Computational and experimental analysis of a Glaucoma flat drainage device

Abstract

This paper presents a computational and experimental analysis of a glaucoma flat drainage device (FDD). The FDD consists of a metallic microplate placed into the eye sclerocorneal limbus, which creates a virtual path between the anterior chamber and its exterior, allowing the intraocular pressure (IOP) to be kept in a normal range. It also uses the surrounding tissue as a flow regulator in order to provide close values of IOP for a wide range of aqueous humor (AH) flow rates. The Neo Hookean hyperelastic model is used for the solid part, while the Reynolds thin film fluid model is used for the fluid part. On the other hand, a gravitational-driven flow test is implemented in order to validate the simulation process. An in vitro experiment evaluated the flow characteristics of the device implanted in fourteen extirpated pig eyes, giving as a result the best-fit for the Young modulus of the tissue surrounding the device. Finally, according to the resulting computational model, for a range of 1.4–3.1 $\mathrm{\mu }$L/min, the device presents a pressure variation range of 6–7.5 mmHg.

Introduction

The Glaucoma disease is affects to many humans around the world, being mostly affected people residing in Asia and Africa (Tham et al., 2014). This illness is defined as a progressive blindness caused by a lesion of the optic nerve due to mainly an abnormal increment of IOP (Casson et al., 2012). It can initially be treated by using medications such as betablockers, carbonic anhydrase inhibitors, alpha-2 adrenergic agonists and prostaglandin analogs (Li et al., 2016, Inga Samaniego et al., 2017). However, there are cases where some patients do not tolerate these medications (Mann, 2019), leading to the implantation of a Glaucoma Drainage device (GDD) as last resort.

There is a wide gamma of these kind of implants, such as the Ahmed Glaucoma Valve (AGV), Krupin implant, Molteno device, Baerveldt device, SolX gold shunt, Ex-Press P-50, iStent, CyPass, Hydrus Stent and Glafkos; being the AGV the most used due to its advantage of present the most favorable risk-efficacy profile (Riva et al., 2017). However, there are some shortcomings that the AGV needs to improve, such as its elevated interval pressure control and its tendency to present obstruction in the micro-pipe. Therefore, new design proposals were presented, such as the Fermat-type spring-mounted micro check valve design developed by Kara and Kutlar (2010), and the flat drainage device invented by Velasquez and Ortiz (2017).

Most of these devices were evaluated by some in vitro experimental procedures. The most common tests are named gravity-driven flow (GDF) test and syringe-pump-driven flow (SPDF) test. The second one was firstly used by Prata et al. (1995), who analyzed the pressure-flow characteristics of the AGV, Baervelt device, Krupin disk device, the OptiMed glaucoma device and the Molteno dual-chamber implant, being the last one implanted and tested in live rabbits. Results from this research showed that the AGV and Krupin implants worked as pressure regulator valves without a certain position where they are opened or closed. Porter et al. (1997) utilized the gravity-driven flow and syringe-pump-driven flow tests to analyze the drainage behavior of eighteen valved and not valved drainage devices. It was observed that, for non-valved devices, the only one viable test was the SPDF test due to a very reduced pressure resistance presented in the GDF test. The valved devices could be tested using both methods, being the most informative the SPDF test. In addition, those results showed that the flow resistance for both valved and non-valved devices were constant over the collected data range. Later, Estermann et al. (2013) analyzed the flow characteristics of 3 different Ex-PRESS models (P-50, R-50 and P-200) using the GDF test. The flow resistance values presented close values for different pressure conditions, being this characteristic of non-valved drainage devices.

Some researchers designed new tests sharing similarities with the GDF and SPDF tests. For instance, Pan et al. (2003) tested the AGV using a microfluidic modified SPDF test. In that case, three Anopore filters in series were connected to the setup outlet in order to reproduce the in vivo tissue capsule porosity which encapsulates the AGV outlet. The experiment also worked as a validation for a Computational Fluid Dynamics (CFD) simulation executed in ANSYS FLUENT, whose results allowed to learn that the frictional pressure losses are negligible. Likewise, Siewert et al. (2013) developed a microfluidic modified GDF test using two hydrostatic fluid columns at the inlet and outlet of the setup, and a flow sensor before the GDD chamber. Kara et al. (2019) pointed that there are some situations that may affects the mentioned in vitro tests, such as the pipe system flexibility and unwanted syringe pump vibrations. In consequence, they proposed a new microfluidic experimental test setup to overcome those issues. That test included an air compressor connected to a flow control system which let an AH-like fluid circulate from a reservoir to an isolated box in which a GDD is placed. Test configurations are mainly dependent on the GDD structure, being able to be tubular, non-tubular, valved or non-valved.

Additionally, computational simulations are necessary in order to analyze the flow behavior through a GDD. It is well known that the GDD material and the tissue around it play an important role in the flow behavior. This happens due to the non-linear behavior of those materials. Hence, when a fluid-structure analysis is performed, the possibility of a non-linearity of the solid part has to be considered, such as the AGV case, where the solid part is the AGV structure which is made of silicon, a non-linear material. The finite element method (FEM) is one of the most used methods to solve the mentioned cases, including linear materials in general; however, there are other methods that are being studied such as the Galerkin’s method, the Rayleigh-Ritz’s method, etc. (Shariati et al., 2020a, Chikr et al., 2020, Shariati et al., 2020b, Al-Furjan et al., 2020, Hussain et al., 2020, Alimirzaei et al., 2019, Karami et al., 2019).

Most researchers employed the fluid-structure interaction in order to obtain the GDD flow characteristics. For example, Stay et al. (2005) evaluated the AGV via an in vitro SPDF test and used its results to validate a CFD model. That model consisted on a fluid-structure analysis; where, for the solid part, a Von Kármán model was considered; and, for the fluid part, a Reynolds model was considered. In addition, the mentioned new GDD model presented by Kara and Kutlar (2010) was also simulated using a software named ANSYS FLUENT. They analyzed all the tubular structure and the compartment where the valve is placed using 2.5D elements. A 3D CFD analysis of the eye was published by Villamarin et al. (2012), where the more important internal parts of the eye were reconstructed using histology images and a case trabeculectomy was also simulated. Furthermore, Mauro et al., 2016 analyzed two non-valved GDD devices, the SOLX Gold Micro Shunt and a novel Silicon Shunt device. Those cases were calculated using the Navier-Stokes equations and the Characteristic Based Split scheme Arpino et al. (2011) to analyse the fluid and porous medias.

As it was explained, there are several numbers of experimental tests oriented to evaluate the GDDs flow characteristics. Some results from these tests are employed to compare and improve existent designs or to create new devices. For that reason, the authors believe that the present article would help other researchers to improve new tests configurations and to create new devices based on the GDD analyzed in the present work.

In the present research, experimental and computational analyses of the FDD are presented. The GDF test is implemented in order to obtain its flow characteristics and compare the results with a reduced fluid-solid coupled FEM model. The experimental procedure considered the device in an extirpated pig eye, with all the assemble submerged under saline solution. On the other hand, the FEM models considered the fluid part to be the AH flowing around the solid device; and the solid part corresponds to be the tissue surrounding the device, which works as a flow regulator of the AH.

This paper is organized as follows. The experimental methodology is explained in Section 2. In Section 3, the numerical model used to represent the physical phenomena in the device is detailed. The results are discussed in Section 4. Finally, the conclusion and representative references are provided.