Catastrophe optics theory unveils the localised wave aberration features that generate ghost images.

Monocular polyplopia (ghost or multiple images) is a serious visual impediment for some people who report seeing two (diplopia), three (triplopia) or even more images. Polyplopia is expected to appear if the point spread function (PSF) has multiple intensity cores (a dense concentration of a large portion of the radiant flux contained in the PSF) relatively separated from each other, each of which contributes to a distinct image. We present a theory that assigns these multiple PSF cores to specific features of aberrated wavefronts, thereby accounting optically for the perceptual phenomenon of monocular polyplopia. The theory provides two major conclusions. First, the most likely event giving rise to multiple PSF cores is the presence of hyperbolic, or less probably elliptical, umbilic caustics (using the terminology of catastrophe optics). Second, those umbilic caustics formed on the retinal surface are associated with certain points of the wave aberration function, called cusps of Gauss, where the gradient of a curvature function vanishes. However, not all cusps of Gauss generate those umbilic caustics. We also provide necessary conditions for those cusps of Gauss to be fertile. To show the potential of this theoretical framework for understanding the nature and origin of polyplopia, we provide specific examples of ocular wave aberration functions that induce diplopia and triplopia. The polyplopia effects in these examples are illustrated by depicting the multi-core PSFs and the convolved retinal images for clinical letter charts, both through computer simulations and through experimental recording using an adaptive optics set-up. The number and location of cores in the PSF is thus a potentially useful metric for the existence and severity of polyplopia in spatial vision. These examples also help explain why physiological pupil constriction might reduce the incidence of ghosting and multiple images of daily objects that affect vision with dilated pupils. This mechanistic explanation suggests a possible role for optical phase-masking as a clinical treatment for polyplopia and ghosting.

A flexible anatomical set of mechanical models for the organ of Corti.

We build a flexible platform to study the mechanical operation of the organ of Corti (OoC) in the transduction of basilar membrane (BM) vibrations to oscillations of an inner hair cell bundle (IHB). The anatomical components that we consider are the outer hair cells (OHCs), the outer hair cell bundles, Deiters cells, Hensen cells, the IHB and various sections of the reticular lamina. In each of the components we apply Newton's equations of motion. The components are coupled to each other and are further coupled to the endolymph fluid motion in the subtectorial gap. This allows us to obtain the forces acting on the IHB, and thus study its motion as a function of the parameters of the different components. Some of the components include a nonlinear mechanical response. We find that slight bending of the apical ends of the OHCs can have a significant impact on the passage of motion from the BM to the IHB, including critical oscillator behaviour. In particular, our model implies that the components of the OoC could cooperate to enhance frequency selectivity, amplitude compression and signal to noise ratio in the passage from the BM to the IHB. Since the model is modular, it is easy to modify the assumptions and parameters for each component.

Phenotypic Models of CAR T-Cell Activation Elucidate the Pivotal Regulatory Role of CAR Downmodulation.

Adoptive cell immunotherapy with chimeric antigen receptor (CAR) showed limited potency in solid tumors, despite durable remissions for hematopoietic malignancies. Therefore, an investigation of ways to enhance the efficacy of CARs' antitumor response has been engaged upon. We previously examined the interplay between the biophysical parameters of CAR binding (i.e., affinity, avidity, and antigen density), as regulators of CAR T-cell activity and detected nonmonotonic behaviors of affinity and antigen density and an interrelation between avidity and antigen density. Here, we built an evolving phenotypic model of CAR T-cell regulation, which suggested that receptor downmodulation is a key determinant of CAR T-cell function. We verified this assumption by measuring and manipulating receptor downmodulation and intracellular signaling processes. CAR downmodulation inhibition, via actin polymerization inhibition, but not inhibition of regulatory inhibitory phosphatases, was able to increase CAR T-cell responses. In addition, we documented trogocytosis in CAR T cells that depends on actin polymerization. In summary, our study modeled the parameters that govern CAR T-cell engagement and revealed an underappreciated mechanism of T-cell regulation. These results have a potential to predict and therefore advance the rational design of CAR T cells for adoptive cell treatments.See related article on p. 872.

Expression of Semaphorin 3A in Malignant and Normal Bladder Tissue: Immunohistochemistry Staining and Morphometric Evaluation.

INTRODUCTION: Our previous studies showed elevated levels of Semaphorin3a (Sema3A) in the urine of patients with urothelial cancer compared to healthy patients. The aim of this study was to analyze the extent of Sema3A expression in normal and malignant urothelial tissue using immune-staining microscopic and morphometric analysis. MATERIALS AND METHODS: Fifty-seven paraffin-embedded bladder samples were retrieved from our pathology archive and analyzed: 14 samples of normal urothelium, 21 samples containing low-grade urothelial carcinoma, 13 samples of patients with high-grade urothelial carcinoma, 7 samples containing muscle invasive urothelial carcinoma, and 2 samples with pure urothelial carcinoma in situ. All samples were immunostained with anti Sema3A antibodies. The area of tissue stained with Sema3A and its intensity were analyzed using computerized morphometry and compared between the samples' groups. RESULTS: In normal bladder tissue, very light Sema3A staining was demonstrated on the mucosal basal layer and completely disappeared on the apical layer. In low-grade tumor samples, cells in the basal layer of the mucosa were also lightly stained with Sema3A, but Seama3A expression intensified upon moving apically, reaching its highest level on apical cells exfoliating to the urine. In high grade urothelial tumors, Seama3A staining was intense in the entire thickness of the mucosa. In samples containing carcinoma in situ, staining intensity was high and homogenous in all the neoplastic cells. CONCLUSIONS: Sema3A may be serve as a potential non-invasive marker of urothelial cancer.

On the geometry of visual starbursts.

The patterns observed by people when they look at stars are collectively called starbursts. Similar patterns are observed when viewing any distant object with sufficiently large pupils. We show here that starbursts are mainly curved, formed by the intersections of caustic surfaces, and associated with a wavefront emitted by a far object, with the retina. In particular, we derive the equations governing these caustic curves, present a few properties of their solutions, and compare the solutions with recent clinical observations. We further classify the starbursts into primary (the caustic curves themselves) and secondary (the diffraction patterns near the caustics).

Preoperative neutrophil to lymphocyte ratio improves recurrence prediction of non-muscle invasive bladder cancer.

BACKGROUND: This study aims to prospectively evaluate the ability of Neutrophil-to-Lymphocyte ratio (NLR) to forecast recurrence in patients with non-muscle invasive bladder cancer (NMIBC). This is a continuation of our two previous retrospective studies that indicated the NLR > 2.5 criterion as a predictor of recurrence in patients with NMIBC. METHODS: Since December 2013, all patients admitted to our department for TUR-BT and agreed to participate, had a blood drawn for cell count and differential 24 h prior to surgery. Patients with pathological NMIBC were followed prospectively for disease recurrence. The end-point of the follow up was either a cancer recurrence or the termination of the study. Univariate and multivariate Cox regressions were performed to assess the NLR > 2.5 predictive capability for recurrence, versus and in conjunction to the pathologically based EORTC score, among additional statistical analyses. RESULTS: The study cohort included 96 men and 17 women with a median age of 72 years. Sixty-four patients (56.6%) have had a recurrence during the study occurring at the median time of 9 months (IQR 6, 13), while the median follow-up time for patients without recurrence was 18 months (IQR 10, 29). Univariate Cox regressions for recurrence demonstrated significance for NLR > 2.5 for the whole cohort (p = 0.011, HR 2.015, CI 1.175-3.454) and for the BCG sub-group (p = 0.023, HR 3.7, CI 1.2-11.9), while the EORTC score demonstrated significance for the 'No Treatment' subgroup (p = 0.024, HR 1.278, CI 1.03-1.58). When analyzed together as a multivariate Cox model, the NLR > 2.5 and EORTC score retained their significance for the aforementioned groups, while also improving the EORTC score significance for the whole cohort. CONCLUSION: NLR > 2.5 was found to be a significant predictor of disease recurrence and demonstrated high hazard ratio and worse recurrence-free survival in patients with NMIBC, especially in those treated with BCG. Additionally, our data demonstrated statistical evidence that NLR > 2.5 might have an improving effect on the EORTC score's prediction when analyzed together.

Overexpression of semaphorin 3A in patients with urothelial cancer.

OBJECTIVE: A highly sensitive and specific urine marker for the detection of recurrent urothelial cancer and for screening healthy population or people at risk for urothelial cancer has not been found yet. As urine cytology is not sensitive enough, patients with non-muscle-invasive bladder cancer need lifelong follow-up involving multiple invasive cystoscopies. Our aims of study were to examine the expression of semaphorin 3A in urothelial cancer patients and to evaluate semaphorin 3A as a potential marker for urothelial cancer. MATERIALS AND METHODS: Urine samples were taken from patients with known bladder tumor, hospitalized for transurethral resection of lesions, from patients with history of urothelial cancer admitted for endoscopic follow up, from patients with other nonmalignant urological conditions such as prostatic hyperplasia, stress incontinence, urethral stricture, ureteral and kidney stones, and from healthy volunteers with no history of urothelial malignancy and no urological symptoms. Semaphorin 3A (sema3A) protein level was measured using enzyme-linked immunosorbent assay in every sample and levels were correlated with endoscopic and pathological findings. In addition, we performed immunohistochemically staining with semaphorin 3A of 15 tissue samples (various tumors and normal bladder tissues). RESULTS: A total of 183 urine samples were tested. Out of them, 116 patients (mean age 70.7; 94 males and 22 females) had positive cystoscopy, and 67 (mean age 64.7; 51 males and 16 females) had negative cystoscopy. Higher sema3A values were significantly correlated (P = 0.006) with presence of urothelial cancer, as determined by positive cystoscopy or urethroscopy and pathological biopsy. Sema3A levels also showed positive correlation with the number of tumors. Sema3A levels combined with urine cytology showed much higher sensitivity compared with cytology alone (66% vs. 33%), with smaller reduction of specificity (77% vs. 90%). Immunohistochemical staining showed intense staining in high stage and grade tumors, and almost no staining in normal tissue. CONCLUSIONS: Semaphorin 3A is overexpressed in urothelial cancer patients, as evidenced both in its presence in urine and in bladder tissue. Semaphorin 3A in urine is a promising potential urothelial cancer biomarker either independently or in conjunction with cytology. Further tests are needed to elucidate the sex difference in the expression of Sema3A in the urine of bladder cancer patients.

Minimal smooth lenses for perfect imaging of two wavefronts.

The problem of designing a lens for perfectly imaging two incident wavefronts into two respective refracted wavefronts is considered. In particular, the problem of deriving a unique such lens of prescribed smoothness is analyzed. Building upon an idea by Benitez and Minano et al., we propose a method for constructing such twice-differentiable lenses and derive equations for computing them. The theoretical considerations are supplemented by a few examples.

Geometrical optics and optimal transport.

The Fermat principle is generalized to a system of rays. It is shown that all the ray mappings that are compatible with two given intensities of a monochromatic wave, measured at two planes, are stationary points of a canonical functional, which is the weighted average of the actions of all the rays. It is further shown that there exist at least two stationary points for this functional, implying that in the geometrical optics regime the phase from intensity problem has inherently more than one solution. The caustic structures of all the possible ray mappings are analyzed. A number of simulations illustrate the theoretical considerations.

Variational principle in optics II: Dissipative wave equations.

The problem of phase retrieval from intensity measurements is examined for the case of dissipative wave equations. Unlike the conservative case, it is not clear if and when the problem is solvable at all. We provide two solutions. First, it is shown that, for a certain class of dissipating potentials, the problem can be fully solved by converting it through a simple transformation to the framework of the weighted least action principle. Second, for all other dissipating potentials, a deep result from the theory of elliptic partial differential equations is used to show that the problem is always solvable up to a scaling of one of the measured intensities. Moreover, the solution in this general case can be obtained by solving a Monge-Ampere type differential equation. Two numerical examples are given to illustrate some of the theoretical considerations.

Neutrophil-to-lymphocyte ratio predicts progression and recurrence of non-muscle-invasive bladder cancer.

OBJECTIVE: Neutrophil-to-lymphocyte ratio (NLR) predicts advanced stage disease and decreased survival in patients undergoing radical cystectomy for urothelial carcinoma of the bladder. The predictive value of NLR in non-muscle-invasive bladder cancer (NMIBC) has not been well studied. We aimed to evaluate whether NLR predicted disease recurrence and progression in NMIBC. MATERIALS AND METHODS: The medical records of 122 consecutive, newly diagnosed, patients with NMIBC treated with transurethral tumor resection, between the years 2003 and 2010, were reviewed. Patients with hematological malignancies (n = 4) and without preoperative NLR (n = 11) were excluded. Cutoff points for NLR were tested separately for recurrence and progression using the standardized cutoff-finder algorithm. Univariate and multivariate Cox regression analyses were used to evaluate the association between NLR and disease recurrence and progression. RESULTS: The study cohort comprised 91 men and 16 women at a median age of 68 years. The median NLR was 2.85 (interquartile range: 2-3.9). In total, 68 patients (64%) had an NLR>2.41. Patients with NLR>2.41 were more often men (P = 0.02) and had T1 category tumors (P = 0.034). Analyzed as a continuous variable, higher NLR showed a weak positive association with high tumor grade (R = 0.21, P = 0.028). The median follow-up for patients without disease recurrence was 40 months (interquartile range: 23-51). The estimated 3-year progression-free survival rate in patients with an NLR>2.41 was 61%, compared with 84% in patients with an NLR≤2.41 (P = 0.004). On multivariate analysis, an NLR>2.41 (hazard ratio [HR] = 3.52; 95% CI: 1.33-9.33; P = 0.012) and high-risk tumors compared with low-intermediate-risk tumors (HR = 4.83; 95% CI: 1.31-17.77; P = 0.018), as defined by the European Organization for Research and Treatment of Cancer risk tables, were associated with disease progression. An NLR>2.43 (HR = 1.75; 95% CI: 1.05-2.92; P = 0.032) and treatment with intravesical instillations (HR = 0.49; 95% CI: 0.28-0.85; P = 0.011) were associated with disease recurrence on multivariate analysis. CONCLUSIONS: NLR is an independent predictor of disease progression and recurrence in patients with NMIBC without hematological malignancies. Prospective studies are required to validate the role of NLR as a prognostic marker in NMIBC.

On the initial propagation of dental caries.

A multi-dimensional model for dental caries is applied to study the shape of caries lesions in a realistic tooth geometry and to examine the rate of progress of caries. An upgraded model, taking into account the outer prismless enamel layer, is derived and solved. The model demonstrates the importance of this layer in delaying the onset of caries. The conclusions are discussed in light of experimental results.

On the relation between power and astigmatism near an umbilic line.

The relation between the variation of power and astigmatism in a progressive power optical element is considered. The classical Minkwitz identity is revisited. Then, it is shown how to extend this identity, which applies to the geometry of surfaces, to optical parameters that are determined by the geometry of reflected or refracted wavefronts.

Wavelength adjustment using an eye model from aberrometry data.

We developed a method to convert aberrometry data obtained in one wavelength to the corresponding data in another wavelength using an eye model. A single map of aberrometry data is used to construct a free-form one-surface eye model. A general algorithm for the surface construction is described and implemented for real aberrometry data. Our method can handle varying conjugate distances of the measurement plane of the aberrometer and can also manage the chief ray prism that may be present. The algorithm is validated with the aid of an artificial plastic eye. The wavefronts in different wavelengths are compared through the Zernike analysis not only for lower-order aberrations, but also for higher-order aberrations. The results show that the changes of the Zernike aberration coefficients due to wavelengths are non-uniform. The defocus term has the highest effect from wavelength changes, which is consistent with the previous literature. Our method is compared with two approximate semi-analytical algorithms. The wavelength adjustments from a multi-surface eye model are contrasted with our method. We prove analytically that the conventional method of wavelength adjustment is based on paraxial analysis. In addition, we provide a method of finding the chief ray using back-projection in some cases and discuss different meanings of prism.

Numerical reconstruction of optical surfaces.

There are several problems in optics that involve the reconstruction of surfaces such as wavefronts, reflectors, and lenses. The reconstruction problem often leads to a system of first-order differential equations for the unknown surface. We compare several numerical methods for integrating differential equations of this kind. One class of methods involves a direct integration. It is shown that such a technique often fails in practice. We thus consider one method that provides an approximate direct integration; we show that it is always converging and that it provides a stable, accurate solution even in the presence of measurement noise. In addition, we consider a number of methods that are based on converting the original equation into a minimization problem.

Intensity control with a free-form lens.

A family of free-form lenses for intensity control is designed. The lens can shape an incident collimated beam with a given intensity distribution I1 into a new collimated beam with intensity distribution I2. No symmetry is assumed for the two intensity profiles. The key idea is that the lens design problem can be formulated and solved in terms of an optimization process involving a specific action functional. It is further shown that the free-form lens can be manufactured by a surfacing process using a convex tool.

Wavefront sensing and reconstruction from gradient and Laplacian data measured with a Hartmann-Shack sensor.

A new wavefront sensing and reconstruction technique is presented. It is possible to measure Laplacian and gradient information of a wavefront with a Hartmann-Shack setup. By simultaneously using the Laplacian and gradient data we reconstruct the wavefront by sequentially solving two partial differential equations.

Weighted Zernike expansion with applications to the optical aberration of the human eye.

We propose to use weighted Zernike functions to represent the aberrations of an eye. Methods for computing the phase of an aberrated ophthalmic wavefront in terms of weighted Zernike functions are discussed. In particular, we consider several options for integrating the phase out of its measured slopes. The weighted functions involve a free parameter. Clinical data on subjective refraction and aberration maps of individual subjects are used to determine an estimate for this parameter.

A variational principle in optics.

We derive a new variational principle in optics. We first formulate the principle for paraxial waves and then generalize it to arbitrary waves. The new principle, unlike the Fermat principle, concerns both the phase and the intensity of the wave. In particular, the principle provides a method for finding the ray mapping between two surfaces in space from information on the wave's intensity there. We show how to apply the new principle to the problem of phase reconstruction from intensity measurements.

Differential relations for the imaging coefficients of asymmetric systems.

We consider imaging properties embedded in the point eikonal for first-order asymmetric optical systems. We provide geometrical interpretations for the coefficients of the eikonal functions and proceed to show that there exist differential relations between them. The differentials are computed with respect to the position of the reference planes in the object or image spaces.