Ocular Fluid Dynamics

A model of a complex system is a facsimile that can be used to investigate the problem at hand by simulating its behavior under specific conditions. Many modeling approaches are used in the applied sciences, including physical, animal, conceptual, and mathematical models. Specific examples will be provided in the chapter to illustrate the synergistic application of modeling to the simulation of biological fluid flow with relevance to ophthalmology.

This chapter provides an overview of the main structural and functional properties of the ocular vasculature. Four major circulatory systems within the eye are considered, namely those nourishing the retina, the optic nerve head, the choroid, and the anterior segment. Some aspects related to vascular regulation and innervation are also discussed, along with outstanding questions that remain a matter of debate.

This chapter reviews the abundant evidence of correlations between vascular alterations and ocular diseases. In particular, we discuss retinal diseases, including age-related macular degeneration, diabetic retinopathy and retinal vessel occlusions, glaucoma, and non-arteritic ischemic optic neuropathy. Current inconsistencies among studies and outstanding controversial questions are emphasized to bring the reader up to date with respect to the main challenges in the field.

This chapter examines the assessment of ocular hemodynamics in health and disease. Beginning with a discussion on ocular perfusion pressure and the physical principles, we systematically present the conceptual basis and details of blood flow measurement technology, paying particular attention to the scientific and clinical strengths and weaknesses of each technique.

Mathematical models linking ocular mechanics, circulation, and oxygenation are needed to improve the interpretation and prediction of key components of ocular health and disease. This chapter presents the most recent achievements in modeling the retinal, retrobulbar, and choroidal vascular beds in the eye. These models incorporate elements of flow regulation, oxygen transport, angiogenesis, and venous collapsibility and are used to answer important questions related to ocular diseases such as glaucoma and age-related macular degeneration.

Steady-state intraocular pressure (IOP) results from the interplay of the inflow, outflow, facility, and pressure of aqueous humor dynamics. A change in any one of these parameters may greatly affect IOP, while a simultaneous change in a second parameter might negate the effect of the first leaving IOP undisturbed. Some IOP changes could be rapid as when moving from a seated to a supine position. Other IOP changes are gradual such as seen seasonally. There is general agreement on the nighttime reduction in aqueous humor production but not on changes that occur during aging. Aging is confounded by many factors affecting IOP including systemic and ocular health, ethnic background, and recreational activities. Evidence suggests that aqueous humor dynamics in children may change rapidly until sexual maturity is reached, but the scarcity of research on children has left a void in our understanding of the developing eye. Efficacy of IOP-lowering treatments can be altered by fluctuations in aqueous humor dynamics, especially at night. The molecular and cellular aspects underlying the changes in aqueous humor dynamics is a rapidly growing field. Effective mathematical modeling of ocular fluid dynamics will benefit from a clearer understanding of the changes in aqueous humor dynamics throughout life.

The chapter describes the anatomical and functional features of the aqueous humor (AH) dynamics with special focus on pathological changes in glaucoma. The main therapeutic approaches to medically and surgically regulate AH production and outflow are discussed.

The aqueous humor outflow (AHO) tract is the pathway by which fluid travels from the eye’s anterior chamber to drain into the venous circulation. This tract plays an important role in the regulation of eye pressure and is likely key in the pathogenesis of glaucoma. As such, the outflow tract is a target for alteration by medical and surgical treatment approaches. To understand this pathway’s anatomy and physiology, numerous structural and functional studies have been conducted. While the ability to conduct such studies has advanced along with modern imaging approaches, many challenges to accurately assessing its structure and function remain.

The aqueous humour (AH) is a transparent fluid with water-like properties that fills the anterior chamber (AC, the region between the cornea and the iris) and the posterior chamber (PC, the region between the iris and the lens) of the eye, which are connected at the pupil. AH is produced at ciliary processes, and it flows from the PC to the AC, where it is drained in the trabecular meshwork. AH flow is important physiologically, as it governs intraocular pressure and delivers nutrients to avascular ocular tissues. Disruption of AH flow may lead to multiple pathological conditions, such as glaucoma and nutrient depletion. Studying aqueous production, flow and drainage is thus relevant to understand eye physiology and pathophysiology.

Mathematical modelling has proven to be a very useful tool for studying AH, as it allows one to understand the mechanisms of the flow by studying them separately. In this chapter we outline the mathematical models of AH production, different AH flow mechanisms and drainage, subsequently. We focus on analytical works and briefly mention the main conclusions of numerical ones.

The translucency of the vitreous makes its full structure and composition challenging to completely elucidate, but what is known about the anatomy and biochemistry of this body and its impact on optic function is fundamental to understanding ocular health and disorders, as it carries out several important functions within the eye. The particular makeup of structural protein fibers is known to play a pivotal role in stabilizing the vitreous and maintaining its morphological integrity, and disruptions in this network, due to genetics, disease, or environmental changes, may result in certain conditions and ocular pathologies. Research has recently shown that the concentrations of ions, nutrients, and other proteins and small molecules in the vitreous can also be affected by disease. Age-related changes to the vitreous are predominantly due to changes in the density and increasing liquefaction, which weaken its structural integrity and adhesion to the internal limiting membrane and may result in posterior vitreous detachment or collapse of the vitreous body. Familiarity with the anatomy, biochemistry, and development of, and changes to the vitreous facilitates an increased knowledge of its role in maintaining overall ocular health and may also further the understanding of certain conditions and ocular pathologies.

The vitreous is involved in a wide variety of pathologies. The vitreoretinal interface is the site of adhesion between the posterior vitreous cortex and the retina’s internal limiting membrane, and a pathological interaction between these two surfaces accounts for pathologies including vitreomacular traction, macular holes, epiretinal membranes, retinal tears and detachments, and macular edema. The vitreous has a structural role in retinal neovascularization, in particular proliferative diabetic retinopathy, retinopathy of prematurity, and familial exudative vitreoretinopathy. Metabolic disorders of the vitreous include amyloidosis and asteroid hyalosis. These diseases of the vitreous and vitreoretinal interface will be discussed in this chapter.

The anatomy of the vitreous and the vitreoretinal interface is important to understand its role in various disease states. However, the transparent nature of the vitreous presents a unique challenge for characterization of its anatomy. This chapter explores the techniques utilized to image the vitreous including slit lamp biomicroscopy, optical coherence tomography (OCT), B-scan ultrasonography, magnetic resonance imaging (MRI), and in vitro techniques. An overview of these technologies with their clinical applications is highlighted.

The vitreous humour is a gel-like substance, which fills the vitreous chamber at the posterior part of the eye. It is a clear transparent material that can be mechanically characterised as a visco-elastic fluid. The vitreous has the important role of holding the retina in contact with the retinal pigment epithelium. During vitreous motion vitreoretinal tractions are generated and this might potentially lead to retinal detachment (RD). Studying the vitreous mechanical behaviour is thus relevant for understanding the physiology and pathophysiology of the eye.

Mathematical modelling has provided significant contributions into understanding vitreous dynamics and the role it has on the occurence of vitreoretinal pathologies. In this chapter we first discuss works addressing vitreous motion induced by eye rotations and the possible generation of large mechanical stresses on the retina. Secondly we discuss models associated with RD, focusing on the progression of rhegmatogenous RD and the formation of exudative RD.

This chapter explores the normal structure and function of the tear film. Normal properties and composition of tears as well as the structure of the aqueous, mucin, and meibomian layers are discussed. The role of supporting structures such as the eyelids, meibomian glands, and goblet cells in the lacrimal functional unit (LFU) is also reviewed. Finally, the physiologic roles of the tear film, including lubrication and nutrition of the ocular surface, visual function, anti-inflammatory and healing properties, and its role in ocular surface nerve modulation are all examined.

This chapter first reviews the pathogenesis of dry eye (DE) and the pathological effects DE has on the properties and composition of the tear film, lacrimal and meibomian glands, and goblet cells. Next, the pathologic changes that occur with two DE related risk factors: aging and the use of glaucoma eye drops are discussed. Finally, the clinical consequences of tear film, lacrimal gland, meibomian gland, and goblet cell alterations, focusing on visual function, nerve modulation, quality of life, and economic burden, are explored.

Significant efforts have been made with the development of various imaging techniques to visualize and understand the tear film dynamics. This chapter reviews three imaging techniques with established impact on imaging the tear film dynamics: fluorescent imaging, interferometry, and optical coherence tomography.

The complex dynamics of the tear film are affected by its many processes and components. Mathematical models of the tear film allow the selective elimination or inclusion of various effects that are not otherwise possible in human subjects. Such models have been able to provide local estimates of osmolarity in tear break up (TBU), for example, which to our knowledge cannot be measured directly. Models also suggest that different modes of TBU must be considered to make sense of in vivo data regarding response of the ocular epithelia and causes of dry eye. More complex models that include tear film formation via blinking are within our grasp, which will no doubt extend our knowledge of the tear film, its dynamics, and its role in ocular surface health.

The cerebrospinal fluid (CSF) is the primary circulating fluid of the central nervous system. It serves numerous important physiologic and maintenance functions, and its production and movement are highly regulated. Herein, we describe the key anatomic structures of importance in regard to CSF production, circulation, and absorption, followed by the regulatory mechanisms responsible for its proper functioning.

It has been speculated that a low orbital cerebrospinal fluid pressure (CSFP) may perhaps play a role in the pathogenesis of glaucomatous optic neuropathy. To verify the hypothesis, we conducted a serial of experimental study on low-CSFP models of monkeys and rats. Our studies showed that a reduction in CSFP could result in the structural and physiological changes of optic nerve and some molecular biology reactions in the optic axons. We hope that our chapter will be helpful for the further research in the pathogenesis of glaucoma.

Intracranial and intraocular pressures are interrelated and relatively independent pressure systems, which keeps themselves in a relatively stable state through aqueous and cerebrospinal fluid circulations. Recently, researchers have focused on intracranial pressure role in eye diseases. This chapter summarizes various instruments to measure and visualize geometrical and functional parameters related to the fluid dynamics of cerebrospinal fluid in the eye.

The present chapter provides an overview of mathematical models that describe the cerebrospinal fluid and its possible interactions with other biofluids or neighboring tissues. The description of the underlying mechanisms stems from the basic principles of fluid and solid dynamics and it is translated into systems of partial or ordinary differential equations. The current review aims at specifying a complementary view with respect to other revisions in the field by illustrating some selected studies that may constitute a first step in the connection between cerebral and ocular fluid dynamics.

First we present lumped-parameter models with a simplified mathematical structure that allow fast computations of the average values of the unknowns and capture the main behavior of the cerebral flow. The discussion then moves onto distributed models, which produce a three-dimensional representation of cerebrospinal fluid flows in complex geometries that may derive from medical imaging. These models allow the investigation of the fluid flow at fine scales, constituting a highly valuable tool in providing a better understanding of pathophysiology.

We acknowledge that significant efforts have already been made in the attempt to unify mathematics and medicine in the context of brain diseases caused by cerebrospinal fluid abnormalities; nevertheless, we report a pressing demand for innovative mathematical models that may achieve the complete description and simulation of the biophysical connections between the eye and the brain.

The retina is directly connected to the central nervous system and the vascular circulation, which uniquely enables three-dimensional retinal tissue structures and blood flow dynamics to be imaged and visualized from the exterior using non-invasive imaging modalities. Rapid advances in the types of diagnostic imaging modalities, combined with image processing, computer vision, artificial intelligence, and machine learning algorithms for quantitative image analytics are opening up a host of new possibilities for early diagnosis and treatment of a broad range of eye and systemic diseases with clinical impact. Incorporating patient-specific imaging to estimate geometric structures of vessel morphology and boundary conditions as input to the mathematical and computational fluid-dynamics modeling frameworks described in earlier chapters will enable new ways to predict treatment outcomes and model physiological effects at the systemic level. This chapter describes a set of widely used retinal imaging modalities, including fundoscopy, fluorescein angiography (FA), and optical coherence tomography (OCT), along with emerging modalities to measure retinal blood flow dynamics like optical coherence tomography angiography (OCTA) and laser speckle flowgraphy (LSFG). We use vessel segmentation and quantification as a prototypical ophthalmology image analysis pipeline that can be applied across imaging modalities, to describe processing techniques for measuring geometrical vascular structures. Current challenges and future opportunities especially in using artificial intelligence and deep learning architectures for patient optimized precision medicine and clinical efficacy are highlighted.

Medical imaging has revolutionized the diagnosis and management of disease in healthcare. Early integration of computers into medical imaging brought control of devices and data acquisition to new heights of precision. As computing power and sophistication of software evolve, we have reached an era of computer-based image interpretation. Machine learning approaches have been developed to automate certain quantitative measures derived from these modalities. Prospects for machine learning in ophthalmology address its potential role in approaching some of the most common causes of blindness worldwide: diabetic retinopathy, glaucoma, and age-related macular degeneration. As these analysis techniques evolve, concurrent advancements are seen in ophthalmology imaging technologies themselves, and today, the aqueous outflow tract and the optic nerve head can be visualized in more detail than ever before. The optimization and assimilation of these tools may hold clinically significant answers to screening, diagnosing, and managing disease.

Statistical models provide a variety of powerful methods for data analysis in medicine. In this chapter, we aim at illustrating the insights that statistical models can provide regarding the study of disease progression. In particular, we analyze a unique dataset on glaucoma progression by means of mixed-effects statistical models, where the form of the probability distribution for the multiple measurements is assumed to be the same for each individual in the study, but the parameters of that distribution can vary over individuals. Two illustrative case studies are presented in the context of structural and functional progression in glaucoma.