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Aqueous Humor Outflow and Intraocular Drug Transport through
Trabecular and Uveoscleral Pathways
Sitian Peng(彭思甜)1, Feng Zhang(张峰)1, 2, a), Liang Hu(胡亮)3, Peng Dong(董
鹏)1, 2, Tiancai Huang (黄添彩)1, Yu Wang(王宇)2, Ting Fu(付婷)2, and Anle Ge(葛安
乐)4.
1
Hubei Key Laboratory of Mechanical Transmission and Manufacturing
Engineering, Wuhan University of Science and Technology, Wuhan 430081,
China
2
Key Laboratory of Metallurgical Equipment and Control Technology of Ministry
of Education, Wuhan University of Science and Technology, Wuhan, Hubei
430081, China
3
National Engineering Research Center of Ophthalmology and Optometry, Eye
Hospital, Wenzhou Medical University, Wenzhou 325027, China
4
Single-Cell Center, Qingdao Institute of Bioenergy and Bioprocess Technology,
Chinese Academy of Sciences, Qingdao 266101, China
a)
Author to whom correspondence should be addressed: [email protected]
ABSTRACT
Accurately predicting the temporal and spatial distribution of intraocular drugs to
enhance anti-glaucoma treatment efficacy remains a significant challenge in clinical
ophthalmology. Developing more precise numerical models of intraocular drug
transport holds substantial clinical value. This study establishes a model of intraocular
drug transport that includes the trabecular meshwork (TM), collector channels (CC),
and uveoscleral outflow pathway, and analyzes the parameters affecting aqueous humor
(AH) outflow and the impact of the uveoscleral pathway on drug transport. Results
indicate that the uveoscleral pathway influences AH outflow, with its porous media
significantly impeding drug clearance, leading to drug accumulation in the anterior
chamber (AC) and higher concentrations in the TM. A reduction in TM porosity or the
number of CC hinders drug transport to varying extents, increasing peak drug
concentration at TM targets by 11.27% and 12.8%, respectively. Furthermore,
neglecting the uveoscleral pathway may result in an 10.93% underestimation of TM
drug concentration. This study provides insights into the pathways involved in antiglaucoma drug transport, contributing to the optimization of drug design for improved
therapeutic outcomes.
1
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I. INTRODUCTION
Glaucoma is one of the primary causes of blindness worldwide,1 and reducing
intraocular pressure (IOP) remains a critical therapeutic approach.2 IOP reduction can
be achieved through medications, peripheral iridectomy, or laser iridectomy.3 However,
the high costs of treatment may deter some patients from seeking medical care.4 Local
administration of anti-glaucoma drugs has emerged as the preferred treatment option
due to its advantages, including cost-effectiveness, the lack of postoperative care, and
minimal surgical risks. Anti-glaucoma treatments are categorized into five classes:
prostaglandin derivatives, receptor antagonists, carbonic anhydrase inhibitors,
sympathomimetics, and combination drugs.5 β-receptor antagonists reduce aqueous
humor (AH) production in the ciliary body (CB),6 while prostaglandin derivatives
enhance outflow by increasing the permeability of the trabecular meshwork (TM).7
However, the efficacy of locally administered drugs is often limited by anatomical
barriers and the eye’s endogenous defense mechanisms, leading to poor ocular
bioavailability.8,9 Achieving therapeutic levels typically requires frequent or high-dose
administration, which can induce corneal toxicity.10 Therefore, improving drug delivery
systems for anti-glaucoma medications is essential to enhance efficacy and minimize
adverse effects.
The interactions between fluid mechanics and ocular health are highly complex,1114
and breakthroughs in ophthalmic treatment techniques rely heavily on advancements
in fluid dynamics research.15-18 Therefore, understanding AH flow is essential for
elucidating the mechanisms of drug delivery in anti-glaucoma therapies. After topical
administration on the ocular surface, the drug penetrates the anterior chamber (AC),
which is filled with AH, and is subsequently distributed via convective AH transport.19
AH outflow occurs through two main pathways: the conventional and the uveoscleral
pathways. In the conventional pathway, AH circulates through the TM, Schlemm's
canal (SC), collector channels (CC), and AH veins into the superficial scleral veins.
Numerical models have been developed to better understand drug transport via AH flow.
Wyatt et al.20 developed a computational model simulating drug and AH dynamics,
confirming that AH convection is the primary mechanism driving drug circulation. Lin
and Yuan21 proposed a two-dimensional(2D) numerical model to simulate the transport
of etacrynic acid (ECA), predicting its concentration distribution in the AC and TM. A
previously developed three-dimensional(3D) model incorporating AH flow, heat
transfer, and mass transport was used to investigate the influence of temperature
distribution on drug convection within the AC.22 Zhang et al.23 presented a 3D
computational model of anterior intraocular drug implantation to study the effects of
AH flow and implantation location on drug delivery. However, their model assumed a
uniform AH outflow along the inner surface of the TM, without considering the
structural impact of the TM on AH flow. TM porosity is a critical factor influencing AH
outflow.24,25 Experimental studies26 have shown that due to the uneven distribution of
2
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pores on the inner walls of the SC and CC, AH outflow occurs in a segmented and
irregular manner.
To accurately investigate intraocular drug transport, it is essential to account for
the influence of the TM on AH dynamics. A number of numerical models have been
developed in current research to simulate AH outflow structures and describe their role
in aqueous flow dynamics. Villamarin et al.27 proposed a 3D model based on
postmortem eyes to evaluate AH flow in both healthy and glaucomatous eyes,
highlighting the significant impact of TM permeability on IOP. Ferreira et al.28
developed a 2D model to simulate drug transport from the lens to the AC of the eye,
highlighting the role of the TM in AH outflow. Mauro et al.29 introduced a 2D model
incorporating the conventional pathway for AH flow and heat transfer, emphasizing that
TM porosity and permeability critically affect IOP. Sánchez et al.30 used optical
coherence tomography to establish a 2D model analyzing the distribution of 14 types
of CCs, concluding that CC location and number minimally affect IOP and AC
temperature, but reducing CC numbers increases the maximum velocity of AH flow.
These models demonstrate that variations in the conventional pathway significantly
influence AH flow, though few studies have explored their effects on drug transport.
The uveoscleral pathway30-32 involves AH drainage through the iris root,
pigmented TM, anterior surface of the ciliary muscle, connective tissue spaces between
the ciliary muscle bundles, and the suprachoroidal space into the sclera. MurgoitioEsandi et al.33 developed a comprehensive a AH flow model that integrates both the
conventional and uveoscleral outflow pathways. Their study examined the relationship
between the extent of circumferential closure and IOP elevation, demonstrating that the
uveoscleral pathway plays a critical role in modulating AH dynamics and regulating
IOP. Nilsson's research34 indicated that less than 15% of AH is drained via the
uveoscleral pathway, and that the contraction and relaxation of the ciliary muscle can
modulate AH outflow. Schachtschabel35 demonstrated that prostaglandins lower IOP by
enhancing AH outflow through the uveoscleral pathway, primarily via ciliary muscle
relaxation and extracellular matrix remodeling mediated by matrix metalloproteinases.
These enzymes may alter ciliary muscle collagen, increasing the interstitial spaces
between ciliary muscle fibers and reducing hydraulic resistance in the AH outflow
pathway. Currently, the uveoscleral pathway holds significant potential for lowering
IOP,36 however, comprehensive intraocular drug delivery models that incorporate this
pathway are rarely reported in the literature and require further development.
Current numerical models of intraocular drug delivery neglect key anatomical and
physiological features such as the porosity of the TM, the number of CC, and the
uveoscleral pathway, thereby compromising the accuracy of simulation results. In this
paper, a 3D eye model incorporating the TM, SC, CC, and the uveoscleral pathway
using the finite element method. Additionally, the model accounts for fundamental
physical processes, including AH secretion and expulsion, heat transfer from the eye,
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post-application behavior of anti-glaucoma drugs on the ocular surface, and pre-tissue
diffusion processes. The impact of TM porosity, the number of CC, and the uveoscleral
pathway on AH flow and anti-glaucoma drug transport was investigated to enhance the
precision of existing numerical models and provide valuable insights for drug
prediction.
II. METHODOLOGY
A. Geometric model
The anterior segment of the eye, which includes the cornea, AC, posterior chamber
(PC), iris, and lens, is essential for maintaining the structure and integrity of the eyeball.
The posterior segment consists of the sclera, vitreous body, and choroid. The structure
of the eyeball, along with the conventional and uveoscleral pathways are illustrated in
Fig. 1. The geometric parameters of the anterior segment were derived from previous
studies,21,37-40 modified based on histological sections of the human eye. The resulting
reconstructed structure is illustrated in Fig. 2.
FIG. 1. Diagram of AH outflow pathways.
FIG. 2. Geometric model of the human eye: (a) 3D model of the human eye; (b)AH outflow facility.
Changes in the pupillary space (the gap between the lens and the iris) within a
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range of 5 to 10 μm affect the flow rate of AH but do not influence drug concentration
in the TM.21 The model sets the pupil distance at the average normal distance for the
human eye, which is 10 μm.38
The TM consists of bundles of connective tissue, including elastic and collagen
fibers, forming a porous filtration structure.39 The radial cross-section of the TM is
porous and uneven, resembling a quadrilateral shape, with a narrow end towards the
cornea and a wider end towards the AC.41 It drains AH from the AC into SC, which is
located at the junction between the cornea and sclera, and is connected to veins on the
scleral surface by 25-30 CCs.25 SC is located above the TM and exhibits an elongated
shape. In the uveoscleral outflow pathway, the intermuscular spaces within the ciliary
muscle also possess a porous media structure.
The construction of the posterior segment model is based on data derived from the
geometric model of the eyeball.40 The exact geometric dimensions used in this model
are provided in Table I.
TABLE I. Geometric dimensions of the eye model.
Domain
Geometric Parameter
Value
Cornea
Thickness
Half-axis (HA) in the x direction
HA in the z direction
0.4 mm
7.3 mm
3 mm
Thickness
0.5 mm
AC
Iris
PC
Lens
Sclera
Choroid
TM
SC
Angle between iris and the x-axis
6°
HA in the x direction
4.8 mm
HA in the z direction
1.5 mm
Upper ellipse HA in the x direction
5 mm
Upper ellipse HA in the z direction
1.5 mm
Lower ellipse HA in the x direction
5 mm
Lower ellipse HA in the z direction
2.5 mm
Thickness
1 mm
HA in the x direction
12.2 mm
Inner HA in the z direction
12.3 mm
Thickness
0.28 mm
HA in the x direction
11.3 mm
Inner HA in the z direction
11.3 mm
Base length
0.47 mm
Top length
0.27 mm
Shorter side length
0.04 mm
Longer side length
0.2 mm
Base length
0.27 mm
Thickest point
0.04 mm
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CC
Diameter
0.052 mm
Height
0.26 mm
Quantity
30
The distribution of the CC in the model developed in this paper is shown in Fig. 3.
Due to the symmetry of model, only half of it is utilized to reduce computation time.
Table II and Fig. 4 show the main differences in the pathway of the four models.
FIG. 3. 3D schematic of the human eye model.
TABLE II. Structural differences among the four models.
Structure
Model
TM
SC
CC
Choroid
1
×
×
×
×
2
○
×
×
×
3
○
○
○
×
4
○
○
○
○
○: feature present; ×: feature absent.
FIG. 4. Pathway structures of AH.
The blue area in Fig.4 represents the region where AH flows, primarily including
the AC and PC. The green area denotes the porous medium, specifically the TM and
the space between the ciliary muscles. These structures play a vital role in the eye, not
only facilitating AH outflow but also influencing the distribution and absorption of
drugs in ocular tissues. The blank area at the exit of AH flow is defined as the boundary
where the drug exits, as once the drug diffuses from the cornea to this point, it is rapidly
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absorbed by surrounding tissues or the circulatory system. Therefore, the target location
of the TM for drug delivery is primarily influenced by AH flow, helping to evaluate the
significance of AH outflow structures in drug transport efficiency and physiological
effects.
B. Numerical model
1. Temperature
Fig. 5(a) shows computational domains (shaded) and corresponding boundaries
for temperature. The temperature distribution within the AC is non-uniform due to the
convective heat transfer associated with the flowing AH. Therefore, it is essential to
investigate the intraocular temperature distribution. The transient heat conductionconvection equation is used for this analysis, i.e.,
(1)
 (  cT ) / t +  c vT =  ( kT ) .
(
)
The thermophysical properties of various tissues are enumerated in Table III.
TABLE III. Thermophysical properties in each region.45-49
Domain
Cornea
Vitreous body
AC
PC
Lens
Iris
TM
CC
CB
Sclera
Choroid
Thermal conductivity
k (Wm-1K-1)
0.58
0.603
0.58
0.58
0.4
1.0042
1.0042
1.0042
1.0042
1.0042
1.0042
Specific heat
c (J kg-1K-1)
4178
4178
3997
3997
3000
3180
3180
3180
3180
3180
3180
Density
 (kgm-1)
1050
1000
996
996
1050
1100
1100
1100
1100
1100
1100
The boundary conditions for Equation (1) are defined as follows: heat conduction
and thermal radiation between the cornea and the surrounding environment are
considered, along with the heat loss due to tear evaporation on the exterior surface of
the cornea, i.e.,
4
(2)
−k T /  n = hamb (T − Tamb ) +  (T 4 − Tamb
) + E, on 1 ,
where hamb the coefficient of convective heat transfer between the cornea and the
environment that surrounds it, Tamb is the ambient temperature,  is the StefanBoltzmann constant,  is the emissivity of the external surface of cornea, and E is
the heat loss resulting from tear evaporation.
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FIG. 5. Simulation domains (shaded region) and boundaries for: (a) temperature, (b) AH flow, (c)
drug concentration.
Considering the eyeball is encased in human vascular tissue, the boundary
condition for the temperature on the external surface of sclera can be articulated as
follows
(3)
−k T /  n = hbl (T − Tbl ) , on  ,
2
where hbl is the convective heat transfer coefficient of the sclera and its surrounding
tissues. Tbl is the temperature of the blood tissue surrounding the sclera. It is assumed
that the temperature of the vascular tissue located deep within the human eye is
consistent with the core body temperature, which is 310 K. The parameters utilized in
Equations (2) and (3) are detailed in Table IV.
TABLE IV. Relevant parameters in temperature boundary conditions.
Parameter
Describe
Value
Tbl
Blood temperature (K)
310
Environment temperature (K)
298
Tamb
hbl
hamb


E
Convection heat transfer coefficient on the outer surface of the
sclera (W m-2K-1)
Convection heat transfer coefficient of external environment (W
m-2K-1)
6547
1045
Emissivity of the outer surface of the cornea
0.97548
Stefan-Boltzmann constant (W m-2K-4)
5.67×10-8
Heat loss in tear evaporation (W m-2)
4043
In the model with the eye in the supine position, a symmetrical temperature
boundary condition is established on the symmetrical surface:
T / r = 0.
(4)
2. AH flow
The shaded regions in Fig. 5(b) represent the anterior and posterior chambers. AH
exhibits properties similar to those of water and flows at low velocities within the eye,
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corresponding to a low Reynolds number (Re≈0.15). Therefore, it is appropriate to
model AH as an incompressible fluid under laminar flow conditions, which can be
described using the continuity equation and the steady-state incompressible NavierStokes equation, i.e.,
(5)
  v = 0,
(
)
 v  v = −p + 2 v +  g ,
(6)
where v is the velocity vector of the AH,  is the density,  is the dynamic
viscosity, p is the pressure, and g is the gravitational acceleration.
This study employs the Boussinesq assumption,51 which proposes a correlation
between the density of buoyancy in the momentum equation and temperature, while all
other density values are presumed constant to model the natural convection of the AH.
Specifically, the density  is expressed as a linear function of temperature:
 = 0 1 −  (T − T0 )  ,
(7)
where  0 is the reference density at temperature T0 , and  is the thermal expansion
coefficient of AH.
To evaluate the influence of temperature-induced density variation on natural
convection, we conducted a sensitivity analysis by varying  within a
physiologically reasonable range (e.g., ( 2.5 ~ 4.5) 10−4 K−1 ), and examining its effect
on velocity fields and flow patterns.
The results confirm that even small temperature gradients, typically observed
across the AC due to corneal cooling and iris heating, can generate non-negligible
buoyancy forces, thereby affecting the flow circulation and AH transport. These effects
are especially relevant in regions with low flow velocities or in pathological conditions
where thermal regulation is impaired. Hence, Equation (6) can be reformulated as
(8)
0 v  v = −p + 2 v + 0 1 −  (T − Tref ) g ,
−2
where  is the density of the AH,  = 0.00074Nsm is the kinematic viscosity of
(
)
the AH, p is the pressure of the AH, g represents gravitational acceleration,
0 = 996kgm −3 is the density of AH,  = 0.000337K −1 is the volume expansion
coefficient of the AH, Tref = 307K is the reference temperature.
After being secreted by CB, AH enters AC through the pupillary space, and then
exits through conventional and uveoscleral pathways. The entrance boundary
conditions for velocity are specified on the surface of the CB. In this study, the AH
inflow is modeled using a parabolic velocity profile, following the parabolic flow
assumption. This approach reflects the laminar flow characteristics typically observed
in low-Reynolds-number ocular environments. While this assumption is idealized and
may not fully capture the complex dynamics of AH secretion in vivo, it serves as a
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practical and widely adopted approximation for simulating steady-state flow behavior
within the AC, i.e.,
(9)
vCB = −Qah / Acb  6  S (1 − S ) ncb , on  ,
3
where Qah = 2.4μL min −1 is the rate of AH secretion,52 and Acb = 4.28 10−4 m 2 is the
area of the inner surface of the CB in our model, S is a dimensionless quantity on the
velocity inlet boundary that changes with the coordinates (ranging between 0 and 1),
n cb is the outward unit normal vector on the boundary of CB.
Given the supine position of the human eye, symmetric boundary conditions are
required on both sides of the model to ensure physiological relevance, i.e.,
(10)
v / r = 0.
The TM and the ciliary muscle interstitial regions in the model are designated as
porous media structures. In this paper, Darcy’s law is employed to characterize the
porous media attributes of the TM and ciliary muscle space,28 i.e.,
(11)
v = − /  p, on  ,
4
where v is the velocity of AH,  is the permeability, and  is the viscosity of the
AH, p is the pressure gradient. The porous structure of the TM was integrated into
the numerical model of the AH flow field to develop a model of AH velocity represented
as a porous medium, with the permeability of the TM assigned to the reference value
.
The Kozeny-Carman model32 serves as the semi-empirical formula utilized for
estimating the permeability of porous media in this paper:
 = d 2 3 / (150 (1 −  ) ),
where d is the average pore diameter, which is 8 μm .28
2
(12)
In this study, the uveoscleral outflow pathway was modeled as a homogeneous
isotropic porous medium, a simplification commonly adopted in steady-state
intraocular flow simulations. The ciliary muscle space of the uveoscleral pathway also
adheres Equations (11) and (12). While this approach neglects the viscoelastic nature
of the ciliary muscle, it provides a reasonable approximation of the bulk flow behavior
under constant IOP. This paper assumes that glaucoma drug does not affect the average
pore size, and the porosity of TM and ciliary muscle space were 0.225 and 0.1
respectively.
The boundary conditions on the other boundaries are no-slip conditions:
(13)
v = 0, on 5 .
3. Anti-glaucoma drug concentration
As shown in the shaded part of Fig. 5(c), the equation of unsteady convective
diffusion is used for the transport of drug concentration, which is driven by the flow of
AH in the AC and PC, i.e.,
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C / t + v C = D 2C ,
(14)
where C is the concentration of the drug, v is the speed of the AH, D is the
diffusion coefficient of the drug. The transport in other locations is ignored and only
passive diffusion is considered, so the flow velocity of the AH in other locations is 0.
The transport of ECA in human eye is used as a case study in this research to
identify general principles of drug transport following ocular surface administration.
ECA can treat glaucoma by promoting the outflow of TM cells.21 Being hydrophobic,
ECA spreads rapidly through ocular tissues, and its diffusion coefficient42,43 is provided
in Table V.
TABLE V. Diffusion coefficients of ECA in different domains.
Diffusion coefficient (cm2s-1)
7.0×10-6
1.31×10-6
1.31×10-6
4.85×10-6 (a)
4.85×10-6 (a)
4.85×10-6 (a)
4.85×10-6 (a)
Domain
AH
Iris
Cornea
Sclera
CB
Lens
Choroid
(a) Assume the diffusion coefficient is the same
During the administration of the ointment, a small amount of the drug is absorbed
by the anterior tissues, while the rest is cleared by tears in accordance with first-order
kinetics. The ointment prolongs the drug's retention in the cornea, with a half-life of
1818 seconds.45 Consequently, the equation that follows can articulate the concentration
of the drug on the exterior surface of cornea:
Ccor = C0  e −0.00038t , on 6 ,
(15)
where C0 is the initial concentration of Ccor , the drug concentration is normalized to
facilitate observation of the results. The initial drug concentration in this application
method is set to 1 mol/m , which serves as the reference concentration ( C0 ). All
3
subsequent results are presented in terms of the normalized drug concentration,
expressed as C / C0 , to facilitate dimensionless comparison.
The inner surface of the TM is assumed to be the outlet of AH flow in Model 1
(Fig. 4). In this case, the process of drug diffusion from the AH to the TM can be
overlooked due to the prevailing influence of convective transport. A characteristic of
convective transport is that the concentration gradient in the direction of the fluid
streamline is 0 at steady-state, i.e.,
(16)
n  (− DC ) = 0, on  .
7
where n is the outward normal unit vector.
In this paper, it is assumed that ECA does not degrade in human eye tissue, and its
primary clearance occurs through absorption into the bloodstream and lymphatic
capillaries. The cornea lacks blood vessels, whereas the sclera is highly vascularized.
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However, drug absorption in the sclera is limited due to the low permeability and small
surface area of its blood vessels. As a result, scleral cells mainly receive nutrients from
the micro vessels in surrounding tissues.43 Drug absorption in both the cornea and sclera
can be neglected, and drug diffusion through the vitreous body is disregarded due to its
slow rate.
As the drug diffuses through the sclera and reaches the outer surface of the AH
outlet, it is promptly discharged. The boundary condition for drug concentration at the
scleral surface and the AH outlet is governed by Equation (16). In this model, with the
eye in a supine position, the boundary conditions are assumed to be axisymmetric:
C / r = 0.
(17)
The blood vessels in the iris rapidly absorb and clear the drug, leading to the
assumption of zero concentration at its center, while the initial concentration outside
the cornea is set to 0:
C = 0, on 8 .
(18)
Although the drug concentration decays exponentially after application, the
primary challenges are the physical and biological barriers of the eye. It takes time for
the drug to reach its target site and may be absorbed by other ocular tissues. A duration
of 6 hours is selected to capture the complete drug transport process for various targets.
4. Numerical details
The commercial finite element software COMSOL Multiphysics 6.1® was
employed to address these challenges. In the AC, PC, AH outflow region, and cornea,
mesh refinement was applied appropriately to ensure numerical convergence.
The temperature distribution in the eye and the velocity profile of the AH were
obtained by simultaneously solving Equations (1), (5), (8), (11) and (12), along with the
associated boundary conditions. To determine the spatiotemporal evolution of the drug
concentration field, the AH velocity, boundary conditions, and initial condition of zero
concentration were incorporated into Equation (14). In this numerical process, relative
and absolute tolerances were set at 0.01 and 0.001, respectively.
The calculation of the Grid Convergence Index (GCI) is performed to verify the
precision of the computational outcomes.53 The expression for GCI is as follows:
GCI = Fs  / (r p −1),
(19)
 = ( f coarse − f fine ) / f fine .
(20)
In Equation (19), Fs ,  , p and r represent the safety factor, grid
convergence error, and convergence accuracy, respectively. In Equation (20), f coarse and
f fine correspond to the numerical results under coarse and fine grids. The safety factor
should be set to 1.2554 for the estimation of the GCI using three or more sets of grids.
TABLE VI. GCI results under the structural grid.
Number of meshes
(million)
Convergence
solution
r
12
ε
GCI/%
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1.64
2.14
2.38
3.13
3.70
4.57
5.74
6.91
-2.5531
-2.5659
-2.5705
-2.5757
-2.5789
-2.5803
-2.5812
-2.5815
1.094
1.036
1.095
1.057
1.074
1.079
1.064
-
0.00394
0.00179
0.00202
0.00124
0.00054
0.00035
0.00012
-
3.22%
3.08%
1.29%
1.34%
0.45%
0.27%
0.11%
-
The computational results for the GCI are presented in Table VI. Notably, the GCI
values for the three consecutive grid sets, 2.38 million, 3.13 million, and 3.7 million,
are all below 3%. This meets the criterion for GCI compliance.55 In other words, once
the grid count exceeds 2.38 million, the simulation results become independent of
further grid refinement. The final mesh of the 3D model consists of 3,145,756
tetrahedral elements, and Fig. 6 provides a visual representation of the grid model.
Although the GCI values presented in Table VI are based on pressure data, the
convergence quantity was obtained from a coupled solution of the momentum and
energy equations, and thus indirectly reflects the behavior of the velocity field. In
addition, to further ensure the reliability of the numerical results across all relevant
physical quantities, additional checks were performed on the maximum AH velocity
and the average drug concentration in the AC using mesh densities ranging from 2.14
to 5.74 million elements. The relative variation of these parameters across refined
meshes remained below 2%, confirming that the final mesh resolution is adequate for
resolving velocity and transport fields.
FIG. 6. Mesh diagram of the 3D model.
C. Model validation
1. Temperature
To validate the accuracy of the simulated temperature distribution, the results were
compared with previously reported experimental measurements of steady-state
temperature profiles in rabbit eyes.49,56 The experimental ambient temperatures reported
in these studies are 23℃ and 23.8℃, respectively. To maintain consistency with the
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experimental data, the computational model in this study adopts the anatomical
geometry and physiological parameters of the rabbit eye. Some of the boundary
conditions in our numerical model for comparison are as follow Tbl = 411.8 K ,
Tamb = 298 K ,
hamb = 20 W/m 2 K , and
hbl = 65 W/m 2 K . Fig. 7 compares
experimental temperature data along the pupillary axis with the simulation results
presented in this paper.
FIG. 7. Comparison of our simulation results with experimental data.
The deviation between the numerical simulation results and the experimental data
reported in the literature49 is within the range of 0.06% to 0.25% for one study, and
between 0.06% and 0.466% for another.56 Consequently, the simulation outcomes are
fundamentally aligned with the experimental findings related to rabbit eye anatomy,
affirming the acceptable accuracy of the simulation results. The modeling approach
itself is generalizable and can be adapted to other species, such as human eyes, by
substituting species-specific parameters.
2. AH flow
To validate the accuracy of the simulated AH flow field, the results were compared
with experimental data reported in the literature.52 As shown in Fig. 8, the AH flow
pattern obtained in the present model is in close agreement with the findings in that
study, suggesting that the observed circulation is driven by natural convection induced
by intraocular temperature gradients. Furthermore, the peak flow rate at the center of
the AC is recorded at 10⁻5 m/s. Although the maximum speed varies due to differences
in models, these discrepancies remain within acceptable limits.
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FIG. 8. Validation of the AH flow field: (a, b) Supine; (c, d) Standing.
Elevated IOP in glaucoma can be attributed to an increase in AH production and a
reduction in outflow through the TM. To further validate the model under pathological
physiological conditions, we followed the approach proposed by Ferreira et al.28,
configuring simulations with varying AH inflow velocities and applying pathological
TM parameters to represent increased outflow resistance. Specifically, the TM was
modeled with reduced permeability  = 2.3 10−15 m 2 and porosity  = 0.15653 ,
consistent with glaucomatous alterations.
Fig. 9 illustrates the relationship between IOP and AH production rate under the
glaucomatous conditions. At the reference inflow velocity v0 , the simulated IOP rises
to approximately 3979 Pa, which exceeds the upper limit of the normal physiological
range and closely matches the pathological value of 3896 Pa reported in the literature.
This result confirms the model's ability to reproduce disease-relevant physiological
behavior, supporting its applicability in simulating intraocular drug transport and flow
dynamics under glaucomatous conditions.
FIG. 9. Validation of the relationship between IOP and AH production rate under pathological
conditions.
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3. Anti-glaucoma drug concentration
The results of the numerical simulation of anti-glaucoma drug transport from the
corneal surface are compared with those reported by Chen et al.22 The rate of intraocular
drug diffusion is influenced by the method of administration. Following the same
approach, this study simulates drug delivery via ophthalmic ointment. Under such
conditions, the drug exhibits a prolonged half-life and a high peak concentration, with
all results normalized to the initial concentration. As shown in Fig. 10, both simulations
reach peak concentrations at approximately 1 hour, indicating a consistent overall trend.
A deviation of less than 3%, which lies within the acceptable range, demonstrates the
reliability of the present model.
FIG. 10. Validation of the concentration of anti-glaucoma drugs.
III. RESULTS
A.Temperature distribution
Fig. 11 and Fig. 12 depict the temperature distribution in the anterior segment of
the eye under four distinct AH drainage configurations, with the eye oriented upward
and horizontally, respectively. As shown in Fig. 11, the temperature distribution in the
upward view of the human eye is symmetric. In contrast, Fig. 12 illustrates that, in the
horizontal view, the isotherms in the anterior segment exhibit curved patterns distinct
from those in the posterior segment. This difference in isothermal contours is primarily
attributed to the convective effects of AH flow. The results indicate that the temperature
of the cornea, as the outermost layer of the eye directly exposed to air, is generally lower,
while the internal regions of the eye maintain a relatively higher temperature. The
cornea's temperature is influenced by environmental factors, resulting in heat exchange
with the surrounding environment and a subsequent reduction in surface temperature.
In contrast, the internal structures, particularly the posterior region, are enveloped by
multiple layers of tissue, including the retina, choroid, and sclera. These tissues not only
provide protection but also effectively maintain a relatively constant local temperature.
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They can store and transfer heat generated within the body, allowing the posterior
region to remain stable and close to core body temperature. Therefore, the temperature
distribution of the eye remains unchanged across different outflow structures. A
comparative analysis indicates that ocular orientation affects the temperature
distribution in the anterior segment of the eye, while the temperature profiles among
the four outflow pathways remain largely similar.
FIG. 11. Temperature distribution of the human eye in four models under up-facing conditions.
FIG. 12. Temperature distribution of the human eye in four models under horizontally-facing
conditions.
B. AH velocity distribution
The flow line distribution of AH flow rates in the AC and PC under four different
outflow pathway structures is illustrated in Fig. 13 and Fig.14. A thorough analysis of
this figure reveals that changes in the conventional pathway structures do not
significantly affect the AH flow trend. Additionally, the uveoscleral pathway structure
also fails to markedly alter the flow trend, indicating that despite differences in pathway
design, their interference with the overall flow pattern is minimal.
As shown in Fig. 13, the AH flow distribution in the upward-facing eye is
symmetric, forming periodic flow patterns within the AC. A relatively high velocity is
observed as the flow passes through the pupil. Compared to Model 1, Model 2
introduces additional outflow resistance via a porous medium at the outlet, resulting in
minimal overall changes in the AH flow field, though recirculation or low-velocity
regions appear in the PC. In Model 3, the addition of CCs narrows the outflow pathways,
leading to significantly higher velocities within the channels. Model 4 incorporates the
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uveoscleral pathway, which alters the outflow streamlines of AH in the AC angle,
allowing a portion of the AH to exit through the uveoscleral pathway. In contrast, as
illustrated in Fig. 14, the AH flow in the forward-facing eye forms a clockwise
circulation, with higher velocities occurring near the corneal side of the AC. Notably,
the streamlines indicate a distinct backflow region only in the lower part of the PC,
reflecting asymmetry in the AH flow field due to ocular orientation. Further analysis of
Models 3 and 4 reveals that the presence of narrow CCs leads to the highest AH
velocities in this region. The differences in flow streamlines among the four outflow
structures exhibit characteristics that are largely consistent with those observed in
Fig. 13.
Although the AH outflow structures differ across models, the internal flow patterns
observed in all experiments demonstrate a high degree of consistency. This suggests
that regardless of the exit structure employed, the fundamental hydrodynamic behavior
of AH remains similar and exhibits natural convection patterns. Due to the increase in
corneal temperature from the center to the periphery, the temperature distribution of AH
beneath the cornea is uneven. The lower density, warmer AH tends to rise along the
inner surface of the cornea, driven by convection. Consequently, temperature
differences induce natural convection, resulting in counterclockwise flow and the
formation of a stable circulation system.
FIG. 13. Streamline comparison of the AH velocity models of the four up-facing models.
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FIG. 14. Streamline comparison of the AH velocity models of the four horizontally-facing models.
As shown in Fig. 15, under the condition of a fixed inflow rate, the outflow of AH
through the TM gradually decreases with the addition of structural components to the
outflow pathway. This is because the newly introduced pathways share part of the total
flow, thereby reducing the portion passing through the TM. The distribution of flow is
determined by the hydraulic resistance of each pathway. In Model 1, the simplest design
excludes any porous media, resulting in the smoothest drainage and the highest flow
velocity. In contrast, Model 2 incorporates the TM, introducing resistance to flow.
Model 3 builds upon Model 2 by adding 30 CCs. Due to their small diameters, the flow
velocity through the CCs increases significantly, but their presence also adds resistance
to outflow. Based on Model 3, Model 4 introduces the uveoscleral pathway. Although
this pathway significantly expands the available outflow area, under constant AH
secretion, the additional pathway causes redistribution of flow, thereby reducing the
amount of AH passing through the TM.
FIG. 15. Comparison of TM Outflow.
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C. Anti-glaucoma drug concentration
The flow of AH not only serves as a mechanism for IOP regulation but also plays
a critical role in the diffusion–convection transport of drugs within the eye. It facilitates
drug distribution, significantly influencing both the spatial distribution and clearance
rate of intraocular drugs, thereby affecting therapeutic efficacy. Consequently,
numerical modeling of intraocular drug transport must account for both diffusive and
convective effects of AH flow. Accurately simulating the AH dynamics is essential for
reliably predicting intraocular drug concentration profiles.
The Peclet number ( Pe ) is calculated to measure the degree of convective and
diffusive transport drug of the drug within the AC. The formula for calculating the Pe
is given as:
Pe = vL / D,
(21)
where v is the characteristic velocity, which in this paper is taken as the maximum
-3
AH velocity in the AC at standing position ( 6.02 10 m/s ). L is the characteristic
-3
length, which corresponds to the half-length of the AC ( 7.19 10 m ). D is identified
as the diffusion coefficient of the drug within AH ( 7 10 m /s ).
Based on the provided information, the Pe within the AC can be estimated to be
-10
2
6.18 104 . As the Pe is the relative ratio of convection to diffusion, indicating that
convective effects dominate drug transport within the AC. The circulating AH flow is
the primary determinant of drug transport within the AC. While the dimensionless Pe
provides a useful preliminary indication of the relative importance of convective and
diffusive transport mechanisms, it represents only an averaged estimation and does not
fully capture the spatial heterogeneity and temporal dynamics of intraocular drug
movement. Moreover, due to the complex geometry of the AC and the non-uniform
flow patterns of AH, localized convective-diffusive interactions can vary significantly
throughout the domain. To overcome these limitations and more accurately evaluate the
transport behavior, detailed numerical simulations are carried out in the following
sections. These simulations account for the complex flow field and enable a more
realistic prediction of spatiotemporal drug concentration profiles.
The site of drug administration is located on the external surface of the cornea, and
the concentration of the drug conforms to Equation (15) across all models. Additionally,
an outflow port for drug egress is positioned on the vitreous body and scleral outer
surfaces in all models. The key distinction among the models is as follows: Model 1
has a drug flow outlet at the TM; Model 2 features a drug flow outlet at the SC; Model
3 has its drug flow outlet at the CC; and Model 4 includes drug flow outlets at both the
CC and the outer choroidal surface.
The comparison of drug concentrations in the AC at specific time points (30
minutes, 120 minutes, and 210 minutes) under up-facing conditions is illustrated in Fig.
16. The distribution of drug concentration within the AC is predominantly influenced
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by the AH flow dynamics. Elevated concentrations are observed along the ocular central
axis, followed by a gradual homogenization and diffusion toward adjacent ocular
tissues. Compared to the other three models, Model 1 exhibited significantly lower drug
concentrations at 120 minutes and 210 minutes. In models incorporating the TM porous
medium (Model 2, Model 3, and Model 4), drug transport experiences a degree of
obstruction. This obstructive effect prolongs the residence time of the drug within the
AC, potentially enhancing its interaction with ocular tissues and improving therapeutic
efficacy. As shown in Fig. 17, due to the clockwise recirculating flow of AH in the AC,
the drug delivered from the corneal surface is carried along with the flow, resulting in
significant accumulation near the center of the circulation. Notably, Model 4 exhibits a
higher scleral drug concentration compared to the other models after 210 minutes; this
phenomenon can be attributed to a lower diffusion coefficient for anti-glaucoma
medications within the sclera, resulting in a reduced diffusion rate throughout this tissue.
Additionally, boundary conditions at uveoscleral flow outlets restrict dispersal toward
the CB, thereby directing drugs toward inferior regions along the uveoscleral pathway.
Although the four pathway models exhibit similar concentration distribution patterns at
the same time point, substantial differences in concentration magnitude are observed.
This indicates that the structural integrity of the aqueous outflow pathways has a
pronounced impact on the simulation of intraocular drug transport.
FIG. 16. Normalized drug concentration distribution along the central cross-section of the eye for
the four models under up-facing conditions.
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FIG. 17. Normalized drug concentration distribution along the central cross-section of the eye for
the four models under horizontally-facing conditions.
The establishment of drug concentration outflow boundary conditions on the
external surface of the sclera facilitates the dispersion of drugs released from the cornea
into the sclera, allowing for their exit through its boundaries. Notably, the drug
concentration at the corneoscleral interface remains continuous, without any
discontinuities, which more accurately represents physiological conditions.
Furthermore, a blank area was designated at the outlet of the AH outflow pathway to
serve as a boundary condition for drug excretion. The drug present within this outflow
pathway originates solely from AH flow and is unaffected by diffusion from
surrounding tissues, particularly the sclera. Consequently, by comparing drug
concentrations at targeted points in the TM, one can assess how structural alterations in
AH outflow pathways influence drug transport dynamics.
Fig. 18 compares drug concentrations among the four structural models under upfacing conditions. The data clearly indicate that Model 1 exhibits a significantly lower
maximum drug concentration compared to the other three models. This observation can
be attributed to the unique structural characteristics of each model. The absence of
porous media in Model 1 facilitates faster drug elimination from the AC, resulting in a
shorter drug retention time and contributing to a lower peak concentration. This aligns
with the observations presented in Fig.16, further confirming the characteristic of rapid
drug clearance in the AC in Model 1. The porous media in the other three models serve
as a drug reservoir, slowing diffusion and outflow, thus prolonging retention times and
increasing peak drug concentrations in the AC; in Model 4, the peak drug concentration
at the TM increased by 25.86% compared with Model 1. This suggests that if the
integrity of the AH structure (including both the conventional and uveoscleral pathways
is not fully considered in simulating the transport of anti-glaucoma drugs, the peak drug
concentration at the TM may be underestimated, thereby affecting the accuracy of the
simulation results. Therefore, the importance of the AH outflow structure in antiglaucoma drug transport cannot be overlooked.
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FIG. 18. Normalized average drug concentration on the inner surface of the TM for the four models.
The study findings indicate that the uveoscleral pathway, particularly the ciliary
muscle, can impede drug transport and affect drug excretion, leading to an increase in
the peak drug concentration at the target site. Therefore, in investigating drug transport
processes within the human eye, the uveoscleral pathway represents a critical factor that
must not be overlooked. Neglecting this aspect may result in an underestimation of drug
concentrations, thereby impacting the therapeutic effect.
IV. DISCUSSION
A.The effect of uveoscleral pathway porosity
The uveoscleral pathway was modeled as a porous medium within the interstitial
spaces of the ciliary muscle. Under controlled inlet flow rates and identical boundary
conditions, simulations were conducted for four different porosities of the porous
medium, 0.05, 0.1, 0.2, and 0.3. The outflow rates through the conventional and
uveoscleral pathways were compared accordingly. As shown in Fig. 19, with a porosity
of 0.05, the flow rate through the conventional pathway is significantly higher than that
through the uveoscleral pathway. This indicates that the uveoscleral pathway exhibits
low permeability and high flow resistance at this level of porosity. Consequently, AH
preferentially exits via the conventional TM route. As the porosity of the ciliary muscle
interstitial space increases, the flow rate through the uveoscleral pathway rises markedly.
This shift results in a greater proportion of AH exiting through the uveoscleral pathway,
leading to a corresponding reduction in flow through the conventional pathway. These
results indicate that the porosity of the uveoscleral pathway affects the partitioning of
AH outflow.
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FIG. 19. AH flow rate at varying CB porosity.
Fig. 20 illustrates the temporal evolution of target drug concentrations at the TM
under four different porosity values of the ciliary muscle gaps. It is evident that changes
in porosity affect the peak concentration at the TM, though the influence is nonmonotonic. An increase in porosity from 0.05 to 0.1 results in the peak concentration
curves at the TM outlet nearly overlapping, accompanied by a slight decrease in peak
value. This is because a very low porosity results in limited permeability of the
uveoscleral pathway, rendering it almost non-functional for outflow. Consequently, the
drug primarily flows toward the TM region, and the influence of the uveoscleral outflow
pathway on TM drug concentration is negligible. As porosity increases from 0.1 to 0.3,
the peak concentration correspondingly rises. This indicates that enhanced porosity
improves convective transport, allowing the drug to reach the TM region more rapidly
and resulting in a higher peak concentration. Notably, the time to reach peak
concentration remained relatively unchanged across all porosity levels, suggesting that
changes in flow partitioning primarily affect drug transport magnitude rather than
timing.
In contrast, drug concentration at the uveoscleral outlet exhibited a more consistent
and monotonic increase with porosity, as shown in Fig. 21. An increase in porosity
resulted in a significant rise in peak concentration, indicating that the drug was
transported more efficiently through the uveoscleral pathways due to decreased flow
resistance.
The influence of different uveoscleral pathway porosities on intraocular drug
concentration can be evaluated by comparing the concentration profiles at the TM and
uveoscleral pathway outlets. Therefore, incorporating the porosity of the uveoscleral
pathway is of significant importance for accurately predicting AH outflow distribution
and simulating intraocular drug transport.
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FIG. 20. Drug concentration in the TM at varying porosity.
FIG. 21. Drug concentration in the CB under varying porosity.
Our simulation results provide meaningful insights for optimizing clinical
strategies in intraocular drug delivery and pressure management. Given the significant
impact of uveoscleral porosity on AH redistribution and drug clearance, surgeons and
clinicians should consider strategies that enhance or preserve the permeability of this
uveoscleral outflow pathway. For instance, minimally invasive procedures that avoid
damaging the ciliary muscle, or pharmacologic agents that promote extracellular matrix
remodeling (e.g., prostaglandin analogs)57 may help sustain higher uveoscleral porosity
and support effective drug transport.
In patients with poor TM function or elevated resistance in the conventional
pathway, enhancing uveoscleral outflow may serve as a compensatory mechanism to
lower IOP and facilitate drug clearance. This supports the targeted use of prostaglandin
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analogs, which increase uveoscleral outflow by relaxing ciliary muscle fibers and
increasing interstitial porosity. Additionally, the development of drug-eluting implants
positioned near the CB could leverage the enhanced convection within a more porous
uveoscleral pathway, thereby improving drug delivery to posterior tissues while
reducing systemic exposure.
From a surgical perspective, implantable drainage devices or stents could be
designed with flow-redirecting features that exploit uveoscleral permeability to regulate
IOP and control drug dispersion more precisely. For example, customizing implant
geometry or positioning to favor the uveoscleral pathway in patients with TM
dysfunction may offer both pressure-lowering and drug-delivery benefits.
B. The effect of TM porosity
Glaucoma is a serious ocular condition characterized by optic disc indentation and
visual field impairment. If left untreated, it can inevitably lead to irreversible vision
loss.4 A critical aspect of understanding the pathogenesis of glaucoma involves
investigating the physiological regulation of AH outflow by the TM. The TM serves as
the primary pathway for intraocular fluid drainage, and any abnormalities in its
structure or function often result in elevated IOP, the primary pathological hallmark of
glaucoma. Glaucoma develops as IOP exceeds the structural tolerance of the eye.
Research indicates that effective management of glaucomatous conditions often
depends on reducing IOP to a normative range of 30-52%.25 Modulating IOP is
therefore a key therapeutic strategy in glaucoma management.
The porosity of the TM plays a crucial role in regulating AH flow and IOP. The
complex porous architecture of the TM determines the resistance faced by AH. Lower
porosity increases the resistance to AH movement, leading to elevated IOP, while higher
porosity reduces resistance, resulting in a corresponding decrease in IOP. To quantify
the effect of porosity variation on flow resistance, steady-state laminar flow simulations
were conducted with different porosity values assigned to the TM region
(  = 0.1, 0.15, 0.225, 0.3, 0.4 ). The flow resistance parameter R = P / Q was
calculated to quantitatively evaluate the regulatory role of the porous structure in
modulating AH outflow resistance. Simulation results showed that as the porosity 
of the TM region decreased, the pressure drop P increased gradually, while the
volumetric flow rate Q decreased significantly, leading to a marked increase in flow
resistance R . Fig. 22 illustrates the variation of flow resistance under different
porosity conditions. The results are consistent with the classical Kozeny-Carman
relationship in porous media, indicating that a reduction in porosity significantly
increases hydraulic resistance. This trend suggests that microstructural alterations in the
TM may play a key role in modulating AH outflow resistance, further supporting the
hypothesis that pathological remodeling of trabecular tissue contributes to elevated IOP.
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FIG. 22. Flow resistance with varying TM porosity.
To examine the relationship between porosity and IOP, simulations were
conducted under five different porosity conditions: 0.1, 0.15, 0.225 (considered normal),
0.3, and 0.4, assuming a null pressure at the AH outflow site. As shown in Fig. 23, IOP
in the AC rises progressively as TM porosity decreases, aligning with the results of
Ferreira.28 Significant changes in IOP are observed within the porosity range of 0.1 to
0.225, highlighting the sensitivity of ocular pressure to small porosity variations. In
contrast, in the porosity range of 0.225 to 0.4, IOP exhibits a less pronounced variation,
suggesting a reduced sensitivity of IOP to changes in porosity within this interval.
FIG. 23. Pressure in the AC with varying TM porosity.
The time-dependent trends of drug concentration on the inner surface of the TM
at five different porosities are illustrated in Fig. 24. As the porosity decreases, there is
a progressive increase in drug concentration on the inner surface, with the peak
concentration at a porosity of 0.1 being 11.27% higher than that at 0.4. This occurs
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because lower porosity increases the resistance to AH flow. As the resistance decreases
with higher porosity, the drug diffusing from the cornea is transported more rapidly into
the AC, reducing its concentration on the inner surface of the TM. In all five models,
porosity is the only varying factor, while other boundary conditions are consistent,
resulting in similar trends and peak times across the models. This reinforces the
importance of TM porosity as a key determinant of drug concentration distribution.
Porous media, with their intricate structural and functional characteristics, are not
only found in the conventional outflow pathways like the TM but are also prevalent in
the uveoscleral outflow pathways, such as the ciliary muscle space. These regions are
crucial for AH outflow, and porous media play an essential role in regulating the
transport of anti-glaucoma drugs.
FIG. 24. Drug concentration in the TM under varying porosity.
These results have direct implications for pharmacological treatment strategies in
glaucoma management. In patients with significantly reduced TM porosity due to
fibrosis, chronic inflammation or age-related degeneration, topical IOP-lowering agents
such as prostaglandin analogs and Rho kinase inhibitors may be particularly effective.58
Prostaglandin analogs enhance uveoscleral outflow, while Rho kinase inhibitors
improve trabecular outflow by relaxing the cytoskeleton and increasing intercellular
space, thereby improving TM porosity and reducing resistance.
Moreover, for individuals with TM porosity below the normal range (e.g., <0.225),
clinicians should be cautious with drugs that rely heavily on TM clearance, as prolonged
residence time could increase local concentration and risk side effects. In such cases,
personalized drug regimens may help achieve therapeutic goals including reduced
dosing frequency, lower concentrations, or localized sustained-release implants while
minimizing adverse outcomes.
Regular monitoring of IOP response and drug tolerance is essential, particularly in
patients suspected of having structurally compromised TM. Incorporating structural
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assessment tools (e.g., OCT-based TM imaging) into routine evaluation may allow for
dynamic adjustment of drug choices based on inferred porosity status, supporting a
precision medicine approach in glaucoma care.
C. The effect of the number of CC
The regulation of AH outflow is crucial for maintaining stable IOP. Studies
indicate that outflow distribution primarily occurs in two regions: SC and CC, with the
latter contributing approximately 50% of the total outflow resistance.25 Research has
shown that complete blockage of the CC can occur in both healthy and glaucomatous
eyes.59 In healthy eye the incidence of fully blocked CC is less than 10% at perfusion
pressures of 10 mmHg and 20 mmHg. However, in glaucoma patients, at a perfusion
pressure of 20 mmHg, 24.8% of CC exhibit complete blockage. The prevalence of fully
obstructed channels increases significantly with rising perfusion pressures, suggesting
that many individuals with glaucoma may experience partial or complete dysfunction
of these channels. As a result, drug transport in glaucoma patients may be impaired due
to this dysfunction. Therefore, investigating the dynamics of anti-glaucoma drug
transport under varying numbers of functional CC is essential for optimizing
therapeutic strategies. Given that anti-glaucoma medications rely on efficient transport
mechanisms to achieve their effects, understanding how different numbers of functional
CC influence drug transport is critical for refining treatment approaches.
To validate the accuracy of the simulated AH velocity, the results were compared
with experimental data reported in literature.52 The AH flow pattern obtained in the
present model is in close agreement with the findings in that study, suggesting that the
observed circulation is driven by natural convection induced by intraocular temperature
gradients. Furthermore, the peak flow rate at the center of the AC is recorded at 10-5m/s.
Although the maximum speed varies due to differences in models, these discrepancies
remain within acceptable limits.
The volumetric flow rate of fluid Q is directly proportional to the pressure
difference across the tube ends P and is inversely related to the viscosity of the fluid
 , the radius of the tube r , and the length of the tube L according to Poiseuille's
law. The specific relationship is expressed as follows:
Q =  r 4 P / 8 L.
(22)
Similarly, this equation applies to the AH flow within the CC. In this paper, the
-4
viscosity coefficient of the AH  is held constant at a fixed value of 7.5 10 Pa  s .
The length of conduit L is precisely delineated as the distance from the superior surface
-4
of the CC to the external surface of SC, which amounts to 2.49 10 m . The radius
r is derived from the CC own radius, measuring 2.6 10-5 m .
-2
The velocity of fluid flow within the CC is ascertained to be 0.16 10 m/s , and
the pressure differential across the two termini of the CC amounts to 3.56 Pa via
computational simulations. Comparing the simulated pressure differential with the
29
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computational results from the model reveals a calculated error margin of 3.87%, which
falls within the acceptable range defined by the established parameters. Thus, the
veracity of simulated results is confirmed.
To explore the role of CC in IOP regulation, this study examined the impact of
varying channel quantities on velocity, temperature, and concentration fields. In the
structurally complete model, 30 CCs are evenly distributed. To assess the effect of
different quantities, three scenarios were simulated with 10, 20, and 30 channels. The
distribution of these varying channel quantities is depicted in Fig. 25, with yellow
rectangles representing the channels. Throughout the simulation, the eye is assumed to
be in a standing position, with gravity acting downward along the x-axis. Except for the
variations in CC quantities, all other boundary conditions and AH flow settings are
consistent with section II.B.2.
FIG. 25. Distribution of three distinct quantities of CC.
To investigate the effect of the number of CCs on the local flow field, we simulated
models under two eye orientations: standing and supine. Fig. 26(a-c) shows the
streamline distributions in the standing orientation, while (d-f) presents the
corresponding results for the supine orientation.
In the standing orientation, the flow distribution across CCs is markedly nonuniform. To highlight this effect, Fig. 26(a-c) displays the local flow field near the
lowermost CC, which exhibits the highest outlet flow under each condition. In contrast,
in the supine orientation, AH flows more evenly toward all CC outlets, and Fig. 26(df) illustrate representative regions, as the flow fields are similar across different outlets.
As shown in the figure, reducing the number of CCs, particularly in the 10-CC
model, causes streamlines to converge more densely toward a few dominant outlets,
resulting in higher local velocity peaks. Under otherwise identical conditions, the
velocity observed in the 20-CC model is significantly lower than that in the 10-CC
model, and both are lower than the velocity observed under the normal condition with
30 CCs. This phenomenon can be attributed to the reduced number of CCs simulating
pathological obstruction, which increases the local flow resistance within the SC and
leads to an uneven pressure gradient along the SC wall. The resulting non-uniform
pressure distribution disrupts streamline continuity and may induce local flow
separation.
As the number of CCs increases to 30, the streamlines become more evenly
distributed among multiple outlets. As seen in Fig. 26(c) and (f), this results in lower
peak velocities at individual CCs, reduced risk of flow separation and recirculation
30
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zones, and a more physiologically stable outflow pattern.
FIG. 26. The distribution of outlet flow at different CC quantities.
The distribution of drug concentration on the inner surface of the TM at different
numbers of CC is illustrated in Fig. 27. As expected, the results show that increasing
the number of CC reduces the drug concentration passing through the TM per unit time.
Specifically, reducing the number of CCs from 30 to 10 increased the peak drug
concentration at the TM by 12.8%. As a key structure in the conventional outflow
pathway of AH, CC play a vital role in the pharmacokinetics of ocular drugs. Under
normal conditions, the number of CC typically ranges between 25 and 30, which is
critical for maintaining the balance of AH and ensuring proper drug distribution. A
reduction in the number of CC significantly affects the excretion of drugs from the AC,
leading to an increase in drug concentration at the target site and potentially triggering
other physiological responses. Fewer CC impede AH flow, resulting in localized drug
accumulation. This accumulation may cause a discrepancy between the therapeutic
dose required and the actual concentration observed, complicating the prediction of
clinical outcomes.
These findings provide valuable guidance for clinical ophthalmology. In modeling
anti-glaucoma drug transport, inaccurate representation of a reduced number of CCs
can result in an overestimation of drug concentration at the target site. Such inaccuracies
not only hinder the development of appropriate treatment plans but may also expose
patients to ineffective or unnecessary therapies.
Surgeons performing glaucoma-related procedures, such as trabeculectomy,
canaloplasty, or microstent implantation, should carefully evaluate the integrity of the
patient's CCs using imaging or preoperative assessment. Preserving or functionally
reconstructing a sufficient number of CCs during surgery may help maintain
physiological AH outflow and ensure accurate drug distribution.
In patients with congenitally fewer or surgically compromised CCs, clinicians
should consider adapting drug regimens accordingly. Strategies such as localized
sustained-release formulations or drug-loaded implants may help achieve therapeutic
31
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concentrations at the TM while minimizing systemic side effects and avoiding IOP
elevation. Personalized drug delivery planning based on CC status could therefore
enhance treatment precision and support long-term IOP control in glaucoma
management.
FIG. 27. Drug concentration on the inner surface of the TM under varying CC numbers.
V. CONCLUSION
In this study, a 3D human ocular drug transport model was developed that
incorporates both the TM and uveoscleral outflow pathways, which are often
underrepresented in previous models. The model comprehensively simulates heat
transfer from the cornea to the sclera, AH secretion and outflow, and the convectiondiffusion behavior of drugs within the AC. The accuracy of the model was validated
through comparison with experimental data.
The results indicate that the structure of the AH outflow pathways has a significant
impact on the transport of anti-glaucoma drugs, while exerting only a minor influence
on AH flow rate and heat transfer. Specifically, the peak drug concentration at the base
of the TM increased by 25.86% in intact AH pathway structures compared to models
excluding the TM. This highlights the importance of both conventional (TM, SC, and
CC) and uveoscleral pathways in drug delivery. The porous characteristics of the
outflow pathways significantly influence the drainage resistance of AH. A reduction in
porosity or a decrease in the number of outflow channels increases the overall flow
resistance, thereby prolonging the residence time of AH in the AC and promoting
localized drug accumulation at the TM.
Moreover, the porosity and number of outflow channels substantially affect AH
drainage resistance and drug accumulation. Reducing CCs from 30 to 10 increased drug
concentration at the TM by 12.8%, while decreasing TM porosity from 0.4 to 0.1
resulted in an 11.27% rise, suggesting prolonged AH retention and enhanced localized
delivery under high-resistance conditions. Neglecting the uveoscleral pathway led to a
32
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10.93% underestimation of drug levels at target sites, indicating that comprehensive
structural representation is essential for accurate drug transport prediction.
The research results of this study provide insights of reference value for clinical
ophthalmology, particularly in the surgical management of glaucoma. Based on the
simulation results, surgeons are advised to carefully consider the preservation or
reconstruction of both conventional and uveoscleral outflow pathways during filtration
surgery or drainage device implantation. Optimizing the number and spatial distribution
of outflow channels, as well as maintaining sufficient TM porosity, may significantly
enhance local drug retention and therapeutic efficacy. For example, surgical techniques
or implant designs that moderately reduce outflow channel density may facilitate drug
accumulation in specific regions without substantially increasing IOP. Moreover, for
patients with compromised outflow or altered TM characteristics, personalized drug
delivery strategies such as localized sustained-release implants should be considered to
overcome elevated outflow resistance and ensure effective drug concentrations at target
sites.
This study provides a comprehensive understanding of intraocular drug delivery
mechanisms and supports the integration of biofluid mechanics and coupled fluid,
thermal, and mass transport processes considerations into clinical decision-making,
advancing the development of more effective and individualized therapies for glaucoma
and other ocular diseases.
ACKNOWLEDGMENTS
This research was funded by the National Natural Science Foundation of China
(Grant Nos. 12102311, 22374107 and 32370098), and this research was supported by
Zhejiang Provincial Natural Science Foundation of China under Grant No.
ZCLTGS24E0601.
AUTHOR DECLARATIONS
Conflict of Interests
The authors have no conflicts to disclose.
Author Contributions
Sitian Peng: Writing–original draft (equal); Software; Visualization. Feng Zhang:
Conceptualization; Supervision; Methodology; Funding acquisition (equal). Liang Hu:
Resources; Funding acquisition (equal). Peng Dong: Writing–original draft (equal);
Validation. Tiancai Huang: Investigation (equal). Yu Wang: Investigation (equal).
Ting Fu: Formal analysis. Anle Ge: Data curation; Funding acquisition (equal).
DATA AVAILABILITY
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The data that support the findings of this study are available from the
corresponding author upon reasonable request.
34
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