Models and Algorithms for the Refinement of Therapeutic Approaches for Retinal Diseases.

We are developing a Virtual Eye for in silico therapies to accelerate research and drug development. In this paper, we present a model for drug distribution in the vitreous body that enables personalized therapy in ophthalmology. The standard treatment for age-related macular degeneration is anti-vascular endothelial growth factor (VEGF) drugs administered by repeated injections. The treatment is risky, unpopular with patients, and some of them are unresponsive with no alternative treatment. Much attention is paid to the efficacy of these drugs, and many efforts are being made to improve them. We are designing a mathematical model and performing long-term three-dimensional Finite Element simulations for drug distribution in the human eye to gain new insights in the underlying processes using computational experiments. The underlying model consists of a time-dependent convection-diffusion equation for the drug coupled with a steady-state Darcy equation describing the flow of aqueous humor through the vitreous medium. The influence of collagen fibers in the vitreous on drug distribution is included by anisotropic diffusion and the gravity via an additional transport term. The resulting coupled model was solved in a decoupled way: first the Darcy equation with mixed finite elements, then the convection-diffusion equation with trilinear Lagrange elements. Krylov subspace methods are used to solve the resulting algebraic system. To cope with the large time steps resulting from the simulations over 30 days (operation time of 1 anti-VEGF injection), we apply the strong A-stable fractional step theta scheme. Using this strategy, we compute a good approximation to the solution that converges quadratically in both time and space. The developed simulations were used for the therapy optimization, for which specific output functionals are evaluated. We show that the effect of gravity on drug distribution is negligible, that the optimal pair of injection angles is (50∘,50∘), that larger angles can result in 38% less drug at the macula, and that in the best case only 40% of the drug reaches the macula while the rest escapes, e.g., through the retina, that by using heavier drug molecules, more of the drug concentration reaches the macula in an average of 30 days. As a refined therapy, we have found that for longer-acting drugs, the injection should be made in the center of the vitreous, and for more intensive initial treatment, the drug should be injected even closer to the macula. In this way, we can perform accurate and efficient treatment testing, calculate the optimal injection position, perform drug comparison, and quantify the effectiveness of the therapy using the developed functionals. We describe the first steps towards virtual exploration and improvement of therapy for retinal diseases such as age-related macular degeneration.

Quantitative evaluation of microvacuole formation in five intraocular lens models made of different hydrophobic materials.

In this laboratory study, we assessed the resistance to microvacuole (glistening) formation in hydrophobic intraocular lenses (IOLs). Glistenings were induced in five lenses each of five different hydrophobic acrylic IOL models, using an established in vitro laboratory model: 800C (Rayner, Worthing, UK), AcrySof SN60WF (Alcon, Fort Worth, USA), Tecnis ZCB00 (Johnson & Johnson Vision, Santa Ana, USA), Vivinex XY1 (Hoya, Tokyo, Japan) and CT Lucia 611P (Zeiss, Oberkochen, Germany). We evaluated the number of microvacuoles per square millimeter (MV/mm2) in the central part of each IOL. Results were analyzed statistically, and mean glistening numbers were ranked, with the highest in the SN60WF which had 66.0 (±45.5) MVs/mm, followed by the 611P with 30.7 (±8.4) MVs/mm2. The 800C and XY1 showed comparable values of 2.0 (±3.6) and 2.7 (±2.4) MVs/mm2, respectively. ZCB00 had the lowest number with 0.9 (±0.6) MVs/mm2. This study shows that the resistance to glistening formation differs depending on the hydrophobic acrylic copolymer composition of the IOL material. Some IOLs from current clinical use are still prone to develop glistenings whereas others, including the ZCB00, 800C and XY1 show high resistance to microvacuole formation.

Quantification of the In Vitro Predisposition to Glistening Formation in One Manufacturer's Acrylic Intraocular Lenses Made in Different Decades.

INTRODUCTION: Foldable hydrophobic acrylic intraocular lenses (IOLs) are prone to develop a long-term postoperative material change called glistenings. The aim of this study was to investigate the changes in the predisposition for glistening formation in one type of hydrophobic acrylic IOL material from its introduction to the present day. METHODS: In a laboratory setup, an in vitro model was used to induce glistenings in hydrophobic acrylic IOLs manufactured by one company (Alcon, Fort Worth, TX, USA) in different years: 23 1990s-manufacture hydrophobic acrylic three-piece IOLs (MA30BA/MA60AC) that were explanted in 1996 and 1997, and five of each of the newer AcrySof IOL models (MA60AC, SA60AT, TFNT00 and SN60WF) from 2014 to 2017. Furthermore, five Clareon (SY60WF) IOLs were put through the same accelerated aging procedure. The number of microvacuoles per square millimeter (MV/mm2) was determined in the central part of each IOL optic and compared between the groups. RESULTS: The mean number of MV was highest in the 1990s-manufacture Alcon acrylic IOLs, with 1289 (± 738) MV/mm2. The number decreased to 650 (± 101), 192 (± 105), 175 (± 112) and 47 (± 26) for MA60AC, SA60AT, TFNT00 and SN60WF, respectively. The lowest count was obtained in the Clareon group, with 1 (± 1) MV/mm2. CONCLUSIONS: A high number of glistenings was induced in the explanted IOLs from the 1990s. The propensity for glistening formation decreased considerably after that decade and now in current use. Even though in vitro glistening formation in today's AcrySof material was low, the Clareon material was essentially glistenings-free.

Stability and Visual Outcomes of the Capsulotomy-Fixated FEMTIS-IOL After Automated Femtosecond Laser-Assisted Anterior Capsulotomy.

PURPOSE: To evaluate stability and performance of a new monofocal anterior capsulotomy-fixated intraocular lens (IOL) (FEMTIS; Teleon Surgical B.V., Spankeren, Netherlands) after femtosecond laser-assisted cataract surgery (FLACS). DESIGN: Prospective, multicenter, interventional, noncomparative case series. METHODS: FLACS with FEMTIS IOL was performed in 336 eyes of 183 cataract patients with fixation of the IOL to the anterior capsulotomy followed up for 12 months. Examination included uncorrected distance visual acuity (UDVA), best-corrected visual acuity (CDVA), subjective refraction, IOL centration, posterior capsule opacification (PCO), and investigators' satisfaction questionnaire. RESULTS: At 12 months, mean IOL rotation was 1.50 ± 1.76 degrees and decentration 0.14 ± 0.14 mm from baseline (day of surgery). Mean horizontal IOL tilt was 0.70 ± 0.60 degrees and vertical 1.15 ± 1.06 degrees relative to the baseline (crystalline lens). Mean distance between IOL and iris was 0.32 mm to 0.36 mm for all measured meridians. Mean UDVA was 0.12 ± 0.14 logMAR (range -0.20 to 0.54 logMAR), mean CDVA -0.01 ± 0.09 logMAR (range -0.30 to 0.20 logMAR). Mean spherical equivalent was 0.35 ± 0.53 diopter (D) and 98% of eyes (n = 235) were within ±1.0 D. Median PCO score was 1 with an Nd:YAG laser rate of 3.1% after 12 months. Most surgeons were very satisfied (median score: 1) with surgery and implanted IOL. CONCLUSIONS: Implantation of FEMTIS IOL provided excellent visual and stable refractive outcomes. IOL decentration was very low compared to other published studies and showed an exceptional high in-the-bag stability over a 12-month period. This lens benefits from femtosecond laser capsulotomies. It can be positioned very predictably and offers an optimal platform for toric and multifocal IOL optics.

Lenticular Imaging: A New Experimental and Quantitative Analysis of Capsular Dynamics, "Choi-Apple View".

PURPOSE: Development of a means for quantitative estimation of lenticular and zonular dynamics by using real-time imaging of human autopsy eyes during implantation of different intraocular lens (IOL) models. METHODS: Isolated lenticular structures from human autopsy eyes were prepared in vitro. The following IOLs were implanted: a one-piece C-loop haptic IOL, a three-piece C-loop haptic IOL, and a one-piece plate-type IOL. The amount of deformation of lenticular structures during implantation was calculated and the movements visualized with two cameras. The results were transformed to two-dimensional graphs using a newly developed image-processing algorithm. RESULTS: For both one-piece plate-type and one-piece C-loop haptic IOLs, the amount of capsular bag deformation from its initial shape was greater in the direction of posterior center of the capsule, as detected by side camera, than in the direction of the equator (or periphery), as detected by front camera. The mean peak deformation values were 51% and 36% (as measured by side and front cameras, respectively) for one-piece plate-type IOL and 25% and 20% for one-piece C-loop haptic IOL. For three-piece C-loop haptic IOL, the capsular bag distention was almost equal in both posterior and peripheral directions, with mean peak deformation values reaching 39% and 38%. CONCLUSIONS: The new experimental means of lenticular imaging and quantified dynamics from two different angles allowed three-dimensional understanding of specific behavior of each IOL. Our model not only exposes the capsular bag for recording during implantation, but also objectively compares the individual movement values and reveals different zonular and capsular stress patterns, depending on IOL model. TRANSLATIONAL RELEVANCE: The novel "Choi-Apple View" allows a three-dimensional quantitative analysis of capsular dynamics and IOL implantation behavior.

Mathematical Models in the Description of Pregnane X Receptor (PXR)-Regulated Cytochrome P450 Enzyme Induction.

The pregnane X receptor (PXR) is a drug/xenobiotic-activated transcription factor of crucial importance for major cytochrome P450 xenobiotic-metabolizing enzymes (CYP) expression and regulation in the liver and the intestine. One of the major target genes regulated by PXR is the cytochrome P450 enzyme (CYP3A4), which is the most important human drug-metabolizing enzyme. In addition, PXR is supposed to be involved both in basal and/or inducible expression of many other CYPs, such as CYP2B6, CYP2C8, 2C9 and 2C19, CYP3A5, CYP3A7, and CYP2A6. Interestingly, the dynamics of PXR-mediated target genes regulation has not been systematically studied and we have only a few mechanistic mathematical and biologically based models describing gene expression dynamics after PXR activation in cellular models. Furthermore, few indirect mathematical PKPD models for prediction of CYP3A metabolic activity in vivo have been built based on compartmental models with respect to drug⁻drug interactions or hormonal crosstalk. Importantly, several negative feedback loops have been described in PXR regulation. Although current mathematical models propose these adaptive mechanisms, a comprehensive mathematical model based on sufficient experimental data is still missing. In the current review, we summarize and compare these models and address some issues that should be considered for the improvement of PXR-mediated gene regulation modelling as well as for our better understanding of the quantitative and spatial dynamics of CYPs expression.

PDE/ODE modeling and simulation to determine the role of diffusion in long-term and -range cellular signaling.

BACKGROUND: We study the relevance of diffusion for the dynamics of signaling pathways. Mathematical modeling of cellular diffusion leads to a coupled system of differential equations with Robin boundary conditions which requires a substantial knowledge in mathematical theory. Using our new developed analytical and numerical techniques together with modern experiments, we analyze and quantify various types of diffusive effects in intra- and inter-cellular signaling. The complexity of these models necessitates suitable numerical methods to perform the simulations precisely and within an acceptable period of time. METHODS: The numerical methods comprise a Galerkin finite element space discretization, an adaptive time stepping scheme and either an iterative operator splitting method or fully coupled multilevel algorithm as solver. RESULTS: The simulation outcome allows us to analyze different biological aspects. On the scale of a single cell, we showed the high cytoplasmic concentration gradients in irregular geometries. We found an 11 % maximum relative total STAT5-concentration variation in a fibroblast and a 70 % maximum relative pSTAT5-concentration variation in a fibroblast with an irregular cell shape. For pSMAD2 the maximum relative variation was 18 % in a hepatocyte with a box shape and 70 % in an irregular geometry. This result can be also obtained in a cell with a box shape if the molecules diffuse slowly (with D=1 µm(2)/s instead of D=15 µm(2)/s). On a scale of cell system in the lymph node, our simulations showed an inhomogeneous IL-2 pattern with an amount over three orders of magnitude (10(-3)-1 pM) and high gradients in face of its fast diffusivity. We observed that 20 out of 125 cells were activated after 9 h and 33 in the steady state. Our in-silico experiments showed that the insertion of 31 regulatory T cells in our cell system can completely downregulate the signal. CONCLUSIONS: We quantify the concentration gradients evolving from the diffusion of the molecules in several signaling pathways. For intracellular signaling pathways with nuclear accumulation the size of cytoplasmic gradients does not indicate the change in gene expression which has to be analyzed separately in future. For intercellular signaling the high cytokine concentration gradients play an essential role in the regulation of the molecular mechanism of the immune response. Furthermore, our simulation results can give the information on which signaling pathway diffusion may play a role. We conclude that a PDE model has to be considered for cells with an irregular shape or for slow diffusing molecules. Also the high gradients inside a cell or in a cell system can play an essential role in the regulation of the molecular mechanisms.

Three-Dimensional Gradients of Cytokine Signaling between T Cells.

Immune responses are regulated by diffusible mediators, the cytokines, which act at sub-nanomolar concentrations. The spatial range of cytokine communication is a crucial, yet poorly understood, functional property. Both containment of cytokine action in narrow junctions between immune cells (immunological synapses) and global signaling throughout entire lymph nodes have been proposed, but the conditions under which they might occur are not clear. Here we analyze spatially three-dimensional reaction-diffusion models for the dynamics of cytokine signaling at two successive scales: in immunological synapses and in dense multicellular environments. For realistic parameter values, we observe local spatial gradients, with the cytokine concentration around secreting cells decaying sharply across only a few cell diameters. Focusing on the well-characterized T-cell cytokine interleukin-2, we show how cytokine secretion and competitive uptake determine this signaling range. Uptake is shaped locally by the geometry of the immunological synapse. However, even for narrow synapses, which favor intrasynaptic cytokine consumption, escape fluxes into the extrasynaptic space are expected to be substantial (≥20% of secretion). Hence paracrine signaling will generally extend beyond the synapse but can be limited to cellular microenvironments through uptake by target cells or strong competitors, such as regulatory T cells. By contrast, long-range cytokine signaling requires a high density of cytokine producers or weak consumption (e.g., by sparsely distributed target cells). Thus in a physiological setting, cytokine gradients between cells, and not bulk-phase concentrations, are crucial for cell-to-cell communication, emphasizing the need for spatially resolved data on cytokine signaling.