of a touch-sensitive computer screen at a fixed distance. With one eye covered, they focus on a central fixation marker and trace with their finger the areas on an Amsler grid that are missing from their field of vision. Increasing degrees of contrast of the Amsler grid are simulated by repeating the test at different gray-scale levels. The results are recorded and then displayed as topographical contour rings by the computer test program. The results can also be rendered as an immediate 3-D depiction of the central hill-of-vision. Several clinical pilot studies have been conducted at the Doheny Eye Institute and more than 200 patients have been examined with this system so far. Conditions such as optic neuritis, anterior ischemic optic neuropathy (AION), age-related macular degeneration (AMD), glaucoma, and ocular hypertension have been successfully assessed by this test. Each condition provides unique patterns that are most evident in 3-D. The 3-D computer-automated threshold Amsler grid test is an innovative and noninvasive visual field test. It provides several advantages over state-of-the-art standard automated perimetry, including: (1) additional information through 3-D depiction of scotomas, such as location, extent, slope, depth, and shape; (2) high angular resolution (1 deg compared with typically 6 deg); (3) a simple test setup (merely a touch-sensitive computer monitor and the test software); (4) excellent patient compliance (spending 4 to 5 min per eye). In light of its promising initial tests, the 3-D visual field test appears to have the potential for the early detection and monitoring of various diseases over time.     

Basic algorithms for random sampling and treatment randomization

Five BASIC programs to select random samples from populations or to randomize treatments are presented. Program 1 is used to obtain randomization of any number of treatments in an equal number of positions or test units for any number of replicates. Program 2 produces latin squares of any size for treatment randomization. Program 3 is used to obtain a specific number of randomly selected samples from a population without replacement. Program 4 produces quasi-latin squares that have treatments repeated equally in all rows and columns, with identical treatments either spaced or not. Program 5 can be used with any size grid to place 3-100 treatments in equal proportions and with spacing of identical treatments. Both programs 4 and 5 allow for horizontal and vertical separation between identical treatments at sampling places while still retaining the quality of randomness. These programs should facilitate random sampling and randomization procedures which are required to correctly analyze experiments by the methods of statistical probability.     

Weak reflection of a wave by a one-dimensional array of randomly spaced elements, with reference to the scattering of ultrasound by blood

The mean reflection coefficient is deduced for a line of elements each of the same thickness, placed at random between two fixed ends, where the reflection coefficient of each element is very small. This theory is applied to the problem of the scattering of ultrasound by blood, and some qualitative agreement with experimental data is found. A simplified theory is also presented, from which the variance of the reflection coefficient is given.     

Solid shape discrimination from vision and haptics: natural objects (<Emphasis Type="Italic">Capsicum annuum</Emphasis>) and Gibson’s “feelies”

A set of three experiments evaluated 96 participants’ ability to visually and haptically discriminate solid object shape. In the past, some researchers have found haptic shape discrimination to be substantially inferior to visual shape discrimination, while other researchers have found haptics and vision to be essentially equivalent. A primary goal of the present study was to understand these discrepant past findings and to determine the true capabilities of the haptic system. All experiments used the same task (same vs. different shape discrimination) and stimulus objects (James Gibson’s “feelies” and a set of naturally shaped objects—bell peppers). However, the methodology varied across experiments. Experiment 1 used random 3-dimensional (3-D) orientations of the stimulus objects, and the conditions were full-cue (active manipulation of objects and rotation of the visual objects in depth). Experiment 2 restricted the 3-D orientations of the stimulus objects and limited the haptic and visual information available to the participants. Experiment 3 compared restricted and full-cue conditions using random 3-D orientations. We replicated both previous findings in the current study. When we restricted visual and haptic information (and placed the stimulus objects in the same orientation on every trial), the participants’ visual performance was superior to that obtained for haptics (replicating the earlier findings of Davidson et al. in Percept Psychophys 15(3):539–543, 1974). When the circumstances resembled those of ordinary life (e.g., participants able to actively manipulate objects and see them from a variety of perspectives), we found no significant difference between visual and haptic solid shape discrimination.     

Assessment of a three-dimensional robotic model for biomechanical-data acquisition of human movement

The use of a kinematic robotic model has not been implemented in the biomechanical-data acquisition protocol, as it has in workplace analysis, ergonomics and design. The purpose of this paper was to assess the use of a kinematic model to retrieve frames of human movements from data obtained at a low sampling frequency. From experimental trials with an original sampling frequency of 60 Hz, the data were sampled again at two lower frequencies, 5 Hz and 10 Hz. The model was then used to reconstitute the data to its original frequency (60 Hz). The results demonstrated that it was possible to retrieve a full 3-D human movement from a sampling rate lower than normal without sacrificing accuracy. It was observed from both reduced sampling frequencies that the error level was comparable to the usual accuracy of a DLT 3-D reconstruction technique. It was therefore concluded that the data retrieved from these two frequencies were very similar to the original data sampled at 60 Hz.     

Approach for the smoothing of three-dimensional reconstructions of the human spine using dual Kriging interpolation

In numerous situations, 3-D reconstructions of the spine are represented as curves in space, with the vertebral centroids as control points. Interpolation functions such as splines, polynomials or Fourier series have been used to minimise measurement errors and to perform specific calculations. A more general approach, dual Kriging, is presented which incorporates in a single formulation several methods, such as piece-wise linear interpolation, splines and least square functions as a limit case. To minimise user interaction and to control the different Kriging parameters, a computer program is developed allowing efficient use of these interpolation techniques in a clinical environment. Given different drift and covariance functions, the program determines the most suitable Kriging model for specific spine geometries and controls the amount of smoothing performed on raw data. Validation of the technique is with analytical 3-D curves, where random noise is added to represent reconstruction errors. A maximum absolute mean difference of 1·85±0·50 mm is found between the analytical and noisy curves smoothed with the Kriging technique for 200 points. Results obtained on actual 3-D reconstructions of scoliotic patients are very promising.     

Methodology for sampling questing nymphs of Ixodes ricinus (Acari: Ixodidae), the principal vector of Lyme disease in Europe

To assess the Lyme borreliosis vector population density we set up a methodology for sampling the Ixodes ricinus L. population host questing on the vegetation. We focused on the collection of the nymphal stage, which is the principal stage of disease transmission to humans. This study was carried out in Rambouillet forest (Yvelines, France) where seven study areas were demarcated. These areas are maximally homogeneous for plant species using a finer scale than the phytosociological classification as defined by the method of landscape diagnostics. Out of 23 collections performed from March 1997 to May 1998, 2,906 I. ricinus nymphs were collected. The sampling technique chosen was the cloth lure technique. The technical parameters were studied and fixed (cloth type, cloth size, sample size, researcher position). It appeared that toweling was the best cloth type to optimize the number of ticks collected; the position of the researcher had no effect on tick samples. To satisfy the criteria for correct sampling, we studied representativity, randomness, and nonselectivity of our methodology. The spatial distribution of nymphs in a homogeneous area was close to random and thus very few subsamples were needed to obtain a relative density which was representative. No significant differences were found between random samples and following transect samples; and nonselectivity was totally satisfied because we only worked on questing nymphs. We grouped the samples that presented no significant differences to attribute a density index, which varied from 0 to 5. This methodology, applied with the same parameters, offers potential for producing comparable results from studies in different geographical areas and at different times of the years.     

The role of three-dimensional information in health care and medical education: the implications for anatomy and dissection

The purposes of medical education can be summarized as learning how to take an effective history, perform a physical examination, and perform diagnostic and therapeutic procedures with minimal risk and maximal benefit to patients. Because patients are three-dimensional (3-D) objects, health care and medical education involve learning and applying 3-D information. The foundation begins in anatomy where students form and confirm or reform their own 3-D ideas and images of the development and structure of the human body at all levels of organization. Students go on to understand the interdependence of structure and function in health and disease. The basic questions for those teaching anatomy are "How do we learn and use 3-D information?" and "How is it taught most effectively?" These are not easy questions for teachers and are rarely asked by those who currently defend or reframe curricula. Unfortunately, there is little information on how we learn 3-D information and no evidence-based literature on the relative long-term vocational effectiveness of methods for teaching it. It is clear that we learn in several distinct modalities and that our students represent a spectrum of learning styles. To support the 3-D learning essential to both medical education and health care, anatomical societies need to provide answers to the following questions: Do the opportunities of dissection (visual, tactile, time, discovery, group process, mentoring) contribute to short- and long-term learning of 3-D information? If so, how? Does dissection offer significant advantages over other methods for learning, confirming, and using 3-D information in anatomy? Answers to these questions will provide a rational basis for decisions about curricular changes in anatomy courses (if, where, and when dissection should occur). This, in turn, will link these changes to society's ultimate purposes for medical education and health care rather than to the fiscal concerns of the businesses of health care and medical education, which is the current practice.     

Regulation of axon guidance and extension by three-dimensional constraints

Axons in vivo are guided by molecular signals acting as attractants and repellents, and possibly by physical constraints encountered in the extracellular environment. We analyzed the ability of primary sensory axons to extend and undergo guidance in three-dimensional (3-D) environments generated using photolithography. Confinement of neurons in fully enclosed square chambers decreased the percentage of neurons establishing axons as a function of chamber width. However, the ability to extend an axon in one or more directions allowed axons to form and extend similarly to those on two-dimensional (2-D) substrata. Live imaging of growth cones interacting with the walls of chambers or corridors revealed that growth cones respond to contact with a 3-D constraint by decreasing surface area, and circumvent constraints by repeated sampling of the constraint until an unobstructed path is encountered. Analysis of the ability of axons to turn around corners in corridors revealed that the angle of the corner and corridor width determined the frequency of turning. Finally, we show that the length of axons can be controlled through the use of 3-D constraints. These data demonstrate that 3-D constraints can be used to guide axons, and control the extent of axon formation and the length of axons.     

Verification of the two-dimensional disector, a method for the unbiased estimation of density and number of myelinated nerve fibers in peripheral nerves

Quantification of the number of myelinated fibers in peripheral nerves is a common requirement in quantitative morphology. This parameter provides important information on the consequences of various physiological, pathological and experimental conditions on the nerve structure and is one of the main indicators of success of peripheral nerve repair. In this paper, the theoretical rationale for the application of stereological principles to obtain unbiased estimates of the density and total number of myelinated fibers in peripheral nerves is discussed and a simple stereological method is described. The method is applied together with a systematic random sampling scheme, that was optimized for the purposes of the present study, and with sampling scheme analysis by calculating the coefficient of error (CE). The stereological method, which consists of a two-dimensional variation of the classical disector procedure (two-dimensional disector), and the sampling scheme are verified by comparing estimates with the true density and total number of myelinated fibers in peripheral nerve trunks where true values have been accurately determined by extensive counting. The verification of the 2-D disector method, both of normal and regenerated nerves, showed that estimates of density and total number of myelinated nerve fibers are unbiased. The method also proved to be efficient (time-saving): Estimation of density and total number of myelinated fibers in a single nerve takes about 2-3 hours.     

Generation and use of measurement-based 3-D dose distributions for 3-D dose calculation verification.

A 3-D radiation therapy treatment planning system calculates dose to an entire volume of points and therefore requires a 3-D distribution of measured dose values for quality assurance and dose calculation verification. To measure such a volumetric distribution with a scanning ion chamber is prohibitively time consuming. A method is presented for the generation of a 3-D grid of dose values based on beam's-eye-view (BEV) film dosimetry. For each field configuration of interest, a set of BEV films at different depths is obtained and digitized, and the optical densities are converted to dose. To reduce inaccuracies associated with film measurement of megavoltage photon depth doses, doses on the different planes are normalized using an ion-chamber measurement of the depth dose. A 3-D grid of dose values is created by interpolation between BEV planes along divergent beam rays. This matrix of measurement-based dose values can then be compared to calculations over the entire volume of interest. This method is demonstrated for three different field configurations. Accuracy of the film-measured dose values is determined by 1-D and 2-D comparisons with ion chamber measurements. Film and ion chamber measurements agree within 2% in the central field regions and within 2.0 mm in the penumbral regions.     

Cross-validated models of the relationships between neck muscle electromyography and three-dimensional head kinematics during gaze behavior

The object of this study was to model the relationship between neck electromyography (EMG) and three-dimensional (3-D) head kinematics during gaze behavior. In two monkeys, we recorded 3-D gaze, head orientation, and bilateral EMG activity in the sternocleidomastoid, splenius capitis, complexus, biventer cervicis, rectus capitis posterior major, and occipital capitis inferior muscles. Head-unrestrained animals fixated and made gaze saccades between targets within a 60° × 60° grid. We performed a stepwise regression in which polynomial model terms were retained/rejected based on their tendency to increase/decrease a cross-validation-based measure of model generalizability. This revealed several results that could not have been predicted from knowledge of musculoskeletal anatomy. During head holding, EMG activity in most muscles was related to horizontal head orientation, whereas fewer muscles correlated to vertical head orientation and none to small random variations in head torsion. A fourth-order polynomial model, with horizontal head orientation as the only independent variable, generalized nearly as well as higher order models. For head movements, we added time-varying linear and nonlinear perturbations in velocity and acceleration to the previously derived static (head holding) models. The static models still explained most of the EMG variance, but the additional motion terms, which included horizontal, vertical, and torsional contributions, significantly improved the results. Several coordinate systems were used for both static and dynamic analyses, with Fick coordinates showing a marginal (nonsignificant) advantage. Thus, during gaze fixations, recruitment within the neck muscles from which we recorded contributed primarily to position-dependent horizontal orientation terms in our data set, with more complex multidimensional contributions emerging during the head movements that accompany gaze shifts. These are crucial components of the late neuromuscular transformations in a complete model of 3-D head-neck system and should help constrain the study of premotor signals for head control during gaze behaviors.     

Two-dimensional phased arrays of sources and detectors for depth discrimination in diffuse optical imaging

We present a multisource, multidetector phased-array approach to diffuse optical imaging that is based on postprocessing continuous-wave data. We previously showed that this approach enhances the spatial resolution of diffuse optical imaging. We now demonstrate the depth discrimination capabilities of this approach and its potential to perform tomographic sectioning of turbid media. The depth discrimination results from the dependence of the sensitivity function on the depth coordinate z. To demonstrate the potential of this approach, we perform an experimental study of a turbid medium containing cylindrical inhomogeneities that are placed 2.0, 3.0, and 4.0 cm from a seven-element, 2-D source array. A single detector element is placed at a distance of 6.0 cm from the source array, and the measurement is repeated after switching the positions of the detector and the source array to simulate the case where both sources and detectors consist of a 2-D array of elements. We find that the proposed phased-array method is able to separate cylinders at different depths, thus showing cross-sectioning capabilities.     

Three-dimensional terahertz pulse imaging of dental tissue

There are unresolved clinical problems that require the provision of accurate 3-D images of tissue structures such as teeth. In particular, measurements of dental enamel thickness are necessary to quantify problems associated with enamel erosion, yet currently there is no nondestructive method to obtain this information. We present a method that relies on the use of pulsed terahertz radiation to gain 3-D information from dental tissues. We discuss results from 14 samples and demonstrate that we can reliably and accurately quantify enamel thickness. We show that in a series of 22 surfaces, we can image pertinent subsurface features 91% of the time. Example images are shown where structures in teeth at depth are rendered accurate to within 10 microm. We discuss issues that arise using this imaging method and propose ways in which it could be used in clinical practice.     

Potential clinical impact of three-dimensional visualization for fluorescent in situ hybridization image analysis

Chromosomal translocation is strong indication of cancers. Fluorescent in situ hybridization (FISH) can effectively detect this translocation and achieve high accuracy in disease diagnosis and prognosis assessment. For this purpose, whole chromosome paint probes are utilized to image the configuration of DNA fragments. Although two-dimensional (2-D) microscopic images are typically used in FISH signal analysis, we present a case where the translocation occurs in the depth direction where two probed FISH signals are overlapped in the projected image plane. Thus, the translocation cannot be identified. However, when imaging the whole specimen with a confocal microscope at 27 focal planes with 0.5-μm step interval, the translocation can be clearly identified due to the free rotation capability by the three-dimensional (3-D) visualization. Such a translocation detection error of using 2-D images might be critical in detecting and diagnosing early or subtle disease cases where detecting a small number of abnormal cells can make diagnostic difference. Hence, the underlying implication of this report suggests that utilizing 3-D visualization may improve the overall accuracy of FISH analysis for some clinical cases. However, the clinical efficiency and cost of using 3-D versus 2-D imaging methods are also to be assessed carefully.     

THE FACTORS EFFECTING CHANGES IN THE SENSITIVITY OF AN IMPEDANCE IMAGING SYSTEM

IntroductionWhenelectricalimpedanceimagesaremadefromlivingsubjects,thesensitivityanditSinfluenceeffectsofthesystemarecriticalfortheapplicationinrealdatecting.Electrodesmustbeusedtoconnecttheinstrumenttothesubjects.Isaacsonacal.showedthatthedistinguishabilityofinhomogeneitiesinatWo-dimensionalimpedanceimagewasmaximizediftheelectrodeswereaswideaspossible,soastonearlyfilltheavailablecircumference[l].ThatstUdygavenoguidanceastotheappropriateelectrodeheight.ThepresentStodywasdesignedtohelpfindsom…     

Three-dimensional reconstructions from non-deparaffinized tissue sections

Three-dimensional (3-D) reconstruction from microscopic images represents a useful tool for the study of biological structures in embryology and developmental biology. However, it is usually necessary to cope with many difficulties connected with the preparation of specimens. In order to minimize mutual displacement of structures in successive sections, the applicability of non-deparaffinized tissue sections for 3-D reconstruction was tested. Chicken embryos were fixed and stained in toto with eosin and then embedded in paraffin. About 30-μm-thick non-deparaffinized serial sections were used for obtaining initial data for 3-D reconstruction of larger stacks of embryonic bodies using either fluorescence or confocal microscope. The same sections served for both collecting optical serial sections of mesonephros as source images for its 3-D reconstruction, and immunohistochemical detection of fibronectin, laminin and vimentin. It was found that sections with retained paraffin preserve the mutual spatial relationships of tissue components as well as provide an excellent differentiation of structure. It makes the process of 3-D reconstruction easier. The localization of the products of immunohistochemical reactions demonstrated the co-localization of fibronectin and laminin in basal laminas and the presence of vimentin in glomeruli and mesenchymal tissue. The use of non-deparaffinized sections represents a less time consuming and more effective alternative to thin histological sections for the purpose of 3-D reconstruction, and enables further application of material.     

Convolution/superposition using the Monte Carlo method

The convolution/superposition calculations for radiotherapy dose distributions are traditionally performed by convolving polyenergetic energy deposition kernels with TERMA (total energy released per unit mass) precomputed in each voxel of the irradiated phantom. We propose an alternative method in which the TERMA calculation is replaced by random sampling of photon energy, direction and interaction point. Then, a direction is randomly sampled from the angular distribution of the monoenergetic kernel corresponding to the photon energy. The kernel ray is propagated across the phantom, and energy is deposited in each voxel traversed. An important advantage of the explicit sampling of energy is that spectral changes with depth are automatically accounted for. No spectral or kernel hardening corrections are needed. Furthermore, the continuous sampling of photon direction allows us to model sharp changes in fluence, such as those due to collimator tongue-and-groove. The use of explicit photon direction also facilitates modelling of situations where a given voxel is traversed by photons from many directions. Extra-focal radiation, for instance, can therefore be modelled accurately. Our method also allows efficient calculation of a multi-segment/multi-beam IMRT plan by sampling of beam angles and field segments according to their relative weights. For instance, an IMRT plan consisting of seven 14 x 12 cm2 beams with a total of 300 field segments can be computed in 15 min on a single CPU, with 2% statistical fluctuations at the isocentre of the patient's CT phantom divided into 4 x 4 x 4 mm3 voxels. The calculation contains all aperture-specific effects, such as tongue and groove, leaf curvature and head scatter. This contrasts with deterministic methods in which each segment is given equal importance, and the time taken scales with the number of segments. Thus, the Monte Carlo superposition provides a simple, accurate and efficient method for complex radiotherapy dose calculations.     

Statistical reconstruction for x-ray CT systems with non-continuous detectors

We analyse the performance of statistical reconstruction (SR) methods when applied to non-continuous x-ray detectors. Robustness to projection gaps is required in x-ray CT systems with multiple detector modules or with defective detector pixels. In such situations, the advantage of statistical reconstruction is that it is able to ignore missing or faulty pixels and that it makes optimal use of the remaining line integrals. This potentially obviates the need to fill the sinogram discontinuities by interpolation or any other approximative pre-processing techniques. In this paper, we apply SR to cone beam projections of (i) a hypothetical modular detector micro-CT scanner and of (ii) a system with randomly located defective detector elements. For the modular-detector system, SR produces reconstruction volumes free of noticeable gap-induced artefacts as long as the location of detector gaps and selection of the scanning range provide complete object sampling in the central imaging plane. When applied to randomly located faulty detector elements, SR produces images free of substantial ring artefacts even for cases where defective pixels cover as much as 3% of the detector area.