Raksha Urs

Visual rating system for assessing magnetic resonance images: a tool in the diagnosis of mild cognitive impairment and Alzheimer disease.

Subjects with mild cognitive impairment (MCI) and mild Alzheimer disease (AD) can be distinguished from elderly subjects with no cognitive impairment (NCI) by the degree of atrophy in the entorhinal cortex (ERC) and the hippocampus (HPC), quantified by volumetric magnetic resonance image (MRI) studies. Because volumetric MRI requires rigorous standards for image acquisition and analysis and is not suitable for routine clinical use, we have used calibrated visual rating to measure atrophy in the ERC, HPC, and perirhinal cortex (PRC) and evaluated its utility in the diagnosis of very early AD. Methods: Thus far, visual rating methods, which have been found to be reliable and sensitive only for measurement of atrophy of the HPC or for the entire medial temporal region, have been found to be relatively insensitive for discriminating mild AD from elderly NCI subjects. We have developed a computer-based visual rating system (VRS) using reference images for calibration of atrophy ratings in several discrete brain regions, including the ERC, HPC, and PRC. The VRS reference images facilitate training of raters and promote standardization of all atrophy ratings. Interrater and intrarater reliability measurements were assessed; subsequently, the ability of VRS to discriminate the diagnoses among 73 elderly subjects was studied (NCI = 27, MCI = 23, and AD = 23). Results: Kappa values for interrater reliability of the ERC, HPC, and PRC were between 0.75 and 0.94, and for intrarater reliability, they were between 0.84 and 0.93, indicating that VRS enables highly reliable ratings to be obtained. Atrophy ratings in the ERC, HPC, and PRC distinguished AD from NCI subjects but did not distinguish AD from MCI subjects who tended to have intermediate levels of atrophy. Right and left ERC ratings and the right HPC rating distinguished MCI from NCI subjects. Conclusions: The visual rating system is the first semiquantitative method that enables reliable measurements of ERC atrophy, and ERC measurement was found to be the best discriminator between MCI and NCI subjects. Visual rating system is a user-friendly tool that can allow a radiologist or a clinician to use structural MRI scans to be used as a biomarker in the diagnosis of prodromal AD.

Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens

PURPOSE To develop an age-dependent mathematical model of the isolated ex-vivo human crystalline lens shape to serve as basis for use in computational modeling. METHODS Profiles of whole isolated human lenses (n=27) aged 6 to 82, were measured from shadow-photogrammetric images. Two methods were used to analyze the lenses. In the two curves method (TCM) the anterior and posterior surfaces of the lens were fit to 10th-order even polynomials and in the one curve method (OCM) the contour of one half-meridional section of the lens was fit to 10th-order polynomials. The age-dependence of the polynomial coefficients was assessed. The analysis was used to produce an age-dependent polynomial model of the whole lens shape. RESULTS The root mean squared errors for the fits ranged from 11 to 70 microm for the OCM, 9 to 27 microm for the posterior surface of the TCM and 8 to 134 microm for the anterior surface of the TCM. The coefficients of the OCM did not display a significant trend with age. The 2nd-, 6th- and 10th-order coefficients of the anterior surface of the TCM decreased with age while the 8th-order coefficient increased. For the posterior surface of the TCM, the 8th-order coefficient significantly decreased with age and the 10th-order coefficient increased. The age-dependent equations of both the models provide a reliable model from age 20 to 60. The OCM model can be used for lenses older than 60 as well. CONCLUSION The shape of the whole human crystalline lens can be accurately modeled with 10th-order polynomial functions. These models can serve to improve computational modeling, such as finite element (FE) modeling of crystalline lenses.PURPOSE To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. METHODS Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. RESULTS Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205 microm. The age-dependent equations provide a reliable lens model for ages 20-60 years. CONCLUSION The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens.

Small animal ocular biometry using optical coherence tomography

A custom-built OCT system was used to obtain images of the whole mouse eye. We developed a semi-automated segmentation method to detect the boundaries of the anterior and posterior corneal, lens and retinal surfaces as well as the anterior surface of the iris. The radii of curvature of the surfaces were calculated using a conic section fit of each boundary. Image distortions due to refraction of the OCT beam at the successive boundaries were corrected using a ray-tracing algorithm. Corrected ocular distances, radii of curvature of the cornea and lens surfaces, and anterior chamber angle were obtained on 3 C57BL/6J mice. In vivo imaging of the whole eye, segmentation, conic function fits and correction were successful in all three animals. The posterior lens surface of one mouse could not be fit accurately with a conic section. Biometric parameters of C57BL/6J mice compared well with previous published data obtained from histological sections. The study demonstrates the feasibility of quantitative in vivo biometry of mouse models.

Model of the Isolated Ex-Vivo Human Crystalline Lens Using Cosine Functions

The purpose of this study is to develop an age dependent model of the whole isolated ex-vivo human crystalline lens shape using a single mathematical function. Contours of whole isolated human crystalline lenses were obtained from shadow-photogrammetric images. 28 lenses (PMT=1 to 5 days) ranging in age from 6 to 90 years were used for this study. Lens contours were extracted using MATLAB’s morphological and edge detection functions. The contours were first fit to a 10th-order even Fourier series containing tilt and decentration terms in a polar coordinate system using MATLAB’s curve fitting toolbox to determine the position of the lens center and the tilt angle. To ensure axis-symmetry, phase terms were excluded from the Fourier series. This preliminary analysis was used to correct for tilt and decentration. The corrected profiles were resampled and the first 11 coefficients of the Fourier decomposition were calculated and analyzed as a function of age. The root mean squared error between the original lens contour and the lens profile reconstructed using the coefficients of the Fourier decomposition ranged from 13 to 66 μm. Only the coefficient of the zeroth-order term (i.e. diameter of the ‘equivalent’ fitted circle) showed a significant increasing trend with age (a0 = 0.007 x Age + 2.675; p< 0.0001). From this study it can be concluded that the shape of the whole human crystalline lens can be accurately modeled with 10thorder Fourier series within a polar coordinate system.