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Heat and Mass Transfer Processes in the Eye

  • Arunn NarasimhanEmail author
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Abstract

Heat and mass transport processes in humans occur at cellular, tissue, organ, and whole-body levels. The subfield of heat and mass transfer in the human eye provides the context for understanding the functions of the eye and to develop protective, diagnostic, and therapeutic processes. The eye is sensitive to the environment because of the absence of blood flow through parts such as cornea and lens, and the absence of thermal sensors and protective reflexes beyond blinking. Heat transfer processes in the eye comprise the continuous evaporation of the tear layer coating the corneal region of a normal eye, the thermal massage across the pupils called the transpupillary thermotherapy (TTT), and the several methods of internal tissue ablation involving lasers. Drug delivery inside the eye is an important man-made mass transfer process that includes the intravitreous and transscleral routes to medicate the retina. This chapter focuses on the exposition of heat transfer processes that drive laser surgical methods and the mass transfer processes that govern drug delivery methods to the retina. In a bridging section, discussion on the combined heat and mass transfer processes involved in the TTT-based convection-assisted drug diffusion to the retina through the vitreous humor is also provided.

1 Introduction

Heat and mass transport processes in humans occur at cellular, tissue, organ, and whole-body levels. Nutrient and energy transport across cell membranes, diffusion of gases across organs, and metabolism and thermoregulation of the whole-body are some common natural heat and mass transport phenomena in the animal system. Drug intervention and thermo therapies are man-made processes that use the principles of mass and heat transfer in human body.

The subfield of heat and mass transfer in the human eye provides the context for understanding the functions of the eye and to develop protective, diagnostic, and therapeutic processes . The eye is sensitive to the environment because of the absence of blood flow through parts such as cornea and lens, and the absence of thermal sensors and protective reflexes beyond blinking. Heat transfer processes in the eye comprise the continuous evaporation of the tear layer coating the corneal region of a normal eye, the thermal massage across the pupils called the transpupillary thermo therapy (TTT), and the several methods of internal tissue ablation involving lasers.

Drug delivery inside the eye is an important man-made mass transfer process that includes the intravitreous and transscleral routes to medicate the retina. While other parts of the eye also require such drug delivery methods for treating cataract, tear duct infection, and so on, they are relatively straight-forward and hence well understood and documented in the past decades of medical research. This chapter focuses on the exposition of heat transfer processes that drive laser surgical methods and the mass transfer processes that govern drug delivery methods to the retina. In a bridging section, discussion on the combined heat and mass transfer processes involved in the TTT-based convection-assisted drug diffusion to the retina through the vitreous humor is also provided.

Experimental determination and observation of the heat and mass transport properties in a live eye are difficult, if not impractical, due to limitations of invasion and ethical constraints and hence modeling and analytical studies in bioheat and mass transfer have become important for developing safe and efficient procedures. Brief overviews of modeling studies in the area of heat and mass transfer in the eye are provided. Finally, these processes are inherently complex to warrant active research for understanding and improving the techniques that have been developed in the past two decades.

2 The Anatomy of the Human Eye

Eyes, the metaphoric windows to the soul, are one of the most complex sense organs of the body, composed of several subdomains with different material properties and complex geometries. The mammalian eye belongs to a general group of eyes called “camera-type eyes” that use a single lens to focus images on a receiving membrane, as against the “compound eyes” of many insects.

In a gross scale, the human eye is an opaque ball, about an inch in diameter. The cornea , a transparent membrane at the front of the eye, lubricated by a thin veil of tears, protects the eye and refracts light entering the eye. The aqueous humor , a clear watery fluid lies in the inner side of the cornea, circulates throughout the front of the eye and maintains constant pressure in the eye. Light that passes the cornea enters the eye through an opening called the pupil, the size of which varies with the quantum of light that enters, much like the aperture of a camera. The size of the pupil is manipulated by the stretching and contraction of the colored diaphragm called the iris. The iris is held by an opaque, fibrous, protective, outer layer containing collagen and elastic fiber, the sclera , commonly referred to as the “white of the eye.”

Light that passes through the pupil opening and traverses the aqueous humor impinges on a transparent crystalline lens. The lens focuses the light to the back of the eyeball, which it reaches through a viscous liquid called vitreous humor. The image is focused on the retina at the back of the eyeball. Photoreceptors called rods and cones on the retina detect the intensity and the frequency of the incoming light and send them as nerve impulses through the optic nerve to the brain to be perceived as “vision.”

The retinal region is provided with blood vessels to bring nutrients to the eye. The vascular layer of the eye is the choroid , which lies between the retina and the sclera. The finer details of the eye’s anatomy are shown in Fig. 1.
Fig. 1

The anatomy of the human eye

3 Thermal Transport in Eye and Heat-Based Treatment of Eye Maladies

The eye is perhaps the most sensitive part of the body with respect to heat flux because of the absence of a barrier (such as skin) to mediate the absorption of an external heat. During waking times, the eye lid covers the eye for 300 ms/s during blinking but for the rest of the time, the eye is exposed to outside heat fluxes. The outer surface structures of the eye must be able to cope with imposed thermal stresses of the environment because of the absence of cooling blood flow in parts other than the retina of the eye, and also because the eye has no thermal sensors and protective reflexes.

The human tear is believed to be at body temperature. Tears serve two purposes: to cool the eye by evaporation and to warm the eye by secretion and spread across the ocular surface; both processes must be at an optimal equilibrium for normal functioning of the eye. In the absence of the 100 nm lipid layer that covers the 3-μm thick human tear film and constant secretion from the tear gland, tears will evaporate at the rate of water, and the film will completely disappear during a single blink. This is an elegant example of natural conjugate heat and mass transfer in the eye.

Even small temperature variations in the range of 3–5 °C can cause physiological effects in the eye. For example, the enzyme systems within the endothelial cells that control the corneal thickness of the cornea are temperature dependent. Increase of temperature at the lens has been known to cause cataracts. The transmission of heat to the inside of the eye can affect blood flow. Temperature changes can affect different tissues of the eye in different ways: cells could die, proteins could be denatured, and metabolism could be altered, all of which could result in pathological changes in the eye.

Apart from natural and environmental thermal stresses, many therapeutic procedures for eye diseases use heat. Laser-based treatments developed in the 1960s have now become standard therapeutic procedures for various eye maladies. Laser eye therapies range from continuous wave photocoagulation to more recent techniques such as selective retinal pigment epithelium (RPE) treatment (SRT), photodynamic therapy (PDT) , and transpupillary thermotherapy (TTT).

The extensive application of laser therapy to the eye hinges on the fact that the eye media such as the cornea, aqueous and vitreous humors, and the lens are all transparent to visible light, enabling visible inspection of its internal structures for both diagnosis and treatment. Furthermore, the presence of pigments such as melanin in many parts of the eye allows absorption of laser energy.

Some widely used laser surgeries of the eye are given in Table 1. Laser-based eye treatment may be broadly categorized into four types – corneal, lens, humor, and retinal, depending upon the target subdomain of the eye.
Table 1

Common laser treatment methods used for eye diseases

Laser treatment for human eye

Disease treated

Target tissue

Type of laser used

Type of tissue interaction

LASIK

(laser assisted in situ keratomileusis)

Vision correction

Cornea

Excimer laser

0.1 MW (1 mJ applied for 10–20 ns)

Vaporization of corneal material, lens shape correction

Laser capsulotomy

Cataract

Lens

Nd-YAG laser

Ablation of lens capsule

Laser vitreolysis

Vitreous hemorrhage

Vitreous humor

Nd-YAG laser

Vaporization of floaters

Laser retinal surgery

Macular degeneration

Diabetic retinopathy

Retinal tear

Retinal detachment

Retina (also affects sclera and choroid)

Nd-YAG laser

0.2–0.5 W (applied for 100–200 ms)

Photocoagulation (heating up to 60 °C)

Transpupillary thermo therapy (TTT)

Intraocular tumors including retinoblastoma and choroidal melanoma

Posterior segment of the eye

Long pulse IR diode laser

Retinal thermal “massage,” controlled “burn”

3.1 Corneal Laser Treatment

The most commonly used laser eye treatment is laser vision correction, in which, laser is used to change the shape of the cornea, in a process called corneal sculpting. A “cool” excimer laser is used for corneal correction; this form of laser does not burn tissue but vaporizes a small section of the cornea. The alteration of the cornea can correct focusing errors and resulting refractive maladies such as short sight, long sight, astigmatism, and presbyopia. To correct nearsightedness (myopia), the curvature of the cornea is reduced; for farsightedness (hypermetropia), the corneal curvature is sharpened; and astigmatism requires the correction of nonuniformities of the corneal surface. Presbyopia is corrected using a monovision laser where the distance vision of one eye is corrected, while the other is intentionally left myopic.

There are three types of corneal laser treatment – photorefractive keratectomy (PRK), laser epithelial keratomileusis (LASEK), and laser in situ keratomileusis (LASIK) . In PRK, the entire outer ephithelial layer of the cornea is removed to expose the cornea to laser. In LASEK, the outer epithelial layer is not removed, but lifted after loosening with alcohol and then put back in place after laser treatment of cornea. In LASIK, a flap of the corneal surface is cut using a microkeratome (a surgical instrument with an oscillating blade). After laser treatment, the flap is folded down to original position and held by natural suction.

3.2 Lens Laser Treatment: Cataract Surgery

Cataract is a common age-related eye disease that involves loss of transparency of the eye’s natural lens. Cataracts are the principal cause of blindness in the world. Femtosecond lasers are used in surgeries to remove the clouded cataract; laser is used in three steps of the cataract surgery:
  • The corneal incision: Laser is used to create a corneal incision with a specific location, depth, and length in all planes. The use of laser rather than surgical instruments for incision prevents surgeon error and variability.

  • The anterior capsulotomy: The natural lens of the eye is surrounded by a very thin, clear capsule, which must be removed to access to the cataract. In laser cataract surgery, anterior capsulotomy is performed using laser.

  • Lens and cataract fragmentation: The final stage of cataract surgery is the softening or phacoemulsification of the cataract to enable removal of the diseased lens. Laser is used to soften the cataract with small chance of burning and distortion of the incision.

3.3 Laser Treatment of the Vitreous Humor: Laser Vitreolysis

Vitreous hemorrhage can occur when blood leaks into the vitreous humor or undissolved vitreous gel particles float in the liquefied humor. Laser vitreolysis, where a laser beam is used to break the “floaters,” is gaining importance in recent years, as an alternative to the more serious vitrectomy, where the entire vitreous humor is drained and replaced by silicone oil or gas bubble.

3.4 Retinal Laser Treatment

The application of laser to the retina is probably the most advanced and complicated form of treatment because the retina is the only part of the eye that has extensive vasculature – blood vessels and blood flow. The first study of laser interaction with retinal tissue dates back to 1954 (Meyer-Schwickerath 1954), which was followed by the first xenon-arc photocoagulator in 1956 (Meyer-Schwickerath 1956). Since then, significant improvements have been made in retinal laser treatment procedures that have been applied extensively in a range of diseases of the eye. A detailed discussion of retinal laser treatment is given in Sect. 6.

3.5 Transpupillary Thermal Therapy

Transpupillary thermal therapy (TTT) is used to cure intraocular tumors and choroidal neovascularization in age-related macular degeneration. Long pulse IR diode lasers of low retinal irradiance and large spot diameter are used for a period of less than 60 s to photocoagulate diseased ocular tissues. During TTT, near infrared wavelength is absorbed by melanin present in the RPE cells and in the melanocytes found in the choroid . The fovea (the region of closely packed cones in the retina) flattens and thus improves vision. While traditional retinal laser treatments use exposures longer than a minute and high power lasers, the much shorter duration and lower irradiances used in TTT are focused not at outright tissue burning but at controlled gradual maximal temperature raise of the tissue up to 10 °C.

Apart from direct photocoagulation , TTT can also induce natural convection in the two fluids of the eye – the aqueous and vitreous humors. Aqueous humor is a dilute liquid and flows even under normal conditions. The flow of aqueous humor is driven by buoyancy caused by the temperature gradient between the front and back of the anterior chamber. Temperature differences as low as 0.2 °C could initiate flow of aqueous humor and can thus cause temperature distribution in the eye (Kumar et al. 2005; Ooi and Ng 2008).

The vitreous humor , although viscous and stagnant under normal conditions, may be diluted as a result of age or other eye treatments such as vitrectomy and can undergo convection by temperature increases of 7 °C during TTT. Steady state and transient natural convection flow in diluted vitreous humor during TTT have been studied using numerical simulations. The peak temperature in retina has been found to drop by 15 °C and 12.5 °C during TTT, due to natural convection flow in the vitreous humor under steady and transient states, respectively. Convection in vitreous humor enhances heat transfer in the regions adjacent to the laser spot. The cooling effect of choroidal blood perfusion in addition to the convection-based heat dissipation has also been studied using the bioheat transfer model along with the conventional energy and Navier–Stokes equation . Blood perfusion has been found to further reduce the peak retinal temperature by 6 °C and 1.5 °C in steady state and transient cases, respectively (Narasimhan and Sundarraj 2013).

TTT induced convection can be used as such for “thermal massaging” or may be combined with drug delivery as will be explained in Sect. 10.

4 Types of Lasers Used in Eye Therapies

Two types of lasers are commonly used for eye therapies.
  1. (a)

    Excimer laser: Excimer lasers are commonly used for corneal refractive surgery. They use a combination of a noble gas (argon, krypton, or xenon) and halogens (fluorine or chlorine) to produce light in the ultraviolet range. The excimer laser is a “cool” laser whose wavelength depends on the type of molecules used. Excimer lasers are absorbed well by biological tissues and organic compounds and the energy levels cause disruption of molecular bonds on the tissue, rather than burning or cutting the tissue itself. Thus, they are commonly used in therapies that are aimed at removing exceptionally fine layers of surface material without heating of surrounding tissues. Argon laser, with a wavelength of 126 nm, is commonly used for eye surgery.

     
  2. (b)

    Femtosecond (FS) laser: Femtosecond lasers are infrared lasers with a wavelength around 1053 nm. These are produced by Nd: YAG and cause photodisruption or photoionization of optically transparent tissue such as the cornea. Femtosecond lasers rapidly generate an expanding cloud of free electrons and ionized molecules. The acoustic shock wave so generated results in disruption of the treated tissue.

     

Recently, there have been studies on the use of near IR lasers for treatments such as TTT.

5 Laser-Eye Interaction

Laser-tissue interactions are caused by a variety of chemical, physical, and biological mechanisms and depend on a variety of factors including laser wavelength, irradiation duration, and material and optical properties of the various parts of the eye subjected to treatment. The light absorbing chromophores present in ocular tissues include water (absorption of infrared wavelengths), proteins (absorption of deep UV), melanin, blood, and macular pigments (absorption of visible wavelengths). Photochemical reactions such as photo-transduction in photoreceptors initiated by the light-induced isomerization of 11-cis retinal to all-trans retinal are typically not associated with a meaningful change in tissue temperature and are beyond the scope of this discussion.

The extent of thermal interaction between the tissue and laser can be quantified by the decline in concentration of a critical molecular component for cellular metabolism as a function of temperature and duration of exposure. The response of the tissue to laser depends upon the power of laser and duration of irradiation.
  1. (a)

    Denaturation of protein : At the chemical level, molecular rearrangements such as protein folding and unfolding commence at temperatures around 40 °C within a time span of milliseconds to seconds and go to completion by 60 °C. Laser irradiation that raises the eye tissue temperature to these levels from the baseline body temperature of ~37 °C can trigger denaturation of proteins. The denatured proteins could become chemically active at this or higher temperatures and react with other molecules in the cell to produce cascading side reactions (Gerstman and Glickman 1999).

     
  2. (b)

    Chemical reactions: Free radicals and active oxygen species formed during laser exposure can also cause photochemical transformations in photoreceptors (Lafond et al. 2003), retinal pigment epithelial (RPE) cells (Szabó et al. 2004), melanin granules (Thompson et al. 1996), etc. It has been experimentally proven that melanin from retinal pigment epithelial (RPE) cells form free radicals during illumination as identified by their rapid oxidation of ascorbic acid added as a marker (Glickman et al. 1993). These active oxygen species and free radicals, if not scavenged immediately, can promote inflammation in tissues, which in turn can trigger cell proliferation in fibroblasts and retinal pigment epithelial cells, leading to neovascularization in the eye (Macular Photocoagulation Study Group 1986). Laser pulses with durations ranging from 10 to 200 ms cause retinal photocoagulation, due to the increase of retinal tissue temperature by tens of degrees centigrade above body temperature. About 5% of laser of 532 nm wavelength incident on the retina is absorbed by neural retina, about half is absorbed in the RPE, and the rest in the choroid (Sramek et al. 2009).

     
  3. (c)

    Microbubble formation : Exposure to lasers at shorter timescales of micro- to nanoseconds could also cause RPE damage due to intracellular microbubble formation inside the RPE cells (Roegener et al. 2004). The expansion and collapse of the microbubbles generate local plasma that can disintegrate the RPE cells or break the cell membrane. Plasma-mediated laser-tissue interactions are used in the fragmentation of the secondary cataract with nanosecond Nd:YAG lasers. Femtosecond laser pulses of much lower energies (~μJ) are used for intrastromal cutting and slicing of the corneal flap for refractive surgery.

     
  4. (d)

    Photo vaporization and mechanical damage: Nonlinear physicochemical damage processes such as shock waves can be caused at subnanosecond exposures to laser. Photo vaporization of tissue can be caused by rapid temperature rise. Cellular mechanical damage can also occur during rapid pulsing of lasers at picosecond to nanosecond timescales due to poor heat dissipation. These nonlinear processes are difficult to predict but can cause severe damage to the eye such as retinal perforation, disruption of choroidal blood vessels with subretinal hemorrhage, and, in severe cases, vitreous hemorrhage (Goldman et al. 1975).

     

The photo-thermal interactions between laser and the eye tissue are used to design therapeutic procedures for eye diseases such as retinopathy and macular degeneration. The effects of laser photocoagulation therapy depend on the targeted disease. Pan retinal photocoagulation (PRP), for example, is a process wherein a laser beam is collimated on target spots on the retina to cause controlled burn or photocoagulation at that spot. Photocoagulation causes scar production, which is useful to treat/prevent retinal detachment . The denaturation of the photoreceptor cells in the outer periphery of the retina is postulated to reduce the overall oxygen demand, and thus neovascularization in diabetes is reduced (Wolbarsht and Landers 1980).

Lasers used for retinal photocoagulation typically have a power of 50–500 mW, which are applied for an irradiation time of 20–200 ms onto one or more spots with diameters ranging between 50 and 500 μm (Brinkmann et al. 2012). Intensely collimated laser beams can result in a retinal irradiance (energy per time unit per unit area) higher than 300 W/cm2 at the target spot, even when low power lasers are used, resulting in rise of spot temperatures to well over 60 °C. Heat diffusion to adjacent retinal spots can cause collateral thermal damage to undiseased sections of the retina. The heat can diffuse into the retina as well and cause coagulation of the photoreceptors. Heat can diffuse up to 200 μm during a 100 ms application of laser and extend the zone of coagulation beyond the targeted spot, a phenomenon called thermal blooming. Lesions are often visible as whitish/grayish lesions under white light visual ophthalmoscopic examination after laser treatment because of increased light scattering after the onset of denaturation. The ratio of the threshold power required to treat the diseased section to that required for producing a mild lesion is called the therapeutic window and is a means of quantifying the relative safety of the retinal photocoagulation procedure.

Local transfer of heat to surrounding healthy tissues during retinal photocoagulation may cause rupture of the Bruch’s membrane (the innermost layer of the choroid) and may cause choroidal hemorrhage or damage to the nerve fiber layer. In extreme cases, overheating of the eye beyond the accepted photocoagulation temperatures of 60 °C, exacerbated by the absence of cooling blood flow through most of the eye, could result in damage to the retina.

Apart from the retina, there have been reports to damage caused by laser to nonvascular components such as the lens and cornea (Wang et al. 2015). Laser treatment of the macular region, in particular, must consider the absorptive properties of the region. The macular retinal layers contain xanthophyll pigment that absorbs strongly between 450 and 500 nm and thus use of lasers in this wavelengths could cause excessive heating and destruction of tissues.

The cornea has a high optical absorption coefficient at 193 nm, and this particular wavelength can break the carbon-carbon bonds interlinking the protein molecules of the cornea. Thus discrete volume of corneal tissue can be removed (“corneal sculpting”) with each pulse of the laser.

In the use of lasers for blood vessel closure, the photon penetration depth for a laser wavelength should be about the same length as the vessel’s diameter so that there is effective bulk heating of the blood column without perforation of the wall of the vessel. Such treatments are usually carried out using lasers of wavelength maximally absorbed by hemoglobin.

6 Laser Treatments in the Retinal Region

While the use of laser for treating nonvascular parts of the eye, such as cornea and lens, are well established, the use of lasers for retinal diseases is more complicated because of the presence of nerves and blood vessels in the area. Lasers are routinely used to treat the following diseases of the retina.

6.1 Diabetic Retinopathy

The retina is the only part of the eye that has a rich supply of blood vessels. Diabetes is often associated with damage to the retinal vasculature that can cause leakage of blood and hemorrhage. In its advanced stage called proliferative diabetic retinopathy (PDR), abnormal blood vessels are created on the surface of the retina, which leads to scarring and eventual loss of vision. Laser surgery is used in diabetic retinopathy in the initial stages to seal the leaks, thereby preventing further vision loss. Laser treatment can also prevent severe vision loss by destroying the new vessels formed. Transpupillary thermotherapy (TTT) is a promising treatment option for choroidal neovascularization.

6.2 Retinal Vein Occlusions

The blood vessels that drain blood from the retina can become blocked, as a result of the natural aging process or due to ailments such as diabetes and hypertension. This blockage can cause the retina to swell with fluid and blood, which can blur vision. As with diabetic retinopathy, new blood vessels may grow and there may be increased eye pressure, resulting in pain and loss of vision. Laser treatment can help reduce swelling and help destroy abnormal blood vessels.

6.3 Age-Related Macular Degeneration

The macula is the region of the retina responsible for central vision. Age-related degeneration of the macular cells causes distortion of central vision. In advances stages, there may be complete loss of central vision and people with very advanced macular degeneration are considered legally blind. Such people retain their peripheral vision, which is not as clear as central vision. When the macular degeneration is associated with blood leakage into the macula, or formation of new blood vessels (neovascularization), it is called wet macular degeneration. Laser photocoagulation is often used for treating wet macular degeneration. The procedure uses laser light to destroy or seal off new blood vessels to prevent leakage.

Recent studies have shown that early stages of age-related macular degeneration is associated with the presence of small fatty deposits called drusen and a thickening of the Bruch’s membrane on the macula. Nanosecond lasers can reduce drusen and thin the Bruch’s membrane without damaging the structure of the retina (Jobling et al. 2015).

6.4 Ocular Histoplasmosis

Histoplasmosis is caused when airborne spores of the fungus Histoplasma capsulatum are inhaled into the lungs. While the lung is the primary target of the fungus, even mild cases of histoplasmosis can later cause a serious eye disease called ocular histoplasmosis syndrome (OHS), which can lead to loss of vision. The spores are believed to cause the development of abnormal blood vessels underneath the retina, which result in scarring and vision loss. The only proven treatment of OHS is laser photocoagulation.

6.5 Retinal Breaks and Detachment

The retina covers the back of the eye like wallpaper. Retinal tears or holes can occur from congenital retinal thinning, as part of aging, or following cataract surgery or eye injury. In such cases, the patient often sees cobweb-like floaters or light flashes when a retinal break develops. Liquid that normally fills the central portion of the eye (the vitreous) can leak beneath the break, lifting the retina away from the eyewall. This is called a retinal detachment. Retinal detachment results in blindness if left untreated. Laser surgery around retinal tears is often able to weld the retina to the underlying eyewall. This can prevent or limit retinal detachment .

6.6 Central Serous Chorioretinopathy

The buildup of fluid under the retina, caused by defective retinal pigment epithelium cells, and consequent distortion of vision is called central serous chorioretinopathy. Laser treatment or photodynamic therapy is used to break the buildup of fluid and restore vision.

6.7 Ocular Tumors

Tumors of the retina are rare and usually benign. Treatment options for such tumors include photocoagulation , cryotherapy, or brachytherapy.

7 Computer Modeling in Laser Retinal Therapies

Developments in safe laser therapies for eye diseases hinge on accurate knowledge of the photothermal effects of laser-induced heating in the various parts of the eye. While there have been experimental studies on animal models to establish laser threshold values (e.g., Kohtiao et al. 1966; Cain et al. 1995), experiments on live human eye (such as Blankenstein et al. 1986) are difficult to conduct and ethically constrained. Noninvasive techniques using bolometer (Mapstone 1968) and IR imaging techniques (Efron et al. 1989) have been used to measure the temperature in the eye, but experimental studies of damage to eye are not possible because of obvious reasons.

Computational methods are increasingly being used to model biological systems; a popular and useful area is the modeling of bioheat transfer in human eye. Computer simulations have been made of the retinal laser surgery (for humans) with various levels of complexity (steady, transient), computational domains (two- and three-dimensional faithful eye geometries), thermophysical properties (constant, sensitive temperature dependency, effective combination of properties, etc.), and modeling equations (various forms of the Pennes-bioheat transfer equation plus the flow equations, along with specific radiation and evaporation models). The conditions of irradiation have been simulated, faithful to the actual surgery, as three-dimensional multi-spot arrays of square and circular distribution, scanned through sequential (in time) and simultaneous (heating of all spots for a while) heating. Indeed, a number of models have been developed in the past decades to describe thermal damage induced by exposure to laser pulses at different parts of the eye. Such models have solved heat transport equations to give the spatiotemporal intraocular temperature distribution together with an assessment of the tissue injury caused by over-heating.

7.1 Heat and Bioheat Transfer Equations for the Eye

Laser induced thermal effects in the eye depend on the rate of heat generation and transfer. In all numerical modeling studies, a suitable energy equation in the eye domain is solved with appropriate boundary conditions, in order to understand the temperature distribution resulting from laser irradiation. The conventional Fourier heat equation can be used as the governing energy equation only if the eye is considered as containing only solid or stagnant fluid. The eye, however, is associated with choroidal blood flow , the effect of which cannot be properly captured by the conventional heat equation, as shown by Pennes (1948). The Pennes heat transfer equation that takes into account blood perfusion can be written as:
$$ \rho {c}_t\frac{\partial {T}_t}{\partial t}=\lambda \left(\frac{\partial^2{T}_t}{\partial {x}^2}+\frac{\partial^2{T}_t}{\partial {y}^2}+\frac{\partial^2{T}_t}{\partial {z}^2}\right)+{Q}^{{\prime\prime\prime} }+{\dot{m}}_b{c}_b\left({T}_b-{T}_t\right) $$
(1)

Here λ is the thermal conductivity of the region at which heat transfer occurs, and c and ρ are the corresponding regional material specific heat capacity and density. The last term of the equation (\( {\dot{m}}_b{c}_b\left({T}_b-{T}_t\right) \)) is the blood perfusion in tissues, where \( {\dot{m}}_b \) is the local blood flow rate in kg/s, T b is the blood temperature, and T t is the tissue temperature. The second last term Q accounts for metabolic heat generation and also the laser irradiation, when the incident radiation in an eye-region (like retina) is accounted as volumetric heat generation (in W/m3).

The retinal and scleral regions of the eye are very small (≤1 mm), compared to the cross sections of the eye (24 mm). The thickness of the retinal pigmented epithelium (RPE) is about 10 μm. Since this is where most of the laser irradiation is absorbed, RPE is often treated as a lumped system. Such treatment does not affect overall temperature distribution in the other sections of the eye during simulations for interpreting the results. The properties of the RPE region, especially its radiation absorption coefficients, are available primarily from Boettner and Wolter (1962) and Chew et al. (2000). The thermophysical properties and laser irradiation absorption coefficients are used to convert the total incident energy into volumetric heat generation rate (Q , in the above equation) for each region of the eye, including the retina.

The metabolic heat generation rate in eye tissue is in the order of 103 Wm−3, while the volumetric heat generation rate in the RPE resulting from a typically applied laser power of 200 mW is in the order of 1010 Wm−3. Thus, metabolic heat generation rate can be safely ignored. Choroidal blood mass flow rate must be measured because the blood perfusion term represents choroidal blood flow that cools the eye from the rear and is calculated as:
$$ {\dot{m}}_b=\omega \times {V}_c $$
(2)
where ω is the blood perfusion rate and V c is the volume of the choroid in the interior of the eyeball. The value of ω can be obtained from sources such as Flyckt et al. (2006).
The rear of the interior layer of the sclera , toward the body, is often considered to be at the core body temperature of 37 °C. Different boundary conditions are used during modeling depending upon the extent of the eye domain used. For example, a modified convection-radiation boundary condition is employed when the cross section of the entire eye is used. If the computational domain ends well within the vitreous, an adiabatic boundary condition (Eq. 3) is applied at the truncated vitreous plane.
$$ \lambda \frac{\partial {T}_t}{\partial n}=0 $$
(3)
Blood perfusion through the choroid can also be modeled using a convection type boundary condition imposed on the sclera, as follows:
$$ \lambda \frac{\partial {T}_t}{\partial \eta}={h}_s\left({T}_t-{T}_{\mathrm{body}}\right) $$
(4)
where h s is the scleral convection heat transfer coefficient that accounts for the convective cooling of the choroidal blood flow. Typical values of h s in literature range between 26 and 300 W/m2 K, the lower limit representing no blood flow and the higher value corresponding to maximum possible choroidal blood flow.

With such simplification of blood perfusion effect, the Pennes bioheat equation becomes superfluous and the conventional Fourier heat equation (Eq. 1 minus the last term) becomes capable of predicting the temperature distribution and evolution in the eye domain.

7.2 Geometry and Properties of the Eye

Numerical modeling of the eye for laser therapy simulations involves solving discretized governing equations over control volumes in the chosen computational domain. The computational domain can be local – pertaining to a single component of the eye like retina – or the entire volume in three dimensions.

For modeling, the following parameters are considered. The diameter of the eye, along the pupillary axis is about 24 mm, while the vertical diameter is about 23 mm. The posterior half of the human eyeball is almost spherical and each eye-region is usually assumed to be homogeneous. The eye is assumed to be symmetrical about the pupillary axis.

The thickness of sclera varies from 0.6 mm at the limbus (the border of the cornea and the sclera) to 0.5 mm at the equator. It is considered to be 1 mm at the exit of optic nerve. The retina varies in thickness from 0.5 to 0.1 mm, being thick around the optical disk and thinner at the equator. Of the ten layers of the retina, the inner nine layers are grouped as neural retina and the outermost layer, about 6–15 μm thick, comprises pigmented epithelium also known as RPE. The various thermal properties of the tissues of the human eye are given in Narasimhan and Jha (2012).

RPE cells are the “nurse cells” for the retina because they absorb and deliver nutrients to the neurosensory retina and transport metabolic end products and waste to the choroid . The pigment melanin, found in RPE, protects the photoreceptors from short-wavelength light damage and shields scattered light from the sclera.

The cooling mechanisms for the eye include convection, radiation, and evaporation at the corneal surface of the eyeball. The choroidal blood flow at the back of the eye cools the rest of the eye. It is assumed that RPE absorb all the energy at the wavelength of argon laser.

Argon laser with power Q = 0.2 W irradiating a spot size of 500 μm is typically used in retinal surgery, and the properties of such a laser are used in numerical simulations. The power range and spot size are variables that are patient and/or disease dependent. The percentage heat generation at different regions of the laser path in the eye varies and this is taken into consideration during modeling.

7.3 Typical 3-D Modeling of Laser Retinal Surgery

Simulation of laser eye surgery involves development of two- and three-dimensional models of the process that closely mimics the actual surgical procedure. During laser surgery of the human eye, a large number (1500–1600) of spots at the posterior section of the eye are irradiated. Computer models of human eye are created in the Cartesian coordinate system with the use of appropriate modeling software such as Gambit® 2.4.6. Quadrilateral finite volume (surface) elements are used to mesh the two-dimensional eye domain. Three-dimensional models are constructed using the results of temperature evolution in the two-dimensional model.

In one such study, two- and three-dimensional models were developed and the discretized equations were solved by the finite volume method (Narasimhan and Jha 2012). Closely mimicking an actual surgery, a 3 × 3 square array formed by nine laser spots, each heated sequentially with 0.2 W power, was modeled and the temperature evolution for 100 ms laser irradiation followed by 100 ms cool down period was studied for several spot distribution and laser power conditions. It was found that at photocoagulation temperature of 60 °C, RPE was subjected to excessive heating and was thus damaged. The RPE temperature must therefore quickly reduce to well below the coagulation temperature within the time span of 200 ms.

When two consecutive spots were placed close together (D ≤ 0.375 mm) surrounding, unheated RPE regions are also heated to 60 °C due to the irradiation of the neighboring spot (Fig. 2). When the interspot distance D ≥ 0.6 mm, the transient heat diffusion from the RPE to the adjacent scleral, choroidal, and vitreous humor regions was sufficient to reduce RPE close to core body temperature of 37 °C during the sequential irradiation process.
Fig. 2

Isotherms for sequential heating of spot 5; square array of 3 × 3 spots; D = (a) 0.75 mm (b) 0.625 mm (c) 0.50 mm (d) 0.375 mm (e) 0.25 mm

Multispot retinal laser surgery has also been analyzed using a truncated three-dimensional model of the human eye. A square array of nine spots and circular array of seven spots were modeled. The two arrays responded differently to the laser irradiation in terms of temperature evolution because of the way in which the spots were arranged. In the square array, the outermost spot was heated first, and the heating proceeded along the rows, whereas in the circular array, the heating was started at the central spot. In the circular array, the interspot distance was uniformly D while in the square array, the effective center-to-center distance between the corner spots (spots 1, 3, 7 and 9) and central spot was √2 D. As irradiation of other spots proceeds, the central spot in the circular array is at a higher temperature than its counterpart in the square array since spots on all sides of the central spot in the former are heated sequentially and there is diffusion of heat from the peripheral spots to the central spot. It is surmised that the spots with least diffusion space should be irradiated in the initial part of irradiation sequence. However, this keeps these spots at elevated temperatures for extended periods of time.

The effect of laser energy attenuation in the choroid due to it pigmentation has also been investigated. The thickness and location of pigmented layer of choroid have significant effect on peak temperature evolution and resulting diffusion in the retinal region. Increase in thickness or moving the location of pigmented layer of choroid away from the RPE results in decrease of peak temperature of the retinal region. Choroidal pigmentation also has a significant effect on retinal temperature distribution, irrespective of blood perfusion.

Simulation results show that for laser-based eye treatment, a temperature of 60 °C is sufficient to coagulate the diseased tissue. Temperatures exceeding this could damage healthy surrounding tissue by diffusion of heat. Even the current settings employed in retinal surgery can cause peak temperature at RPE to reach 103 °C that could lead to permanent long-term damage.

One feasible way to prevent overheating is to pulsate the irradiation to reduce the peak temperature of the domain. Indeed, numerical simulations have shown that such pulsation can prevent overheating (Narasimhan et al. 2010) (Fig. 3).
Fig. 3

Temperature evolution using pulsating laser

Another solution is to carefully control the sequence of irradiation of spots. The spot with least diffusion space should be irradiated first. Otherwise, it will be at elevated temperature for extended periods of time due to temperature gradient adverse to cooling. Yet another route to reducing peak temperature is to reduce laser power. Simulation studies show that the peak temperatures of spots of both square and circular array reach 60 °C at power settings as low as 0.072 W. Using laser of such low power can minimize collateral thermal damage of healthy neighboring ocular tissues.

Studies on numerical modeling of retinal laser surgery have successfully captured the geometry of human eye at the continuum level using available computational tools. Both finite element (FEM) and finite volume method (FVM) based models invoke continuum physics and are valid irrespective of whether bioheat equation is invoked or not. Understanding the thermal aspects of laser surgery in local regions at a micro-scale resolution requires modeling involving molecular level simulations, lattice Boltzmann method (LBM) based approach, etc. Likewise, as the blood perfusion effect in the Pennes bioheat equation deals with blood perfusion at the macroscopic level. Microscale detailing of local eye regions would also require development of more sophisticated bioheat transfer models to be adopted in the simulations.

The numerical analysis and solutions proposed to limit thermal damage during surgery require corresponding experimental verification to make a direct impact in the medical practitioner’s surgical process. An interdisciplinary team of practicing medical doctors, computational engineers, and experimental biologists can contribute in this direction.

8 Ocular Cryotherapy

Ocular cryotherapy is the application of cold temperatures to treat disorders of the lids and eyes. Cryotherapy has been known in ophthalmology since the mid-1960s and has been largely used as a surface technique, with the probe being applied to the lids or eye without any incision into the tissue. Because of the absence of an incision, it is considered to be a less invasive type of procedure than incisional surgery. Liquid nitrogen cryotherapy techniques used for surface eye disease are summarized in Fraunfelder (2008).

There is now an increasing trend to use cryotherapy to treat retinal disorders such as retinal tear or detachment. It is used when retinopathy occurs in the far periphery of the retina, out of reach of laser. It is also considered for treating retina when vitreous hemorrhage or dense cataract prevents the travel of laser to the retina.

In retinal cryotherapy, a very cold metal probe is placed against the wall of the eye so that all of the eye’s layers, including the retina, are frozen. Opthalmological cryotherapy primarily uses freon (−29.8 °C to −40.8 °C), nitrous oxide (−88.5 °C), or solid carbon dioxide (−79 °C); the method of cryotherapy and types of cryogens used in the treatment of eye disease are not standardized (Fraunfelder 2008). Application of a cryoprobe to the sclera for 5 s was shown to create a white area in the underlying retina, and this cryotherapy could seal retinal tears and holes. The freezing temperatures create a scar that adheres the retina to the wall of the eye, akin to laser treatment. In layman terms, it is often said that cryotherapy is like glue while laser is like a stapler to attach a torn or detached retina to the eye wall.

In rare cases, cryotherapy is also used to freeze and destroy tumors or to destroy peripheral retina. Such treatments are usually performed for small retinoblastomas, hemangiomas, and angiomas.

9 Mass Transfer in the Eye

There are three main types of natural mass transfer processes associated with the eye:
  1. (i)

    T ear dynamics (Fig. 4): The tear film, a 3-μm thin layer of fluid, serves to nourish, protect, and enhance the differentiation of surface epithelial cells of the eye. The lacrimal glands situated in the upper-outer portion of each eye orbit secrete lacrimal fluid, or “tear,” which flows through ducts into the space between the eyeball and lids. The fluid spreads across the surface of the eye as a film when the eyes blink, by pumping action. Surface tension smoothens the tear film, thus giving it an even optical surface. The tear gathers in the lacrimal lake, is drawn into the puncta (minute openings found in the margins of the eyelids) by capillary action, and then flows through the inner corner of the eyelids entering the lacrimal sac. From there, the tears are drained into the nasolacrimal duct. The human nasolacrimal ducts comprise upper and lower lacrimal canaliculi, the lacrimal sac, and the nasolacrimal duct. The tears are finally drained into the nasal cavity. Thus, tears undergo four fluid flow processes: production by the lacrimal gland, film formation by blinking, evaporation from the anterior surface, and final drainage through the nasolacrimal duct. The rate of human tear flow is difficult to measure because irritation to the eye and psychological stimuli during measurement itself can cause rapid fluctuations in the flow .

     
  2. (ii)

    A queous humor: The production of aqueous humor by the ciliary processes, its flow through the pupil, and its circulation in the anterior chamber before draining from the eye are typical fluid flow processes found naturally in the eye. Additionally, the flow of the aqueous humor can also be driven thermally by the temperature gradient that exists between the posterior surface, which is closer to body temperature and the anterior chamber (Fig. 1 earlier), which is closer to atmospheric temperature. The buoyancy-driven anterior chamber flow has been experimentally proven by the application of hot and cold packs to the closed lids of the human eye (Wyatt 1996). Such convection induced mass transfer is believed to increase the efficacy of nutrient delivery and is also associated with diseases when the aqueous humor contains particulate material such as blood cells or pigment particles.

    Other physical mechanisms that can cause flow/transfer of aqueous humor include interaction between buoyancy and gravity while sleeping in a face-up position, flow generated by phakodenesis (lens tremor), and that generated by rapid eye movement (REM) during sleep. Apart from circulating nutrients and waste products to and from the eye, the flow of the humor serves to generate a positive pressure to stabilize the otherwise flabby eye, thus enabling accurate positioning of the functional elements of the eye such as the lens. Abnormalities in drainage of this fluid lead to imbalanced ocular pressure, eventually causing diseases such as glaucoma. In almost all cases of glaucoma, pressure increase is caused by an increase in hydrodynamic resistance to the drainage of aqueous humor .

     
  3. (iii)

    V itreous humor : The vitreous chamber of the eye is filled by a clear gel-like material called the vitreous humor. In young people, the vitreous humor is gel-like and there is not much bulk fluid flow under normal circumstances; the movement of the eye and head causes the gel to merely shake but not move substantially. However, under a few eye diseases and conditions (for example, retinal detachment) the gel is removed (vitrectomy) and replaced by a more dilute fluid of the type found in the anterior chamber. The vitreous humor also naturally liquefies with age, and in such cases, it becomes mobile. A difference in temperature between the front and back of the posterior segment of the eye could set up convection-driven mass transport in the liquefied vitreous humor. This is important for drug delivery applications, as will be discussed in later sections .

     
  4. (iv)

    C horoidal blood flow: The retina of the eye houses a complex network of blood vessels associated with various types of blood flows. The high metabolic rate in the retina requires a substantial circulation of blood. Collapse of the ocular blood vessels, driven by intraocular pressure changes, could cause them to behave like a Starling resistor. Lipid buildup between the RPE and the retinal blood vessels in age-related macular degeneration can hinder nutrient transport to photoreceptors leading to vision loss .

     
Fig. 4

Physiology of tear production

10 Conjugate Heat and Mass Transfer in Drug Delivery

The application of heat (laser treatment) and drug delivery are currently disjoint therapeutic procedures. Recent studies have shown that they may be combined for ensuring better bioavailability of the drug at the retina for treatment of retinal diseases such as macular degeneration.

When a drug is introduced into the vitreous humor, there is mass transport in it caused by diffusion and convection. In the young, normal eye, the vitreous humor is viscous and diffusion is the predominant process by which drug is transmitted to the retina. The effect of natural convection on drug distribution depends on the molecular weight of the drug and the nature of the vitreous; studies have shown that diffusion is more pronounced than natural convection in the transport of low molecular weight compounds in the mouse eye (Stay et al. 2006). It has also been shown that in the normal human eye, natural convection accounts for roughly 30% of the total intravitreal drug transport for small molecules. For larger molecules, there is a higher contribution by natural convection than diffusion (Xu et al. 2000). Investigations on the effects of saccadic eye rotations on the flow in the vitreous humor of the eye and consequent drug distribution have shown that there was better drug dispersal across the eye with fluid flow than without (Repetto et al. 2010).

Many retinal treatment methods including laser treatment for retinal tear involve a process where the gel-like vitreous humor is replaced by a less viscous liquid. Introduction of a drug into the less viscous liquid can increase both diffusion and convection induced drug transport in the vitreous and consequent drug availability at the retina. Indeed, a study of flow dynamics due to saccadic movements in liquefied vitreous showed increased diffusion of the drug (Abouali et al. 2012).

Mass transfer by convection is caused by the steady permeating flow through the vitreous driven by a pressure drop between the anterior and the posterior surfaces or by active transport through the retinal pigment epithelium. Permeation is generally described by the Darcy Law :
$$ {v}_{\mathrm{fluid}}=\frac{K}{\mu_{\mathrm{fluid}}}\nabla P $$
(5)
where v fluid is the velocity of the permeating fluid, K is the hydraulic conductivity of the vitreous, μ fluid is the viscosity of permeating fluid, and ∇P is the gradient of pressure. Since the pressure drop across the vitreous is very small, diffusion has been considered to be the main mechanism for drug transport in the vitreous. Techniques such as iontophoresis – the application of low density electric current to enhance penetration of charged molecules – have been studied but have not found widespread clinical acceptance because of potentially damaging side effects such as focal chorioretinal lesions. Coulomb-controlled iontophoresis has been proposed as a safer alternative (Behar-Cohen et al. 2002).

There is conceivably one safe route to enhance drug distribution by inducing convection in the vitreous humor that has been diluted artificially (e.g., in vitrectomy) or by age – application of heat. Heating a fluid region can induce circulation due to local buoyancy differences caused by the density reduction due to heating – natural convection. This convection requires a certain temperature gradient for the local fluid mass to move and circulate. Larger the temperature gradient, stronger the circulation. Transpupillary thermal therapy, described in Sect. 3.5 earlier, can be used to induce natural convection in the fluids of the eye to enhance drug delivery to the target tissues. As explained in the earlier section, TTT uses laser with diffused heating and hence results a temperature difference of 5–10 °C between the colder cornea and the relatively hotter retina. This temperature gradient is sufficient to cause convective circulation, provided the vitreous has been diluted by age or prior eye therapy such as retinal surgery. Drug introduced into a convectively “stirred” vitreous humor can reach the target retina faster.

Indeed, preliminary numerical and experimental modeling studies on TTT-aided intravitreal drug delivery have shown the expected enhanced drug penetration across the vitreous (Narasimhan and Jha 2015). Drug transport by TTT-induced vitreous convection was modeled and measured as an average concentration on the inner retinal region and compared to drug delivery by diffusion across the vitreous humor.

To understand the effects of vitreous circulation on intravitreal drug delivery , one needs to analyze theoretically the combined heat and mass transfer processes. This has been performed using numerical simulations. In various regions of the eye that are considered solid, such as cornea, aqueous humor, and lens and sclera, the temperature distribution was obtained by solving the energy conservation equation similar to Eq. 1 of this chapter minus the last term. For the choroid with blood perfusion, Eq. 1, the Pennes perfusion equation in its full form has been used.

The vitreous circulation also involves the simultaneous solution of both the heat and mass transfer equations. The mass transfer equations to be solved are as follows:
$$ \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0 $$
(6)
$$ \rho \left(\frac{\partial u}{\partial t}+ u\frac{\partial u}{\partial x}+ v\frac{\partial u}{\partial y}\right)=-\frac{\partial p}{\partial x}+\mu {\nabla}^2\mathrm{u} $$
(7)
$$ \rho \left(\frac{\partial v}{\partial t}+ u\frac{\partial v}{\partial x}+ v\frac{\partial v}{\partial y}\right)=-\frac{\partial p}{\partial y}+\mu {\nabla}^2\mathrm{u}-{g}_y{\beta}_{\rho}\left( T-{T}_{\infty}\right) $$
(8)
$$ \rho c\left(\frac{\partial T}{\partial t}+ u\frac{\partial T}{\partial x}+ v\frac{\partial T}{\partial y}\right)= k{\nabla}^2 T+{Q}^{{\prime\prime\prime} } $$
(9)
where, μ is the dynamic viscosity of vitreous humor, u and v are the velocity of vitreous humor in x and y directions, respectively, p is the pressure, g y is the gravitational acceleration in y direction, T is the temperature inside the eye, and T  is the initial temperature of vitreous humor. The above equations are solved using the following initial conditions:
$$ T\left( t=0\right)={T}_s $$
(10)
where T s is steady state temperature calculated inside the computational domain without considering heat source term in the energy equation. This is the initial condition for human eye functioning under normal conditions. The initial velocity of the vitreous humor is taken as the velocity of steady state natural convective flow without heat source, i.e., u = u s  and v = v s  at t = 0. u s and v s are the steady state natural convective flow velocities in x and y directions, respectively.
The boundary conditions at the cornea and sclera are given by
$$ -{k}_c\frac{\partial T}{\partial n}={h}_c\left( T-{T}_a\right)+\sigma \varepsilon \left({T}^4-{T_a}^4\right) $$
(11)
$$ -{k}_c\frac{\partial T}{\partial n}={h}_c\left( T-{T}_b\right) $$
(12)
where k c is the thermal conductivity of cornea, and k s that of the sclera , n is the unit outward normal, and σ is the Stephen-Boltzmann constant. Using values from literature, a two-dimensional computational model was developed for drug delivery under TTT process in a human eye under postretinal treatment. It was found that for a centrally injected drug, the average drug mass fraction on the target retinal region was 5.7 times higher for the convection-assisted delivery over the pure diffusion case (Fig. 5) (Narasimhan and Jha 2015).
Fig. 5

Concentration profile showing drug reaching the posterior (retinal) segment for a central deposit (a) Diffusion case at t = 2.7 h (b) TTT-induced convection enhanced diffusion at t = 0.5 h (Further results are available in Narasimhan and Sundarraj (2013))

Preliminary experimental studies have been performed using a model glass eye chamber, a mimic of liquefied vitreous humor and a drug mimic (rhodamine B ). The experiments showed that laser-induced convection resulted in three times faster drug delivery to the retina than purely diffusion induced drug delivery. For centrally deposited drug, the drug traversed the vitreous mimic and reached the retina mimic within a minute by diffusion alone, whereas heat induced convection in the vitreous mimic carried the drug to the target in 20 s (Narasimhan and Sundarraj 2016).

It must be mentioned that TTT-convection induced intravitreal drug delivery is at the research level and further studies are required before translation into therapeutic applications.

11 Mass Transfer in Ocular Drug Delivery

The delivery of pharmaceutical ingredients to the eye depends critically on the mass transfer characteristics in the eye. Drug administration to eye is complex because of various static and dynamic barriers that protect the eye from physical damage. The many layers of cornea, sclera, and retina are physical barriers to drug delivery while blood flow and fluid (lymphatic and nasolacrimal ) drainage cause rapid drug clearance from the eye, thus reducing bioavailability. Most drug delivery protocols to the eye involve prolonged administration of the drug.

The eye is divided physically into two segments for drug delivery purposes (not to be confused with the anterior and posterior “chambers” containing the aqueous humor, in Fig. 1) (Fig. 6). The anterior “segment” of the eye contains the cornea, conjunctiva, aqueous humor, iris, ciliary body, and lens and the posterior “segment” includes the sclera, choroid , retinal pigment epithelium, neural retina, optic nerve, and vitreous humor. Diseases such as glaucoma , allergic conjunctivitis, anterior uveitis, and cataract are associated with the anterior segments of the eye, while age-related macular degeneration and diabetic retinopathy are associated with the posterior segment of the eye.
Fig. 6

(a) Posterior and (b) anterior segments of the eye

11.1 Drug Delivery to the Anterior Segment

  1. (i)

    Topical administration of drug

    Diseases of the anterior segment of the eye are usually treated with topical administration of drugs, such as application of eye drops, ointments, and lotions. Although the process of administration is easy and largely noninvasive, the bioavailability of the drug during topical delivery is poor (<5%) because of anatomical and physiological constraints such as reflex blinking, nasolacrimal drainage, and physical ocular barriers such as the lens. Although lacrimal turnover rate is only about 1 μl/min, the applied fluid can be flushed to the nasolacrimal duct within minutes. Another process by which the topically administered drug is eliminated is by the venous blood flow through the anterior uvea (the pigmented layer of the eye, lying beneath the sclera and cornea). This elimination depends on the ability of the drug to penetrate the endothelial walls of the vessels – lipophilic drugs are cleared faster than hydrophilic drugs. The natural flow of aqueous humor from the posterior chamber of the eye to the anterior chamber is another impediment to the inward flow of the administered drug.

    The half-lives of drugs in the anterior chamber are typically in the order of an hour. The peak concentration of drug in the anterior chamber is reached after 20–30 min after administration, but this peak concentration, due to nasolacrimal drainage, is more than two orders of magnitude lower than the administered concentration. The drug may bind to melanin once it reaches the iris and ciliary body, from where it could be released gradually, thereby prolonging drug bioavailability.

    The decline in topically applied drug concentration in the eye follows approximate first order kinetics. Various techniques are used to improve bioavailability and permeation, such as addition of viscosity enhancers such as cellulose derivatives and permeation enhancers such as EDTA salts and PEG ethers. The former enhance precorneal residence time of the topical drug and prevent run off while the latter modify corneal integrity and allow easier penetration of the drug. The use of penetration enhancers is fraught with risks of collateral damage to tissue. Use of lipophilic carriers such as cyclodextrins to deliver the drugs directly to the surface of the target membrane is also being studied.

     
  2. (ii)

    Subconjunctival injections

    Subconjunctival or sub-Tenon’s injections used for diseases of the anterior segment can help increase contact time and thus drug absorption. Injecting drugs subconjunctivally bypasses the lipid layers of the bulbar conjunctiva and brings the drugs into contact with the water-permeable sclera , increasing water-soluble drug penetration into the eye. Drugs that cannot easily penetrate the cornea, such as antibiotics and corticosteroids, are usually delivered by this route.

    Subconjunctival injections are also used to transport drug to the anterior segment of the eye, in transscleral administration.

     

11.2 Drug Delivery to the Posterior Segment

Diseases of the posterior segment are treated using invasive drug delivery processes such as systemic administration, intravitreal injections, and transscleral procedures.
  1. (i)

    Systemic administration

    Systemic administration of drugs (oral medication/intravenous dosage, etc.) is sometimes used to treat both ocular diseases. However, such treatments of the anterior and posterior segments of the eye are impeded by the blood–aqueous barrier and blood–retinal barrier, respectively. In the anterior segment, the endothelium of the iris/ciliary blood vessels and the nonpigmented ciliary epithelum layers provide a blood–aqueous barrier and prevent the entry of solutes from the uveal blood flow into the aqueous humor. In the posterior segment, the blood–retinal barrier made of retinal pigmented epithelial (RPE) cells and retinal capillary endothelial cells restrict the entry of the therapeutic molecules from blood into the posterior segment.

     
  2. (ii)

    Intravitreal injections

    Intravitreal delivery bypasses the cornea–conjunctiva barrier and can deliver the drug directly to the vitreous and retina. Nevertheless, there are a few dynamic, static, and metabolic barriers that limit bioavailability of transvitreally administered drug. The distribution of the drug in the viscous vitreous humor is often nonuniform. Chemical reactions between the hyaluronan, a negatively charged glycosaminoglycan present in the vitreous, and cationic lipid, polymeric, and liposomal DNA-based drugs can impede diffusion of the drug. The inner limiting membrane that separates the retina and vitreous is a static barrier to delivery of transvitreally administered drug to the retina. Drug transport from the vitreous to the outer segments of retina and choroid is also hindered by the RPE.

    Drugs administered intravitreally are eliminated either through drug diffusion across the vitreous into the aqueous humor , followed by aqueous turnover and uveal blood flow . Posterior elimination may also occur across the blood–retinal barrier but those are rarer and require active transport mechanisms. Hydrophilic and large molecular weight carriers of drugs can increase the half-life of intravitreally administered drugs. Intravitreal injections are associated with potential risks of retinal detachment hemorrhage, endophthalmitis, and cataract and require repeated treatments. As mentioned earlier, the bioavailability of intravitreally administered drug could conceivably be enhanced by the induction of convection in the liquefied vitreous humor.

     
  3. (iii)

    Transscleral drug delivery

    Intravitreal injections have been known to cause various side effects such as hemorrhage and retinal detachment and poor patient tolerance and are being increasingly replaced by transscleral drug delivery with periocular administration . Delivering drug across the sclera offers the following advantages:
    • The high scleral surface area (~17 cm2) increases rate and extent of drug absorption.

    • The high degree of hydration associated with the sclera allows diffusion of hydrophilic molecules,

    • The metabolic inactivity of the sclera facilitates delivery of molecules that are sensitive to enzymes,

    • The high permeability of the scleral surface to macromolecules enhances bioavailability, and

    • It is possible to administer controlled and sustained release drug forms.

    Transscleral drug delivery is discussed in detail in the following section.

     

12 Transscleral Drug Delivery

12.1 Anatomy of the Sclera

See Fig. 7.
Fig. 7

Sclera: determination of scleral permeability as K = 1.3 nm2 using porous medium methods (Explained in detail in Narasimhan (2012))

The sclera forms the supporting wall of the eyeball and is commonly known as the “white” of the eye. It is covered by the conjunctiva, which lubricates it (hence the high degree of hydration mentioned earlier). The adult human sclera is thinner near the anterior segment and thicker toward the optic nerve. The thickness and opacity of the sclera increase with age. The sclera itself is composed of the following layers: The outer episclera and the Tenon’s capsule that are provided with vasculature, and the inner stroma, spur and lamina fusca layers.

Drugs transsclerally administered reach the target largely by diffusion through the vitreous humor. Some of them may be distributed by through aqueous absorption through uveal vasculature, although these are rarer and of less importance than direct diffusion.

12.2 Modes of Transscleral Administration of Drugs

Drugs can be administered transsclerally through the following approaches:
  • The subconjuntival route involves drug injection below the conjunctiva.

  • The sub-tenon route involves introducing the drug into the Tenon’s capsule, a sheath of connective tissue located between the eye globe and extraocular tissues.

  • The retrobulbular route where the drug is introduced into the conical retrobulbular cavity at the back of the eye.

  • The peribulbular route where the drug is introduced outside of the conical retrobulbar cavity.

  • Posterior juxtascleral in which, the therapeutic agent is delivered in close contact with the sclera, near the macula, without puncturing the eye ball. This is a recent development in transsleral drug delivery.

12.3 Modeling Transscleral Drug Delivery

The usefulness of any drug delivery technique hinges on the effective release of sufficient amounts of the active pharmaceutical ingredients from delivery vehicles to the target tissues. The release of a drug from its carrier is mediated by rate-controlling release mechanisms such as diffusion, erosion/chemical reactions, swelling, and osmosis. Computational fluid dynamics simulation can help predict the spatial and temporal variation of drug transport in living tissues. For therapeutic procedures involving the eye, accurate delivery of the drug in the eye is critical, given the eye’s vulnerability to damage, and computational studies help in predicting optimal delivery patterns.

Pharmacokinetic models (simplified in Fig. 8) can be used to explain the transfer rates of drug through the posterior eye tissues (Lee and Robinson 2004).
Fig. 8

A simple pharmacokinetic model of transscleral drug delivery by the subconjuntival route

In the above model, three rate constants are used to mathematically model drug levels in the vitreous humor; k 1 is a rate constant for drug loss from the subconjunctival (or indeed any periocular) space; k 2 for drug absorption/penetration from the subconjunctival space into the vitreous humor and k 3 for the elimination rate constant from the vitreous humor. The percentage vitreal bioavailability (B v ) of the drug is calculated using Eq. 13.
$$ {B}_v=\frac{k_2}{k_1+{k}_3}\times 100 $$
(13)

The above model is a simplified model in that it lumps drug penetration into vitreous humor into a single rate constant k 2. In reality, however, this is a complex phenomenon; the drug injected into the periocular space must permeate several layers before reaching the vitreous humor. The barriers are different in the anterior and posterior segments of the eye; the choroid-RPE-neural retina layers the posterior segment while various layers of ciliary body are barriers in the anterior segment. The thickness of the sclera itself varies, being thicker near the optic nerve than elsewhere. Thus the site of drug application decides the bioavailability of the drug in the vitreous. A pharmacokinetic simulation model by Ranta and Urtti (2006) uses the scleral permeability coefficient, which accounts for circulation loss and predicts the overall permeation flux through the sclera.

The flow of blood in the choroid can affect the diffusion of the drug that has been introduced into the sclera. Porous medium models are elegant for the study of transscleral drug delivery in the presence of choroidal blood flow. Balachandran and Barocas (2008) reported a 3D porous medium approach using finite element method; the model accounted for diffusion and convection losses, assuming linear effect of choroidal blood flow on the drug delivery.

A porous medium model of sclera and choroid has been recently developed in Narasimhan and Ramanathan (2012), to study the effect of choroidal blood flow on transscleral delivery of the drug anecortavete acetate to the retina via juxtascleral administration. The permeation of the drug through the direct penetration pathway was modeled as a diffusion process and studied using Fick’s second law of diffusion, in conjunction with an effective diffusivity for the porous media, in the presence of various blood flow rates in the choroid. Figure 9 shows the concentration profiles of the drug at t = t max in the sclera and choroid, before it is deposited onto the retinal surface. As the rate of choroidal blood flow (U b ) is increased from 0.01 to 10 cm/s, the drug is “washed” or convected strongly in the choroid before it reaches the retinal surface. Such modeling studies are useful to estimate the expected deposition characteristics of the drug because choroidal blood flow varies for different humans both by person and in time.
Fig. 9

(a) Porous media modeling of transscleral drug delivery; effect of choroidal blood flow on drug delivery (b) Effect of blood flow rate on mean peak plasma concentration (Narasimhan and Ramanathan 2012)

The simulations also predicted the transient mean plasma concentration of a drug in the choroid and the effect of choroidal blood flow on the mean peak plasma concentration. Increasing choroidal blood flow rate decreased the average plasma concentration of the drug (Fig. 9b). The choroidal blood flow is not constant but is pulsatile because of the pumping of the heart. In keeping with the above trend, peak mean plasma concentration of the drug was found to decrease by about 70% as rate of choroidal blood flow increased from the end diastolic velocity to peak cystolic velocity.

The distribution of transsclerally injected drug is also affected by active transport by the RPE. It has been shown by simulations studies that the higher outward permeability of the blood-retinal barrier than inward permeability is due to the active transport mechanism (Yoshida et al. 1992). Drug losses can occur due to clearance by the conjunctival lymphatics and episcleral blood flow (Robinson 2006).

13 Drug Development for Enhanced Drug Bioavailability

Various drug delivery vehicles and techniques have been developed to enhance bioavailability of the drug delivered to the eye by various means. The traditional use of liquid eye drops, while being the most widely used for minor anterior eye diseases, is associated with very short clearance time in the eye surface due to nasolacrimal drainage and thus results in poor bioavailability of the drug at the target tissue. The half-life of a solution that has been topically administered depends on the viscosity of the carrier, the osmolality, and the instilled volume. Ocular retention may be prolonged by enhancing viscosity or altering pH of the administered solution. Viscosity enhancing vehicles include polymers such as hydroxy propyl methyl cellulose (HPMC), poly(lactic acid) (PLA), poly (lactide-co-glycolide) (PLGA), poly ethylene glycol (PEG), poloxamers, carbopol, chitosan, collagen, poly (ortho esters), poly (vinyl alcohol), and poly(1- vinyl-2-pyrrolidinone) (PVP).

Ophthalmic inserts impregnated or coated with drugs have the advantages of extended ocular residence, possibility of controlled release of drugs, reduction of systemic absorption, and accurate dosage. Recent research efforts have focused on designing novel dosage forms such as nanoparticles, liposomes, emulsions, and hydrogels. Particulate drug delivery systems include nanoparticles, microparticles, and nano- and micro-capsules that are impregnated with the drug. Drug-bearing bioadhesives that bind to the surface of epithelial tissue, or form a mucous coating, can penetrate the intracellular spaces of the tissue, creating a greater exposed surface area for the drug. Hydroxypropyl methylcellulose (HPMC), carboxymethylcellulose (CMC), and polyacrylic acid (PAA) derivatives, as well as hyaluronic acid (HA) are bioadhesive polymers most commonly used to encapsulate or carry the ophthalmic drug.

Drugs can also be encapsulated inside microscopic phospholipid bilayers, called liposomes. Liposomes readily bind to cell surfaces due to their affinity to cell membranes and can thus facilitate drug transfer. Liposomal ophthalmic drug delivery methods are being actively researched because they offer promise for slower, more consistent release (Arifin et al. 2006). Drugs coated on contact lens can also enhance bioavailability because of their proximity to the target tissues. Drug-eluting contact lens development must focus on maintenance of lens transparency, maintenance of the surface characteristics of the lens, and good oxygen transmissibility. Methods to incorporate drugs into contact lens have included coating contact lens surfaces with the drug, sandwiching the drug between two “slices” of lens material, and introducing drug eluting nanocapsules into the polymeric matrix of the lens.

For intravitreal drug delivery, there have been studies to develop implants that can release drug to the posterior segment of the eye. Such implants must be surgically inserted into the vitreous and could be nonbiodegradable or biodegradable. The former types of implants require a second surgery for removal. Implant-borne drug delivery has advantages of consistent drug release and avoidance of pulse effect. However, implants have the risk of infection following insertion.

The selection of the drug type and vehicle ultimately hinges on the physicochemical properties of the drug molecule, those of the targeted tissue (retina, choroid, vitreous humor, etc), type of release required (immediate or controlled release), and dosage. In the diffusion mechanism, the drug is released through the pores of the matrix at a controlled rate into the eye fluid. This controlled release can be augmented by the gradual dissolution of the matrix itself in the solution. Diffusive release of drug from the matrix is said to follow Fick’s “square root of time” kinetics but zero order transport has also been postulated to occur. When polymers are used as the matrix, the drug does not diffuse through pores, but in the presence of the liquid, the polymer swells, resulting in drug diffusion, followed by gradual dissolution of the polymer itself. Linear amorphous polymers, as expected, dissolve faster than cross-linked or partially crystalline polymers.

14 Conclusion

Just as in other human organs, the functioning and well-being of the eye involves several biothermo-fluid processes, the role of which are only to be amplified during the deployment of medical treatment procedures. The subfield of medical optics bloomed with the advent of lasers in the 1960s and has since been actively researched. Ablation and photocoagulation using lasers are now established medical treatment processes, although the actual in situ temperatures involved and their long-term thermal damage to the treated and associated regions of the eye remain to be analyzed and ascertained. Experimental research with noninvasive measuring techniques during actual surgeries seems to be the best way to obtain such results, while in reality, one may need to contend with animal experiments combined with judicious simulation procedures for improving the understanding in this area.

Drug delivery methods, primarily a mass transfer process although conjugate methods are possible as discussed in the chapter, have also been developed. One factor that drives research on opthalmic drug delivery methods is the realization of the need for quick application of a drug in the target areas that are inaccessible in a short time scale for the normal modes of mass transfer offered by the systemic blood circulation. Advent of drugs involving nanomaterial for effective remedy has also propelled the research in suitable drug delivery methods for those drugs. Developing effective drug eluting methods and corresponding equipment for newer drugs involving multiple effects and duration of use in the eye seems to be the direction for future research, as is the development of noninvasive local measuring techniques.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Heat Transfer and Thermal Power LaboratoryIndian Institute of Technology MadrasChennaiIndia

Section editors and affiliations

  • Ram Devireddy
    • 1
  1. 1.Department of Mechanical and Industrial EngineeringLouisiana State UniversityBaton RougeUSA

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