Graefes Arch Clin Exp Ophthalmol (2016) 254:739–744 DOI 10.1007/s00417-016-3304-3

REFRACTIVE SURGERY

Effect of hole size on fluid dynamics of a posterior-chamber phakic intraocular lens with a central perforation by using computational fluid dynamics Takushi Kawamorita 1 & Kimiya Shimizu 2 & Nobuyuki Shoji 1

Received: 10 November 2015 / Revised: 5 February 2016 / Accepted: 9 February 2016 / Published online: 19 February 2016 # Springer-Verlag Berlin Heidelberg 2016

Abstract Background A modified implantable collamer lens (ICL) with a central hole with a diameter of 0.36 mm, referred to as a hole-ICL, was created to improve aqueous humour circulation. The aim of this study is to investigate the ideal hole size in a hole-ICL from the standpoint of the fluid dynamic characteristics of the aqueous humour using computational fluid dynamics. Methods Fluid dynamics simulation using an ICL was performed with thermal-hydraulic analysis software FloEFD V 12.2 (Mentor Graphics Corp.). In the simulation, three-dimensional eye models based on a modified Liou-Brennan model eye with a conventional ICL (Model ICM, Staar Surgical) and a hole-ICL were used. The holeICL was −9.0 dioptres (D) and 12.0 mm in length, with an optic zone of 5.5 mm. The vaulting was 0.50 mm. The quantity of aqueous humour produced by the ciliary body was set at 2.80 μL/min. Flow distribution between the anterior surface of the crystalline lens and the posterior

surface of the ICL was calculated, and trajectory analysis was performed. Results With an increase in the central hole size, the velocity of the aqueous humour increased, with the peak velocity occurring at a diameter of approximately 0.4 mm. Once the diameter had increased above 0.4 mm, the velocity then decreased. The velocity difference between the cases of a central hole size of 0.1 mm and 0.2 mm was significant. Conclusion The desirable central hole size was 0.2 mm or larger in terms of flow dynamics. The current model, based on a central hole size of 0.36 mm, was close to ideal. The optimisation of the hole size should be performed based on results from a long-term clinical study so as to analyse the incidence rate of secondary cataract and optical performance.

Presentation at a conference: An earlier version of this paper was presented at the 67th Annual Congress of Japan Clinical Ophthalmology, Kanagawa, 2 November 2013.

Introduction

* Takushi Kawamorita [email protected]

1

Department of Orthoptics and Visual Science, Kitasato University School of Allied Health Sciences, 1-15-1 Kitasato, Minami-ku, Sagamihara City, Kanagawa, Japan 252-0373

2

Department of Ophthalmology, Kitasato University School of Medicine, Sagamihara, Japan

Keywords Fluid dynamics . phakic IOL . ICL . Hole-ICL . Aqueous humour circulation

Recently, a new Visian implantable collamer lens phakic intraocular lens with a central artificial hole (i.e., a holeICL) KS-AquaPORT TM (Staar Surgical, Co., Ltd.) was developed [1, 2]. The advantages of the hole-ICL include improvements in aqueous humour circulation and no need for laser iridotomy (LI). It has been reported that the central hole size of 0.36 mm of the current model did not affect the retinal image quality in vivo and in vitro, because the hole size was very small [3, 4]. Additionally, improvements in the aqueous humour circulation in a

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Graefes Arch Clin Exp Ophthalmol (2016) 254:739–744

Fig. 1 Three-dimensional models of eyes and hole-ICL created in FloEFD software

surrounding crystalline lens were noted. The increase in flow velocity of aqueous humour in the surrounding crystalline lens decreases the risk of secondary cataracts [5, 6]. In our previous computational fluid dynamics study, we reported that the hole-ICL improved the circulation of aqueous humour to the anterior surface of the crystalline lens [7]. If the central hole size of the hole-ICL increases, the circulation of aqueous humour in the surrounding crystalline lens improves. However, the retinal image quality decreases [6]. Fluid dynamics and optical characteristics are in a trade-off relationship. The effect of hole size in a hole-ICL on fluid dynamics has not yet been reported. Therefore, the aim of this study is to investigate the relation between hole size and flow velocity in the surrounding crystalline lens of a posterior-chamber phakic intraocular lens with a central hole using computational fluid dynamics.

Results

Materials and methods The computer simulation for fluid dynamics was performed using the thermal-hydraulic analysis software program FloEFD FE 12.2.0. (Mentor Graphics Corp., Wilsonville, Oregon, USA). Three-dimensional eye models of hole-ICLs with various central hole sizes were created using the software

Table 1

(Fig. 1). The details of the model are shown in Table 1. The hole sizes in the hole-ICL ranged from 0 to 0.6 mm; LI was not required. As a condition of calculation , the inflow locations for aqueous humour were in the ciliary body, and the outflow locations were set to allow uveoscleral outflow (10 %) and trabecular outflow (90 %) (Fig. 2). The quantity of aqueous humour from the ciliary body was set at 2.80 μL/min. The solid-state properties of the aqueous humour were set to be the degree of viscosity of aqueous humour 7.1917 × 10−4 Pa · s at a temperature of 95 °F. The initial pressure was set at 1 atm. The flow distribution between the anterior surface of the crystalline lens and the posterior surface of the ICL (0.25 mm from the centre of the crystalline lens) was also calculated (Fig. 3). In addition, trajectory analysis was performed for the hole-ICLs.

The flow velocity, 0.25 mm in front of the centre of the crystalline lens, was 0.0004 mm/s, 0.0180 mm/s, 0.1023 mm/s, 0.1367 mm/s, 0.1602 mm/s, 0.1288 mm/s, and 0.1106 mm/s, for hole sizes of 0 mm, 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, and 0.6 mm, respec-

Parameters of eye model

Corneal thickness

0.5 mm

Posterior corneal surface – iris plane Iris thickness ICL vaulting Gap between iris and ICL

2.1 mm 0.5 mm 0.5 mm 0.05 mm

Iridocorneal angle

33.0 deg Fig. 2 Locations of inflow and outflow in aqueous humour

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Fig. 3 Locations of a central hole of hole-ICL and analysed lines of flow velocity along the long axis of the cross-sectional surface

tively (Fig. 4). Furthermore, the flow distribution between the anterior surface of the crystalline lens and the posterior surface of the hole-ICL reached a peak for a hole size of 0.4 mm, similar to the trend illustrated in Fig. 4 (see Fig. 5). The difference in the flow distribution between a hole size of 0.1 mm and 0.2 mm was significant (Fig. 5). Outward flow from the hole in the hole-ICL was confirmed by trajectory analysis (Fig. 6).

Discussion Fujisawa et al. [5] and Shiratani et al. [6] reported on the hole size of a hole-ICL, and indicated that improving the aqueous humour circulation in the hole-ICL resulted in inhibitory effects for cataracts. However, their reports were based on animal experiments using miniature pigs, which have an anatomical structure of the anterior chamber that is different from that of humans. Furthermore, the hole diameter was large, at 3.0 mm. Therefore, we investigated the effect of a central hole size of a hole-ICL on fluid dynamics.

Fig. 4 The relation between hole sizes and velocity of the aqueous humour fluid

Fig. 5 Flow distribution along the long axis of the cross-sectional surface of the hole-ICL for various hole sizes

In the present results, as the hole size increased, the aqueous humour flow rate around the crystalline lens increased, reaching a peak at roughly 0.4 mm, and then decreased. In addition, flow rates near the lens were significantly different between 0.1 mm and 0.2 mm. These results show that a small hole size could improve aqueous humour circulation; specifically, a hole size of 0.2 mm or larger is desirable. To optimise the hole size, the current model with a diameter of 0.36 mm was considered to be the most suitable, because the peak diameter was observed to be roughly 0.4 mm. The diameter size of 0.36 mm was reported to cause no issues in terms of optics [3, 4]. However, if new reports indicate negative impacts on optics and visual functions, the size can be reduced to roughly 0.2 to 0.3 mm without losing the benefits in terms of aqueous humour circulation. In addition, if long-term prevention of cataracts is not possible at 0.36 mm, the diameter could be increased to approximately 0.40 mm. However, if the hole size is increased beyond this size, optical analysis, including imaging performance and illumination optics, is necessary. Currently, there are useful clinical reports with similar visual functions as the conventional ICL [1, 2, 8] [9] (Table 2). The hole-ICL is expected to continue to lower the risk of cataracts. Huseynove et al. [9] compared the outcomes between ICLs, one with and one without a central artificial hole. They reported that there was no difference in IOP at a 3-month follow-up, although there was a temporary and small increase in IOP at 1 week and 1 month (postoperative). Additionally, postoperative acute angle-closure glaucoma for hole-ICL has not been reported (Table 2). In the future, the optimum size should be determined based on these simulation results, the results of optical analysis, and long-term clinical results regarding visual performance and complications.

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Fig. 6 Trajectory analysis for various hole sizes. (Top) central hole size of 0.2 mm, (middle) central hole size of 0.4 mm, and (bottom) central hole size of 0.6 mm

The limitation of this research is that it was a computer simulation performed using a representative model of an eye. The pumping action associated with eye adjustments and individual differences were not taken into consideration. However, regarding the validity of this simulation, accuracy was confirmed, because the measured values were similar to the theoretical values[10]. Even if the absolute value is slightly off, it is unlikely

that the results associated with the improved aqueous humour flow rate due to changes in the hole size would change. In conclusion, the central hole diameter of 0.36 mm in the present hole-ICL model is almost ideal in terms of fluid dynamics. In the future, minute adjustments should be considered based optical properties and the on long-term clinical results of the incidence rate of cataracts.

Follow-up

Overview of hole-ICL studies Group

Study Population

13.1 ± 1.7

1 d: 11.3 ± 2.6 1 wk: 13.2 ± 3.2

6 mo: 13.0 ± 3.0

6 mo: 2720 ± 268

– – –

6 mo

2798 ± 225

– – –

12.8 –

12.1

1 mo: 12.9 ± 3.3 3 mo: 12.8 ± 2.5

20 patients (20 eyes); age 32 ± 8 yrs

– – –

– – –

12.9 –

12.6

1 mo 3 mo

Hole-ICL

28 patients (28 eyes); age 30 ± 6 yrs 58 patients (29 eyes); age 32 ± 8 yrs 58 patients (29 eyes); age 32 ± 8 yrs

Hole-ICL Conv ICL* Hole-ICL

2911 ± 318 –

2812 ± 303

2879 ± 343 –

2812 ± 248

Postop

Preop

Preop

Postop

Postoperative IOP (mmHg)

Postoperative ECD (cell/mm2)

*This study evaluated patients who underwent hole-ICL implantation in one eye and conventional ICL implantation in the other eye with random assignment

Conv: conventional; ICL: implantable collamer lenses; ECD: endothelial cell density; IOP: intraocular pressure

Shimizu et al., 2012 [2]

1d 1 wk

3 mo

Shimizu et al., 2012 [1]

Time course in Hole ICL group

3 mo

Kamiya et al., 2013 [8]

44 patients (44 eyes); age 35 ± 9 yrs 24 patients (24 eyes); age 30 ± 6 yrs

Hole-ICL Conv ICL

Comparison between conventional ICL group and hole-ICL group Huseynova et al., 2014 [9] 3 mo Conv ICL 21 patients (21 eyes); age 35 ± 6 yrs

Study

Table 2

None encountered

None encountered Glare or halos 13.8 % Glare or halos 0.0 % Glare or halos, both eyes 24.1 %

None encountered None encountered

None encountered

Postoperative Complications

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Acknowledgments The authors thank Dr. Hiroshi Uozato, Kozo Keikaku Engineering Inc. (Mr. Osamu Kuwahara, Mr. Soichi Masuda, and Dr. Tsuyoshi Yamada) for technical support and editing in a critical reading of the manuscript. Compliance with ethical standards For this type of study, formal consent is not required. Funding This study was supported by a grant from the Kitasato University School of Allied Health Sciences (Grant-in-Aid for Research Project, No. 2010–1029) (T.K.), a Kitasato University Research Grant for Young Researchers 2010–2015) (T.K.), and a Grant-in-Aid for Young Scientists (B) (T.K.). The sponsor had no role in the design or implementation of this research. Conflict of interest Dr. Kawamorita and Dr. Shoji declare no conflict of interest associated with this manuscript. Dr. Shimizu received a consulting fee from Staar. Informed consent This article does not contain any studies with human participants or animals.

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