Computer-based Quantification of Acellular Capillaries to Assess Experimental Diabetic Retinopathy

poster abstractDiabetic retinopathy (DR) is a disease of small blood vessels in the retina. The increase in the number of acellular capillaries is used as a marker to assess the severity of DR. The traditional approach for identifying acellular capillaries is manual counting of the capillaries either directly under the microscope or using the captured images. However, these methods are cumbersome and often involve inconsistencies among researchers. The purpose of this study is to reduce discrepancies in the enumeration of acellular capillaries using computer-based image processing algorithms. The retinas of control and diabetic mice were processed using trypsin digestion. The high resolution png format images of retinal quadrants were prepared from the trypsin digested retina. The computer programming was performed using the Python language along with open source packages such as OpenCv, Python Imaging Library (PIL), NumPy (Numerical Python) and SciPy. The images initially corrected for a Gaussian Blur and a Median blur to remove noise followed by the histogram based image segmentation. After image segmentation, a binary image was generated based on a histogram analysis. The segmentation threshold for binary image was determined and the medial axis transform (MAT) algorithm was applied to the binary image. The MAT representation was used to skeletonize the blood vessels and to detect branches and branch-points in those blood vessels. As part of the MAT computation, the distances from the skeleton to the vessel boundaries are encoded. The thin capilleries, i.e., acellular capilleries, were identified using a threshold on this distance which encodes the thickness of the vessel. Finally, acellular capillaries were counted by connected component algorithm. In conclusion, we have designed an automated computer-based system to enumerate the acellular capillaries. This computer-based automated system will help to maintain consistency in retinopathy assessment and may reduce time for analysis

A Wave-Chaotic Approach To Predicting And Measuring Electromagnetic Field Quantities In Complicated Enclosures

The coupling of short-wavelength electromagnetic waves into large complicated enclosures is of great interest in the field of electromagnetic compatibility engineering. The intent is to protect sensitive electronic devices housed within these enclosures from the detrimental effects of high-intensity external electromagnetic radiation penetrating into the enclosure (which acts as a resonant cavity) through various coupling channels (or ports). The Random Coupling Model introduced by Zheng, Antonsen and Ott is a stochastic model where the mechanism of the coupling process is quantified by the non-statistical "radiation impedance" of the coupling-port, and the field variations within the cavity are conjectured to be explained in a statistical sense through Random Matrix Theory- by assuming that the waves possess chaotic ray-dynamics within the cavity. The Random Coupling Model in conjunction with Random Matrix Theory thus makes explicit predictions for the statistical aspect (Probability Density Functions-PDFs) of the impedance, admittance and scattering fluctuations of waves within such wave-chaotic cavities. More importantly, these fluctuations are expected to be universal in that their statistical description depends only upon the value of a single dimensionless cavity loss-parameter. This universality in the impedance, admittance and scattering properties is not restricted to electromagnetic systems, but is equally applicable to analogous quantities in quantum-mechanical or acoustic systems, which also comprise of short-wavelength waves confined within complicated-shaped potential wells or acoustic-resonators. In this dissertation, I will experimentally show the validity of the "radiation impedance" to accurately quantify the port-coupling characteristics. I will experimentally prove the existence of these universal fluctuations in the impedance, admittance and scattering properties of quasi-two-dimensional and three-dimensional wave-chaotic systems driven by one-port or two-ports, and validate that their statistical nature is described through Random Matrix Theory. Finally, I will utilize the Random Coupling Model to formulate a prediction-algorithm to determine the shape and scales of induced voltages PDFs at specific points within complicated enclosures, such as computer boxes, when irradiated by high-intensity, short-wavelength electromagnetic energy. The insight gained from the experimental validation of the Random Coupling Model allows one to conceive of certain design-guidelines for cavity-enclosures that are more resistant to attack from an external short-wavelength electromagnetic source

Universal Impedance Fluctuations in Wave Chaotic Systems

We experimentally investigate theoretical predictions of universal impedance fluctuations in wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. Our approach emphasizes the use of the radiation impedance to remove the non-universal effects of the particular coupling from the outside world to the scatterer. Specific predictions that we test include the probability distribution functions (PDFs) of the real (related to the local density of states in disordered metals) and imaginary parts of the normalized cavity impedance, the equality of the variances of these PDFs, and the dependence of the universal PDFs on a single control parameter characterizing the level of loss. We find excellent agreement between the statistical data and theoretical predictions.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let

Universal Statistics of the Scattering Coefficient of Chaotic Microwave Cavities

We consider the statistics of the scattering coefficient S of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental S data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized, complex scattering coefficient whose Probability Density Function (PDF) is predicted to be universal in that it depends only on the loss (quality factor) of the cavity. We compare experimental PDFs of the normalized scattering coefficients with those obtained from Random Matrix Theory (RMT), and find excellent agreement. The results apply to scattering measurements on any wave chaotic system.Comment: 10 pages, 8 Figures, Fig.7 in Color, Submitted to Phys. Rev.

Characterization of Fluctuations of Impedance and Scattering Matrices in Wave Chaotic Scattering

In wave chaotic scattering, statistical fluctuations of the scattering matrix $S$ and the impedance matrix $Z$ depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. This paper considers the impedance and scattering variance ratios, $VR_z$ and $VR_s$, where $VR_z=Var[Z_{ij}]/\{Var[Z_{ii}]Var[Z_{jj}] \}^{1/2}$, $VR_s=Var[S_{ij}]/\{Var[S_{ii}]Var[S_{jj}] \}^{1/2}$, and $Var[.]$ denotes variance. $VR_z$ is shown to be a universal function of distributed losses within the scatterer. That is, $VR_z$ is independent of nonuniversal coupling details. This contrasts with $VR_s$ for which universality applies only in the large loss limit. Explicit results are given for $VR_z$ for time reversal symmetric and broken time reversal symmetric systems. Experimental tests of the theory are presented using data taken from scattering measurements on a chaotic microwave cavity.Comment: 6 pages, 5 figures, updated with referees' comment

Correlation Widths in Quantum--Chaotic Scattering

An important parameter to characterize the scattering matrix S for quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c T_c (where d is the mean resonance spacing, T_c with 0 <= T_c <= 1 the "transmission coefficient" in channel c and where the sum runs over all channels) provides a very good approximation to Gamma_{corr} even when the number of channels is small. That same conclusion applies also to the cross-section correlation function

Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption

We present the results of experimental and numerical study of the distribution of the reflection coefficient P(R) and the distributions of the imaginary P(v) and the real P(u) parts of the Wigner's reaction K matrix for irregular fully connected hexagon networks (graphs) in the presence of strong absorption. In the experiment we used microwave networks, which were built of coaxial cables and attenuators connected by joints. In the numerical calculations experimental networks were described by quantum fully connected hexagon graphs. The presence of absorption introduced by attenuators was modelled by optical potentials. The distribution of the reflection coefficient P(R) and the distributions of the reaction K matrix were obtained from the measurements and numerical calculations of the scattering matrix S of the networks and graphs, respectively. We show that the experimental and numerical results are in good agreement with the exact analytic ones obtained within the framework of random matrix theory (RMT).Comment: 15 pages, 8 figure

Automated Computer-Based Enumeration of Acellular Capillaries for Assessment of Diabetic Retinopathy

Diabetic retinopathy (DR) is the most common complications of diabetes; if untreated the DR can lead to a vision loss. The treatment options for DR are limited and the development of newer therapies are of considerable interest. Drug screening for the retinopathy treatment is undertaken using animal models in which the quantification of acellular capillaries (capillary without any cells) is used as a marker to assess the severity of retinopathy and the treatment response. The traditional approach to quantitate acellular capillaries is through manual counting. The purpose of this investigation was to develop an automated technique for the quantitation of acellular capillaries using computer-based image processing algorithms. We developed a custom procedure using the Python, the medial axis transform (MAT) and the connected component algorithm. The program was tested on the retinas of wild-type and diabetic mice and the results were compared to single blind manual counts by two independent investigators. The program successfully identified and enumerated acellular capillaries. The acellular capillary counts were comparable to the traditional manual counting. In conclusion, we developed an automated computer-based program, which can be effectively used for future pharmacological development of treatments for DR. This algorithm will enhance consistency in retinopathy assessment and reduce the time for analysis, thus, contributing substantially towards the development of future pharmacological agents for the treatment of DR