Calibrating corneal material model parameters using only inflation data: an ill-posed problem

Corneal retardation time as an ocular hypertension disease indicator

Objective.A detailed analysis of the corneal retardation timeτas a highly related parameter to the intraocular pressure (IOP), and its plausible role as an indicator of ocular hypertension disease.Approach.A simple theoretical expression forτis derived within the corneal viscoelastic model of Kelvin-Voigt with 3 elements. This retardation time can be easily calculated from the well-known signal and pressure amplitudes of non-contact tonometers like the Ocular Response Analyzer (ORA). Then, a population-based study was performed where 100 subjects aged from 18 to 30 were analyzed (within this group, about 10% had an elevated IOP with more than 21 mmHg).Main results.A clear relationship between the corneal retardation time and the corneal-compensated intraocular pressure (IOPcc) was found, underlying the risk for ocular hypertensive (OHT) subjects with lowerτvalues to develop hypertension illnesses (due to the inability of poorly viscoelastic corneas to absorb IOP fluctuations, resulting in probable optic nerve damage).Significance.Our results might provide an useful tool to systematically discern which OHT patients (and even those with normal IOP values) are more likely to suffer glaucoma progression and, consequently, ensure an early diagnosis.

Computational homogenization of histological microstructures in human prostate tissue: Heterogeneity, anisotropy and tension-compression asymmetry

Human prostatic tissue exhibits complex mechanical behaviour due to its multiphasic, heterogeneous nature, with hierarchical microstructures involving epithelial compartments, acinar lumens and stromal tissue all interconnected in complex networks. This study aims to establish a computational homogenization framework for quantifying the mechanical behaviour of prostate tissue, considering its multiphasic heterogeneous microstructures and the mechanical characteristics of tissue constituents. Representative tissue microstructure models were reconstructed from high-resolution histology images. Parametric studies on the mechanical properties of the tissue constituents, particularly the fibre-reinforced hyper-elasticity of the stromal tissue, were carried out to investigate their effects on the apparent tissue properties. These were then benchmarked against the experimental data reported in literature. Results showed significant anisotropy, both structural and mechanical, and tension-compression asymmetry of the apparent behaviours of the prostatic tissue. Strong correlation with the key microstructural indices such as area fractions of tissue constituents and the tissue fabric tensor was also observed. The correlation between the stromal tissue orientation and the principal directions of the apparent properties suggested an essential role of stromal tissue in determining the directions of anisotropy and the compression-tension asymmetry characteristics in normal human prostatic tissue. This work presented a homogenization and histology-based computational approach to characterize the apparent mechanical behaviours of human prostatic or other similar glandular tissues, with the ultimate aim of assessing how pathological conditions (e.g., prostate cancer and benign prostatic hyperplasia) could affect the tissue mechanical properties in a future study.

Cerebral Vasculature Influences Blast-Induced Biomechanical Responses of Human Brain Tissue

Multiple finite-element (FE) models to predict the biomechanical responses in the human brain resulting from the interaction with blast waves have established the importance of including the brain-surface convolutions, the major cerebral veins, and using non-linear brain-tissue properties to improve model accuracy. We hypothesize that inclusion of a more detailed network of cerebral veins and arteries can further enhance the model-predicted biomechanical responses and help identify correlates of blast-induced brain injury. To more comprehensively capture the biomechanical responses of human brain tissues to blast-wave exposure, we coupled a three-dimensional (3-D) detailed-vasculature human-head FE model, previously validated for blunt impact, with a 3-D shock-tube FE model. Using the coupled model, we computed the biomechanical responses of a human head facing an incoming blast wave for blast overpressures (BOPs) equivalent to 68, 83, and 104 kPa. We validated our FE model, which includes the detailed network of cerebral veins and arteries, the gyri and the sulci, and hyper-viscoelastic brain-tissue properties, by comparing the model-predicted intracranial pressure (ICP) values with previously collected data from shock-tube experiments performed on cadaver heads. In addition, to quantify the influence of including a more comprehensive network of brain vessels, we compared the biomechanical responses of our detailed-vasculature model with those of a reduced-vasculature model and a no-vasculature model for the same blast-loading conditions. For the three BOPs, the predicted ICP values matched well with the experimental results in the frontal lobe, with peak-pressure differences of 4-11% and phase-shift differences of 9-13%. As expected, incorporating the detailed cerebral vasculature did not influence the ICP, however, it redistributed the peak brain-tissue strains by as much as 30% and yielded peak strain differences of up to 7%. When compared to existing reduced-vasculature FE models that only include the major cerebral veins, our high-fidelity model redistributed the brain-tissue strains in most of the brain, highlighting the importance of including a detailed cerebral vessel network in human-head FE models to more comprehensively account for the biomechanical responses induced by blast exposure.

The importance of modeling the human cerebral vasculature in blunt trauma

BACKGROUND

Multiple studies describing human head finite element (FE) models have established the importance of including the major cerebral vasculature to improve the accuracy of the model predictions. However, a more detailed network of cerebral vasculature, including the major veins and arteries as well as their branch vessels, can further enhance the model-predicted biomechanical responses and help identify correlates to observed blunt-induced brain injury.

METHODS

We used an anatomically accurate three-dimensional geometry of a 50th percentile U.S. male head that included the skin, eyes, sinuses, spine, skull, brain, meninges, and a detailed network of cerebral vasculature to develop a high-fidelity model. We performed blunt trauma simulations and determined the intracranial pressure (ICP), the relative displacement (RD), the von Mises stress, and the maximum principal strain. We validated our detailed-vasculature model by comparing the model-predicted ICP and RD values with experimental measurements. To quantify the influence of including a more comprehensive network of brain vessels, we compared the biomechanical responses of our detailed-vasculature model with those of a reduced-vasculature model and a no-vasculature model.

RESULTS

For an inclined frontal impact, the predicted ICP matched well with the experimental results in the fossa, frontal, parietal, and occipital lobes, with peak-pressure differences ranging from 2.4% to 9.4%. For a normal frontal impact, the predicted ICP matched the experimental results in the frontal lobe and lateral ventricle, with peak-pressure discrepancies equivalent to 1.9% and 22.3%, respectively. For an offset parietal impact, the model-predicted RD matched well with the experimental measurements, with peak RD differences of 27% and 24% in the right and left cerebral hemispheres, respectively. Incorporating the detailed cerebral vasculature did not influence the ICP but redistributed the brain-tissue stresses and strains by as much as 30%. In addition, our detailed-vasculature model predicted strain reductions by as much as 28% when compared to current reduced-vasculature FE models that only include the major cerebral vessels.

CONCLUSIONS

Our study highlights the importance of including a detailed representation of the cerebral vasculature in FE models to more accurately estimate the biomechanical responses of the human brain to blunt impact.

Individualized Characterization of the Distribution of Collagen Fibril Dispersion Using Optical Aberrations of the Cornea for Biomechanical Models

Purpose

The spatial distribution of collagen fibril dispersion has a significant impact on both corneal biomechanical and optical behaviors. The goal of this study was to demonstrate a novel method to characterize collagen fibril dispersion using intraocular pressure (IOP)-induced changes in corneal optical aberrations for individualized finite-element (FE) modeling.

Methods

The method was tested through both numerical simulations and ex vivo experiments. Inflation tests were simulated in FE models with three assumed patterns of collagen fibril dispersion and experimentally on three rhesus monkey corneas. Geometry, matrix stiffness, and the IOP-induced changes in wavefront aberrations were measured, and the collagen fibril dispersion was characterized. An individualized corneal model with customized collagen fibril dispersion was developed, and the estimated optical aberrations were compared with the measured data.

Results

For the theoretical investigations, three assumed distributions of fibril dispersion were all successfully characterized. The estimated optical aberrations closely matched the measured data, with average root-mean-square (RMS) differences of 0.29, 0.24, and 0.10 µm for the three patterns, respectively. The overall features of the IOP-induced changes in optical aberrations were estimated for two ex vivo monkey corneas, with average RMS differences of 0.57 and 0.43 µm. Characterization of the fibril dispersion in the third cornea might have been affected by corneal hydration, resulting in an increased RMS difference, 0.8 µm.

Conclusions

A more advanced corneal model with individualized distribution of collagen fibril dispersion can be developed and used to improve our ability to understand both biomechanical and optical behaviors of the cornea.

Biomechanics of the keratoconic cornea: Theory, segmentation, pressure distribution, and coupled FE-optimization algorithm

Understanding of the corneal biomechanical properties is of high interest due to its potential application in the early diagnosis of keratoconus (KC). KC by itself is a non-inflammatory eye disorder causes corneal structural and/or compositional anomalies. The biomechanically weakened cornea is no longer able to preserve the normal shape of the cornea against the intraocular pressure (IOP) and gradually starts to bulge outward, invoking a conical shape and subsequent distorted vision. The most popular way to measure the in vivo corneal biomechanical properties is the CorVis-ST, which enables to analyze the dynamic response of the cornea under a temporary air puff pressure. However, the complications, such as the lack of knowledge on the accurate air-puff pressure distribution on the cornea's surface as a function of the distance from the apex of the cornea as well as the time, hinder us to have a reliable estimation of the cornea's mechanical parameters. This study aims to establish patient-specific geometries of the healthy and KC corneas and calculate the pressure distribution on the cornea's surface as a function of both the distance from the apex of the cornea and time, and thereafter, the viscoelastic mechanical properties of both the healthy and KC corneas using a coupled finite element (FE)-optimization algorithm. To do that, the dynamic deformation response of six healthy and six KC corneas were measured via CorVis-ST. The videos of the in vivo deformation of the corneas under the applied air puff pressure were segmented using our segmentation algorithm to determine the anterior and posterior curvatures of the corneas during the dynamic movement of the cornea. The FE model of the corneas were established using the segmented data and subjected to a negative (pre-stress), positive IOP, and air puff pressure while the floating boundary conditions were applied to the two ends of the corneas' FE models. The simulation results were imported into a loop of FE-optimization algorithm and analyzed until the deformation amplitude at the apex of the cornea reaches to its minimum difference compared to the clinical data by CorVis-ST. The results revealed that the pressure distributions found in the literature as a function of the distance from the apex of the cornea and time unable to provide satisfactory results. Therefore, the pressure distributions both as a function of the distance and time were optimized using our coupled FE-optimization algorithm and employed to estimate the viscoelastic properties of the healthy and KC corneas. The mean percentage error (MPE) of 8.45% and 10.79% were found for the healthy and KC corneas compared to the clinical data of CorVis-ST, respectively. The results also revealed a significantly higher short-time shear modulus for the KC (62.33 MPa) compared to the healthy (37.45 MPa) corneas while the long-time shear modulus of both the healthy and KC corneas were almost the same (4.01 vs. 3.91 MPa). The proposed algorithm is a noninvasive technique capable of accurately estimating the viscoelastic mechanical properties of the cornea, which can contribute to understand the mechanism of KC development and improve diagnosis and intervention in KC.

Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method

The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.

A numerical-experimental protocol to characterize corneal tissue with an application to predict astigmatic keratotomy surgery

Tonometers are intended to determine the intraocular pressure (IOP) and the quality of corneal tissue. In contrast to the physiological state of stress of the cornea, tonometers induce non-physiological bending stress. Recently, the use of a single experiment to calibrate a set of corneal mechanical properties was suggested to be an ill-posed problem. Thus, we propose a numerical-experimental protocol that uses inflation and indentation experiments simultaneously, restricting the optimization space to circumvent the ambiguity of the fitting. For the first time, both corneal behaviors, i.e., biaxial tension (physiological) and bending (non-physiological), are taken into account. The experimental protocol was performed using an animal model (New Zealand rabbit's cornea). The patient-specific geometry and IOP were registered using a MODI topographer (CSO, Italy) and an applanation tonometer, respectively. The mechanical response was evaluated using inflation and indentation experiments. Subsequently, the optimal set of material properties is identified via an inverse finite element method. To validate the methodology, an in vivo incisional refractive surgery (astigmatic keratotomy, AK) is performed on four animals. The optical outcomes showed a good agreement between the real and simulated surgeries, indicating that the protocol can provide a reliable set of mechanical properties that enables further applications and simulations. After a reliable ex vivo database of inflation experiments is built, our protocol could be extended to humans.

Air-puff associated quantification of non-linear biomechanical properties of the human cornea in vivo

With the advent of newer techniques to correct refraction such as flapless laser procedure and collagen crosslinking, in vivo estimation of corneal biomechanical properties has gained importance. In this study, a new 3-D patient specific inverse finite element method of estimating corneal biomechanical properties from air-puff applanation was developed. The highlight of the model was inclusion of patient-specific corneal tomography, fiber dependent hyperelastic model, cross links between collagen lamellae and epithelium layer. A lumped mass, spring and dashpot model was included to model the resistance to motion and deformation of the eye globe caused by air-puff applanation. 10 normal eyes of 10 human subjects were used for the study. 3-D finite element models were constructed and custom routines were scripted for performing the inverse calculations. The model for each eye was perturbed to estimate the effect of measured intraocular pressure on the estimated biomechanical variables. The study demonstrated that the inverse method was effective in quantification of material properties and was sensitive to intraocular pressure alterations. Specifically, in vivo fiber dependent hyperelastic biomechanical properties of human corneas were estimated for the first time.