Effect of intraocular pressure on the hemodynamics of the central retinal artery: a mathematical model

The ocular mathematical virtual simulator: A validated multiscale model for hemodynamics and biomechanics in the human eye

We present our continuous efforts from a modeling and numerical viewpoint to develop a powerful and flexible mathematical and computational framework called Ocular Mathematical Virtual Simulator (OMVS). The OMVS aims to solve problems arising in biomechanics and hemodynamics within the human eye. We discuss our contribution towards improving the reliability and reproducibility of computational studies by performing a thorough validation of the numerical predictions against experimental data. The OMVS proved capable of simulating complex multiphysics and multiscale scenarios motivated by the study of glaucoma. Furthermore, its modular design allows the continuous integration of new models and methods as the research moves forward, and supports the utilization of the OMVS as a promising non-invasive clinical investigation tool for personalized research in ophthalmology.

Similarities and differences in systemic risk factors for retinal artery occlusion and retinal vein occlusion: A nationwide case-control study

BACKGROUND

To investigate the relationship between risk factors for retinal artery occlusion (RAO) and retinal vein occlusion (RVO) and thereby identify similarities and differences between the two types of retinal vascular occlusions.

METHODS

In this case-control study, 5708 patients with RAO were included and matched with three patients with RVO each. The patients with RVO were matched on sex and age at index date. All patients, personal information, diagnoses, and prescriptions were obtained from the Danish nationwide registries. Adjusted conditional logistic regression was used to investigate the association of RAO and RVO with the included risk factors.

RESULTS

RAO was stronger associated with arterial hypertension, heart failure, ischemic heart disease, peripheral artery disease, and stroke than RVO, with effect measures ranging from 1.10 to 2.21. RVO was associated with cataract and glaucoma with effect measures of 0.80 (95% CI 0.73-0.87) and 0.65 (95% CI 0.56-0.76), respectively.

CONCLUSION

Differences in the level of associations with the included risk factors suggests differences in the pathophysiologies of the two diseases. The main pathophysiology associated with RAO was atherosclerosis, whereas the main pathophysiology associated with RVO was changes in the pressure gradients of the eyes.

Similarities and differences in systemic risk factors for retinal artery occlusion and stroke: A nationwide case-control study

BACKGROUND

Retinal artery occlusion (RAO) has been considered a stroke equivalent. This study compares risk factor profiles for thromboembolism among patients with RAO and stroke, respectively.

METHODS

This case-control study is based on 5683 RAO patients entered in the Danish National Patient Register between 1^st of January 2000 and 31^st of December 2018. Cases were matched on sex, year of birth, and age at event with 28,415 stroke patients. The Danish nationwide registries were used to collect information about age, sex, previous diagnoses, and drug prescriptions. Adjusted conditional logistic regression models were used to investigate the association between hypothesised risk factors and the patient outcome.

RESULTS

For atrial fibrillation, a substantially stronger association to stroke was found, with an odds ratio (OR) of 0.52 (95% CI: 0.47-0.58) when comparing RAO patients with stroke patients. RAO was stronger associated with arterial hypertension, peripheral artery disease, retinal vein occlusion, cataract, and glaucoma with OR's ranging from 1.21-11.70. The identified effect measures reached equivalence or was close to equivalence for diabetes, heart failure, ischemic heart disease, and renal disease.

CONCLUSION

The differences in risk factor profiles between RAO and stroke suggests differences in the pathophysiology of the two diseases. These variations in pathophysiologies between the two diseases may indicate that different interventions are needed to ensure the optimal long-term prognosis for the patients.

Clinical risk factors for retinal artery occlusions: a nationwide case-control study

PURPOSE

This study seeks to examine potential risk factors for the development of retinal artery occlusions (RAO).

METHODS

We used data obtained from Danish nationwide registries to evaluate potential risk factors for RAO present up to 5 years prior to the RAO diagnosis. The study included 5312 patients diagnosed with RAO registered in the Danish National Patient Register and 26,560 controls assessed from the general population matched on sex and age at index date. Adjusted conditional logistic regression was used to estimate the odds ratio of included risk factors for RAO diagnosis. We conducted supplementary analyses stratified on sex and age, and on RAO subtype. In addition, interaction analyses were performed between strata in the stratified analyses.

RESULTS

Risk factors associated with the development of RAO included diabetes, arterial hypertension, ischemic heart disease, peripheral artery disease, stroke, renal disease, cataract, and glaucoma, with ORs ranging from 1.33 to 4.94. Atrial fibrillation and sleep apnea yielded effect measures close to equivalence. The presence of a risk factor was generally associated with higher odds of RAO among the population ≤ 55 of age. Arterial hypertension was stronger associated with RAO in male patients than in female patients. The association with arterial hypertension was stronger for CRAO than for BRAO subtype.

CONCLUSION

The investigated risk factors suggest that atherosclerosis and conditions changing the intraocular pressure are involved in the pathophysiology of RAO.

A multi-scale/multi-physics model for the theoretical study of the vascular configuration of retinal capillary plexuses based on OCTA data

The retinal tissue is highly metabolically active and is responsible for translating the visual stimuli into electrical signals to be delivered to the brain. A complex vascular structure ensures an adequate supply of blood and oxygen, which is essential for the function and survival of the retinal tissue. To date, a complete understanding of the configuration of the retinal vascular structures is still lacking. Optical coherence tomography angiography has made available a huge amount of imaging data regarding the main retinal capillary plexuses, namely the superficial capillary plexuses (SCP), intermediate capillary plexuses (ICP) and deep capillary plexuses (DCP). However, the interpretation of these data is still controversial. In particular, the question of whether the three capillary plexuses are connected in series or in parallel remains a matter of debate. In this work, we address this question by utilizing a multi-scale/multi-physics mathematical model to quantify the impact of the two hypothesized vascular configurations on retinal hemodynamics and oxygenation. The response to central retinal vein occlusion (CRVO) and intraocular pressure (IOP) elevation is also simulated depending on whether the capillary plexuses are connected in series or in parallel. The simulation results show the following: (i) in the in series configuration, the plexuses exhibit a differential response, with DCP and ICP experiencing larger pressure drops than SCP; and (ii) in the in parallel configuration, the blood flow redistributes uniformly in the three plexuses. The different vascular configurations show different responses also in terms of oxygen profiles: (i) in the in series configuration, the outer nuclear layer, outer plexiform layer and inner nuclear layer (INL) are those most affected by CRVO and IOP elevation; and (ii) in the in parallel configuration the INL and ganglion cell layer are those most affected. The in series results are consistent with studies on paracentral acute middle maculopathy, secondary to CRVO and with studies on IOP elevation, in which DCP and ICP and the retinal tissues surrounding them are those most affected by ischemia. These findings seem to suggest that the in series configuration better describes the physiology of the vascular retinal capillary network in health and disease.

Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator

We propose an uncertainty propagation study and a sensitivity analysis with the Ocular Mathematical Virtual Simulator, a computational and mathematical model that predicts the hemodynamics and biomechanics within the human eye. In this contribution, we focus on the effect of intraocular pressure, retrolaminar tissue pressure and systemic blood pressure on the ocular posterior tissue vasculature. The combination of a physically-based model with experiments-based stochastic input allows us to gain a better understanding of the physiological system, accounting both for the driving mechanisms and the data variability.

Neurodegenerative Disorders of the Eye and of the Brain: A Perspective on Their Fluid-Dynamical Connections and the Potential of Mechanism-Driven Modeling

Neurodegenerative disorders (NDD) such as Alzheimer's and Parkinson's diseases are significant causes of morbidity and mortality worldwide. The pathophysiology of NDD is still debated, and there is an urgent need to understand the mechanisms behind the onset and progression of these heterogenous diseases. The eye represents a unique window to the brain that can be easily assessed via non-invasive ocular imaging. As such, ocular measurements have been recently considered as potential sources of biomarkers for the early detection and management of NDD. However, the current use of ocular biomarkers in the clinical management of NDD patients is particularly challenging. Specifically, many ocular biomarkers are influenced by local and systemic factors that exhibit significant variation among individuals. In addition, there is a lack of methodology available for interpreting the outcomes of ocular examinations in NDD. Recently, mathematical modeling has emerged as an important tool capable of shedding light on the pathophysiology of multifactorial diseases and enhancing analysis and interpretation of clinical results. In this article, we review and discuss the clinical evidence of the relationship between NDD in the brain and in the eye and explore the potential use of mathematical modeling to facilitate NDD diagnosis and management based upon ocular biomarkers.

Microcirculatory model predicts blood flow and autoregulation range in the human retina: in vivo investigation with laser speckle flowgraphy

In this study, we mathematically predict retinal vascular resistance (RVR) and retinal blood flow (RBF), we test predictions using laser speckle flowgraphy (LSFG), we estimate the range of vascular autoregulation, and we examine the relationship of RBF with the retinal nerve fiber layer (RNFL) and ganglion cell complex (GCC). Fundus, optical coherence tomography (OCT), and OCT-angiography images, systolic/diastolic blood pressure (SBP/DBP), and intraocular pressure (IOP) measurements were obtained from 36 human subjects. We modeled two circulation markers (RVR and RBF) and estimated individualized lower/higher autoregulation limits (LARL/HARL), using retinal vessel calibers, fractal dimension, perfusion pressure, and population-based hematocrit values. Quantitative LSFG waveforms were extracted from vessels of the same eyes, before and during IOP elevation. LSFG metrics explained most variance in RVR (R² = 0.77/P = 6.9·10^-9) and RBF (R² = 0.65/P = 1.0·10^-6), suggesting that the markers strongly reflect blood flow physiology. Higher RBF was associated with thicker RNFL (P = 4.0·10^-4) and GCC (P = 0.003), thus also verifying agreement with structural measurements. LARL was at SBP/DBP of 105/65 mmHg for the average subject without arterial hypertension and at 115/75 mmHg for the average hypertensive subject. Moreover, during IOP elevation, changes in RBF were more pronounced than changes in RVR. These observations physiologically imply that healthy subjects are already close to LARL, thus prone to hypoperfusion. In conclusion, we modeled two clinical markers and described a novel method to predict individualized autoregulation limits. These findings could improve understanding of retinal perfusion and pave the way for personalized intervention decisions, when treating patients with coexisting ophthalmic and cardiovascular pathologies.NEW & NOTEWORTHY We describe and test a new approach to quantify retinal blood flow, based on standard clinical examinations and imaging techniques, linked together with a physiological model. We use these findings to generate individualized estimates of the autoregulation range. We provide evidence that healthy subjects are closer to the lower autoregulation limit than thought before. This suggests that some retinas are less prepared to withstand hypoperfusion, even after small intraocular pressure rises or blood pressure drops.

Ocular blood flow as a clinical observation: Value, limitations and data analysis

Alterations in ocular blood flow have been identified as important risk factors for the onset and progression of numerous diseases of the eye. In particular, several population-based and longitudinal-based studies have provided compelling evidence of hemodynamic biomarkers as independent risk factors for ocular disease throughout several different geographic regions. Despite this evidence, the relative contribution of blood flow to ocular physiology and pathology in synergy with other risk factors and comorbidities (e.g., age, gender, race, diabetes and hypertension) remains uncertain. There is currently no gold standard for assessing all relevant vascular beds in the eye, and the heterogeneous vascular biomarkers derived from multiple ocular imaging technologies are non-interchangeable and difficult to interpret as a whole. As a result of these disease complexities and imaging limitations, standard statistical methods often yield inconsistent results across studies and are unable to quantify or explain a patient's overall risk for ocular disease. Combining mathematical modeling with artificial intelligence holds great promise for advancing data analysis in ophthalmology and enabling individualized risk assessment from diverse, multi-input clinical and demographic biomarkers. Mechanism-driven mathematical modeling makes virtual laboratories available to investigate pathogenic mechanisms, advance diagnostic ability and improve disease management. Artificial intelligence provides a novel method for utilizing a vast amount of data from a wide range of patient types to diagnose and monitor ocular disease. This article reviews the state of the art and major unanswered questions related to ocular vascular anatomy and physiology, ocular imaging techniques, clinical findings in glaucoma and other eye diseases, and mechanistic modeling predictions, while laying a path for integrating clinical observations with mathematical models and artificial intelligence. Viable alternatives for integrated data analysis are proposed that aim to overcome the limitations of standard statistical approaches and enable individually tailored precision medicine in ophthalmology.

Biofluid modeling of the coupled eye-brain system and insights into simulated microgravity conditions

This work aims at investigating the interactions between the flow of fluids in the eyes and the brain and their potential implications in structural and functional changes in the eyes of astronauts, a condition also known as spaceflight associated neuro-ocular syndrome (SANS). To this end, we propose a reduced (0-dimensional) mathematical model of fluid flow in the eyes and brain, which is embedded into a simplified whole-body circulation model. In particular, the model accounts for: (i) the flows of blood and aqueous humor in the eyes; (ii) the flows of blood, cerebrospinal fluid and interstitial fluid in the brain; and (iii) their interactions. The model is used to simulate variations in intraocular pressure, intracranial pressure and blood flow due to microgravity conditions, which are thought to be critical factors in SANS. Specifically, the model predicts that both intracranial and intraocular pressures increase in microgravity, even though their respective trends may be different. In such conditions, ocular blood flow is predicted to decrease in the choroid and ciliary body circulations, whereas retinal circulation is found to be less susceptible to microgravity-induced alterations, owing to a purely mechanical component in perfusion control associated with the venous segments. These findings indicate that the particular anatomical architecture of venous drainage in the retina may be one of the reasons why most of the SANS alterations are not observed in the retina but, rather, in other vascular beds, particularly the choroid. Thus, clinical assessment of ocular venous function may be considered as a determinant SANS factor, for which astronauts could be screened on earth and in-flight.

Study on the deformations of the lamina cribrosa during glaucoma

The lamina cribrosa is the primary site of optic nerve injury during glaucoma, and its deformations induced by elevated intraocular pressure are associated directly with the optic nerve injury and visual field defect. However, the deformations in a living body have been poorly understood yet so far. It is because that integral observation and precise measurement of the deformations in vivo are now almost impossible in the clinical diagnosis and treatment of glaucoma. In the present study, a new mechanical model of the lamina cribrosa is presented by using Reissner's thin plate theory. This model accurately displays the stress and deformation states in the lamina cribrosa under elevated intraocular pressure, in which the shear deformation is not presented by the previous models, however, is demonstrated to play a key role in the optic nerve injury. Further, the deformations of the structures, involving the optic nerve channels and the laminar sheets in the lamina cribrosa, are first investigated in detail. For example, the dislocation of the laminar sheets reaches 18.6μm under the intraocular pressure of 40mmHg, which is large enough to damage the optic nerve axons. The results here confirm some previously proposed clinical speculations on the deformations of the pore shape in the lamina cribrosa under elevated intraocular pressure during glaucoma. Finally, some essentially clinical questions existed during glaucoma, such as the pathological mechanism of the open-angle glaucoma with normal intraocular pressure, are discussed. The present study is beneficial to deeply understanding the optic nerve injury during glaucoma.

STATEMENT OF SIGNIFICANCE

The lamina cribrosa is the primary site of the optic nerve injury induced by elevated intraocular pressure during glaucoma. Under high intraocular pressure, the optic nerve channel near to the periphery of the lamina cribrosa (Channel A) is deformed to become into a tortuous elliptical horn from a straight cylinder, while the optic nerve channel near to the center of the lamina cribrosa (Channel B) is deformed to become into a straight horn from a straight cylinder. These deformations cause both the axoplasm flow obstacle in the axon fibers and the blocked blood flow in the capillaries which pass through the channels, and trigger the visual field defect during glaucoma.

Deep Retinal Layer Microvasculature Dropout Detected by the Optical Coherence Tomography Angiography in Glaucoma

PURPOSE

To investigate factors associated with dropout of the parapapillary deep retinal layer microvasculature assessed by optical coherence tomography angiography (OCTA) in glaucomatous eyes.

DESIGN

Cross-sectional study.

PARTICIPANTS

Seventy-one eyes from 71 primary open-angle glaucoma (POAG) patients with β-zone parapapillary atrophy (βPPA) enrolled in the Diagnostic Innovations in Glaucoma Study.

METHODS

Parapapillary deep-layer microvasculature dropout was defined as a complete loss of the microvasculature located within the deep retinal layer of the βPPA from OCTA-derived optic nerve head vessel density maps by standardized qualitative assessment. Circumpapillary vessel density (cpVD) within the retinal nerve fiber layer (RNFL) also was calculated using OCTA. Choroidal thickness and presence of focal lamina cribrosa (LC) defects were determined using swept-source optical coherence tomography.

MAIN OUTCOME MEASURES

Presence of parapapillary deep-layer microvasculature dropout. Parameters including age, systolic and diastolic blood pressure, axial length, intraocular pressure, disc hemorrhage, cpVD, visual field (VF) mean deviation (MD), focal LC defects βPPA area, and choroidal thickness were analyzed.

RESULTS

Parapapillary deep-layer microvasculature dropout was detected in 37 POAG eyes (52.1%). Eyes with microvasculature dropout had a higher prevalence of LC defects (70.3% vs. 32.4%), lower cpVD (52.7% vs. 58.8%), worse VF MD (-9.06 dB vs. -3.83 dB), thinner total choroidal thickness (126.5 μm vs. 169.1 μm), longer axial length (24.7 mm vs. 24.0 mm), larger βPPA (1.2 mm² vs. 0.76 mm²), and lower diastolic blood pressure (74.7 mmHg vs. 81.7 mmHg) than those without dropout (P < 0.05, respectively). In the multivariate logistic regression analysis, higher prevalence of focal LC defects (odds ratio [OR], 6.27; P = 0.012), reduced cpVD (OR, 1.27; P = 0.002), worse VF MD (OR, 1.27; P = 0.001), thinner choroidal thickness (OR, 1.02; P = 0.014), and lower diastolic blood pressure (OR, 1.16; P = 0.003) were associated significantly with the dropout.

CONCLUSIONS

Systemic and ocular factors including focal LC defects more advanced glaucoma, reduced RNFL vessel density, thinner choroidal thickness, and lower diastolic blood pressure were factors associated with the parapapillary deep-layer microvasculature dropout in glaucomatous eyes. Longitudinal studies are required to elucidate the temporal relationship between parapapillary deep-layer microvasculature dropout and systemic and ocular factors.

Optical Coherence Tomography Angiography Vessel Density in Glaucomatous Eyes with Focal Lamina Cribrosa Defects

PURPOSE

To investigate whether vessel density assessed by optical coherence tomography angiography (OCT-A) is reduced in glaucomatous eyes with focal lamina cribrosa (LC) defects.

DESIGN

Cross-sectional, case-control study.

PARTICIPANTS

A total of 82 patients with primary open-angle glaucoma (POAG) from the Diagnostic Innovations in Glaucoma Study (DIGS) with and without focal LC defects (41 eyes of 41 patients in each group) matched by severity of visual field (VF) damage.

METHODS

Optical coherence tomography (OCT) angiography-derived circumpapillary vessel density (cpVD) was calculated as the percentage area occupied by vessels in the measured region extracted from the retinal nerve fiber layer (RNFL) in a 750-μm-wide elliptical annulus around the disc. Focal LC defects were detected using swept-source OCT images.

MAIN OUTCOME MEASURES

Comparison of global and sectoral (eight 45-degree sectors) cpVDs and circumpapillary RNFL (cpRNFL) thicknesses in eyes with and without LC defects.

RESULTS

Age, global, and sectoral cpRNFL thicknesses, VF mean deviation (MD) and pattern standard deviation, presence of optic disc hemorrhage, and mean ocular perfusion pressure did not differ between patients with and without LC defects (P > 0.05 for all comparisons). Mean cpVDs of eyes with LC defects were significantly lower than in eyes without a defect globally (52.9%±5.6% vs. 56.8%±7.7%; P = 0.013) and in the inferotemporal (IT) (49.5%±10.3% vs. 56.8%±12.2%; P = 0.004), superotemporal (ST) (54.3%±8.8% vs. 58.8%±9.6%; P = 0.030), and inferonasal (IN) (52.4%±9.0% vs. 57.6%±9.1%; P = 0.009) sectors. Eyes with LC defects in the IT sector (n = 33) had significantly lower cpVDs than eyes without a defect in the corresponding IT and IN sectors (P < 0.05 for all). Eyes with LC defects in the ST sector (n = 19) had lower cpVDs in the ST, IT, and IN sectors (P < 0.05 for all).

CONCLUSIONS

In eyes with similar severity of glaucoma, OCT-A-measured vessel density was significantly lower in POAG eyes with focal LC defects than in eyes without an LC defect. Moreover, reduction of vessel density was spatially correlated with the location of the LC defect.

Microgravity-induced fluid shift and ophthalmic changes

Although changes to visual acuity in spaceflight have been observed in some astronauts since the early days of the space program, the impact to the crew was considered minor. Since that time, missions to the International Space Station have extended the typical duration of time spent in microgravity from a few days or weeks to many months. This has been accompanied by the emergence of a variety of ophthalmic pathologies in a significant proportion of long-duration crewmembers, including globe flattening, choroidal folding, optic disc edema, and optic nerve kinking, among others. The clinical findings of affected astronauts are reminiscent of terrestrial pathologies such as idiopathic intracranial hypertension that are characterized by high intracranial pressure. As a result, NASA has placed an emphasis on determining the relevant factors and their interactions that are responsible for detrimental ophthalmic response to space. This article will describe the Visual Impairment and Intracranial Pressure syndrome, link it to key factors in physiological adaptation to the microgravity environment, particularly a cephalad shifting of bodily fluids, and discuss the implications for ocular biomechanics and physiological function in long-duration spaceflight.

Intraocular pressure, blood pressure, and retinal blood flow autoregulation: a mathematical model to clarify their relationship and clinical relevance

PURPOSE

This study investigates the relationship between intraocular pressure (IOP) and retinal hemodynamics and predicts how arterial blood pressure (BP) and blood flow autoregulation (AR) influence this relationship.

METHODS

A mathematical model is developed to simulate blood flow in the central retinal vessels and retinal microvasculature as current flowing through a network of resistances and capacitances. Variable resistances describe active and passive diameter changes due to AR and IOP. The model is validated by using clinically measured values of retinal blood flow and velocity. The model simulations for six theoretical patients with high, normal, and low BP (HBP-, NBP-, LBP-) and functional or absent AR (-wAR, -woAR) are compared with clinical data.

RESULTS

The model predicts that NBPwAR and HBPwAR patients can regulate retinal blood flow (RBF) as IOP varies between 15 and 23 mm Hg and between 23 and 29 mm Hg, respectively, whereas LBPwAR patients do not adequately regulate blood flow if IOP is 15 mm Hg or higher. Hemodynamic alterations would be noticeable only if IOP changes occur outside of the regulating range, which, most importantly, depend on BP. The model predictions are consistent with clinical data for IOP reduction via surgery and medications and for cases of induced IOP elevation.

CONCLUSIONS

The theoretical model results suggest that the ability of IOP to induce noticeable changes in retinal hemodynamics depends on the levels of BP and AR of the individual. These predictions might help to explain the inconsistencies found in the clinical literature concerning the relationship between IOP and retinal hemodynamics.