**Purpose**:
Age-related nuclear cataract is the opacification of the clear ocular lens due to oxidative damage as we age, and is the leading cause of blindness in the world. A lack of antioxidant supply to the core of ever-growing ocular lens could contribute to the cause of this condition. In this project, a computational model was developed to study the sutural fluid inflow of the aging human lens.

**Methods**:
Three different SOLIDWORKS computational fluid dynamics models of the human lens (7 years old; 28 years old; 46 years old) were created, based on available literature data. The fluid dynamics of the lens sutures were modelled using the Stokes flow equations, combined with realistic physiological boundary conditions and embedded in COMSOL Multiphysics.

**Results**:
The flow rate, volume, and flow rate per volume of fluid entering the aging lens were examined, and all increased over the 40 years modelled. However, while the volume of the lens grew by ∼300% and the flow rate increased by ∼400%, the flow rate per volume increased only by very moderate ∼38%.

**Conclusions**:
Here, sutural information from humans of 7 to 46 years of age was obtained. In this modelled age range, an increase of flow rate per volume was observed, albeit at very slow rate. We hypothesize that with even further increasing age (60+ years old), the lens volume growth would outpace its flow rate increases, which would eventually lead to malnutrition of the lens nucleus and onset of cataracts.

^{1}These fibre cells are bundled together in layers to form different regions within the lens, namely the outer cortex, the inner cortex, and the core.

^{2}In order to stay transparent, the lens is avascular. However, the lens cannot rely on passive diffusion alone to provide nutrients and remove wastes from its core as this would be too slow.

^{3}Instead, the physiological optics homeostasis of the lens is maintained through an active process called the microcirculation system.

^{4}Briefly, in this system, solutes enter the lens via anterior and posterior poles, predominantly through sutures.

^{5}These solutes and accompanying water then move extracellularly toward the core of the lens, where at some point, they cross the cell membrane into the cytoplasm of fibre cells. When in intracellular space, the water and solute move outwardly from cell layer to next through a vast network of gap junctions. Then at the surface of the lens, they are pumped out of the lens predominantly at the equator (Fig. 1).

^{3}

^{6,7}such as protein: water concentration,

^{8}overall shape,

^{9}and known sutural geometry.

^{10}Specifically, in humans, the lens volume increases with age as new cells are created and added to the bulk of the tissue.

^{11}One could imagine that a larger lens volume, and increased cell numbers, requires a greater influx of nutrients, such as antioxidants, especially in oldest part of the tissue, which is its nucleus.

^{8}It then follows that if the aged lens core does not receive sufficient antioxidants, there will be accelerated accumulative oxidative damage to the cells of this region, leading to onset of age-related nuclear cataract.

^{12}Hence in an aging lens, enhanced nutrition delivery can only be achieved by a higher extracellular flow velocity and/or a greater sutural surface area. Focusing on the latter component, it has been shown that the sutural structure becomes progressively more complex in primates, which also increases its surface area and volume.

^{10}In particular, there are four distinct age-groups of sutures patterns throughout the lens, which considerably improves the optical performance of the lens.

^{13,14}Throughout the embryonic development, the sutures are “Y” shaped; later, they become star shaped during adolescence. As the lens continues to age, the star-shaped sutures become more complicated as new branches are formed. Several different computer models in the form of cylindrical map projections (CMP) and computer aided design (CAD) had been used to describe the process of sutures growth.

^{10,15}However, these models were generic and not representative of true aging process in humans.

^{16–18}(Fig. 2). These images were initially thresholded and the geometry of human lens sutures were extracted at three different ages.

^{2}These sutural branches were difficult to see in our images, so they were approximated by examining and rotating the respective anterior suture (Fig. 2). The sutural branches were initially modelled with a constant width and abrupt edges. Design tools on SOLIDWORKS (SolidWorks Corporation, Concord, MA, USA) were then used to make the edges of the sutures, as shown in Figure 2. The final dimensions for the sutural branches were 0.6 mm wide, 1.5 mm long and all three branches centred around a 0.1-mm diameter circle. The anterior sutures formed an upright Y-shape with the sutural branches spaced 120 degrees apart. The posterior sutures were also centred around a 0.1-mm diameter circle; however, they formed an inverted Y-shape with the branches also spaced 120 degrees apart. The branches off the original “Y” sutures were created manually and using the design tool of SOLIDWORKS, to visually match the clinical images (Fig. 2).

^{1,2}and Table 1. It was assumed that the lenses are rotationally symmetric about the visual axis, and the dimensions of the core and the inner cortex can be determined by a ratio to the lens' overall dimension. The SOLIDWORKS sketch tool was used to create a two-dimensional projection of the core, the inner cortex and the outer cortex, respectively. A revolved structure with these projections with an axis of revolution of 360° were then created to form the solid structures.

^{11,19,20}The product of this design is presented in Figure 3. To model human lens changes with age the generic model here was than morphed to 7-, 28-, and 46-year-old lens models to match our sutural data set.

^{6,7}Since the growth of the lens is not at a constant rate, the dimensions of the lens at different ages cannot readily be predicted. The lens dimensions were obtained from an in vivo magnetic resonance imaging (MRI) study on healthy and diabetic participants, from which the former data set was selected.

^{21}The dimensions for both the 28- and 46-year-old lens were based on the control groups in a study about the lens shape and refractive index distribution in type 1 diabetes. There was no available data for the dimensions of a 7-year-old lens. The lens dimensions were instead determined through interpolation on MATLAB (Mathworks, Natick, MA, USA). Interpolation requires information about the trend on either side of the desired value and the final results are summarized (Table 1) and shown (Fig. 3).

^{9,10}In this instance of applying the boundary conditions, we determined the general inflow velocity magnitude to be 2e

^{−4}and 6e

^{−5}mm/s at the surfaces of the anterior and posterior sutures, respectively. These conditions were applied with a “normal to surface” condition selected within COMSOL Multiphysics programming platform. The modelling software then correctly applied the boundary conditions, with respect to the geometrical structure of the model. Thus, the velocity boundary condition is always normal to the surface and the user did not have to create an explicit set of boundary conditions to supply to the software.

^{22–24}It assumed the fluid in the lens is an incompressible Newtonian fluid with a spatially constant viscosity at steady state. The second assumption is that the fluid flow in the lens is a creeping or low-Reynolds number flow with negligible turbulence.

^{8}From these assumptions, the full Navier-Stokes equations were simplified to the Stokes equations (Equation 1 and Equation 2).

*u*is the velocity (

*p*is the hydrostatic pressure (

*μ*is the dynamic viscosity (

*f*is the body force per unit mass (

^{25}and

^{26}respectively, which mimics the typical flow velocities in the aqueous and vitreous humour, respectively.

^{4,27,28}is that there exists a pressure difference between the anterior and posterior lens.

^{9–11}This difference in pressure was calculated by a MATLAB script, which utilises the ratio between the intraocular pressure (IOP) of the anterior chamber. IOP has a wide normal range in humans (10–21 mm Hg).

^{29}However, since the sutural model needed a single value as boundary condition, we chose the typical IOP for human to be 16 mm Hg, the pressure of the vitreous cavity was set to be 20.5 mm Hg.

^{30}This pressure gradient within the suture can be calculated by Equation 3 and as shown by the blue arrows in Figure 4.

^{28,31}It was necessary to assume an extracellular pressure gradient, for our sutural model to be solvable. Hence, it was decided to “mirror” the measured the intracellular pressure. By “mirror,” we mean low extracellular pressure where intracellular pressure is high, and high extracellular pressure where intracellular pressure is low.

^{31}Hence, the “mirror” assumption implies a higher extracellular pressure at the surface and lower extracellular pressure at the core of the lens, based on observed “mirrored” intra\extracellular distributions of electrical voltage and solute concentrations.

^{32,33}

^{11,34–38}This process is accompanied by compaction of fibre cells, especially in the core and inner cortex of the lens, overall flattening of the lens and branching of the originally Y-shaped sutures into *-shape ultrastructure.

^{10,39–41}Although complex in nature, the main outcome of this process is for the core of the lens to buried deeper inside the tissue and becoming less accessible by eye's humours. This in turn translates to reduced supply of nutrients (especially antioxidants) to the lens core with advancing age, accumulated oxidative damage, and ultimately onset of age-related nuclear cataract. However, most humans can live without significant cataract for six decades, and sometimes much longer. We believe that sutures “branching” with age, is an evolutionary compensatory mechanism that could to some extent improves the lens core accessibility.

*r*

^{3}), while sutural surface area increase is related to radius-square (

*r*

^{2}). Since the sutural flow rate changes with aging in humans have not been measured experimentally, using the results of our study here, we can speculate that the flowrate per volume might then begin to decline, leading to reduced delivery of antioxidants to the central region of the lens, leading to onset of age-related nuclear cataract.

^{1,4}The current form of the microcirculation implementation is a bi-domain continuum model.

^{22–24}As the name suggests, the bi-domain model is consisted of two domains, namely the intracellular and extracellular spaces. Each element of the bi-domain continuum model, by design, includes predefined ratios locally varying ratios of intracellular and extracellular spaces of the lens. The bi-domain continuum model then tries to simulate the “net effect” of fluid dynamics of those domains. The bi-domain continuum model is based on the symmetrical nature of the lens. As a result, the asymmetrical structure of the sutures, especially in primates are not currently captured. Hence, the disruptive geometry, fluid dynamics, and age-related changes of sutures of the lens are not currently captured by the bi-domain model. Our current work is a step toward a comprehensive model of the lens microcirculation, by capturing the asymmetrical nature of the lens sutures, and its nonlinear changes with age. We are improving our model toward a comprehensive computational predictive tool, “connecting” the sutural and microcirculation models, so that clinicians could “estimate” an age of cataract onset, based on individual patient data and accurate fluid dynamics modelling.

**H.-T.D. Wu**, None;

**L.A. Howse**, None;

**E. Vaghefi**, None

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