In vivo noninvasive measurement of spatially resolved corneal elasticity in human eyes using Lamb wave optical coherence elastography

Current elastography techniques are limited in application to accurately assess spatially resolved corneal elasticity in vivo for human eyes. The air‐puff optical coherence elastography (OCE) with an eye motion artifacts correction algorithm is developed to distinguish the in vivo cornea vibration from the eye motion and visualize the Lamb wave propagation clearly in healthy subjects. Based on the Lamb wave model, the phase velocity dispersion curve in the high‐frequency is calculated to obtain spatially resolved corneal elasticity accurately with high repeatability. It is found that the corneal elasticity has regional variations and is correlated with intraocular pressure, which suggests that the method has the potential to provide noninvasive measurement of spatially resolved corneal elasticity in clinical practice.     

Energy dissipation and pulse wave attenuation in the canine carotid artery

This paper presents methods for calculating, for a segment of artery in vivo, (1) viscous and viscoelastic energy dissipation as a function of time, and (2) the viscous and viscoelastic components of the frequency-dependent attenuation coefficient. The calculations require measurement of arterial diameter and of intra-arterial pressure and flow-rate at two sites along the vessel. Viscous energy dissipation is calculated from the radius-dependent velocity shear in the lumen given by linear theory from the pressure measurements. The attenuation coefficient for a given harmonic of heart rate is calculated as half the sum of the viscous and viscoelastic components at that frequency of the energy dissipated per unit length by forwardtravelling waves, divided by the forward-wave flow work input to the segment at that frequency. Measurements in canine carotid arteries indicate that wall viscoelasticity contributes relatively little to energy dissipation per cardiac cycle and pulse wave attenuation.     

Viscoelastic properties' characterization of corneal stromal models using non-contact surface acoustic wave optical coherence elastography (SAW-OCE)

Viscoelastic characterization of the tissue-engineered corneal stromal model is important for our understanding of the cell behaviors in the pathophysiologic altered corneal extracellular matrix (ECM). The effects of the interactions between stromal cells and different ECM characteristics on the viscoelastic properties during an 11-day culture period were explored. Collagen-based hydrogels seeded with keratocytes were used to replicate human corneal stroma. Keratocytes were seeded at 8 × 10³ cells per hydrogel and with collagen concentrations of 3, 5 and 7 mg/ml. Air-pulse-based surface acoustic wave optical coherence elastography (SAW-OCE) was employed to monitor the changes in the hydrogels' dimensions and viscoelasticity over the culture period. The results showed the elastic modulus increased by 111%, 56% and 6%, and viscosity increased by 357%, 210% and 25% in the 3, 5 and 7 mg/ml hydrogels, respectively. To explain the SAW-OCE results, scanning electron microscope was also performed. The results confirmed the increase in elastic modulus and viscosity of the hydrogels, respectively, arose from increased fiber density and force-dependent unbinding of bonds between collagen fibers. This study reveals the influence of cell-matrix interactions on the viscoelastic properties of corneal stromal models and can provide quantitative guidance for mechanobiological investigations which require collagen ECM with tuneable viscoelastic properties.     

Determination of ultrasound phase velocity in trabecular bone using time dependent phase tracking technique

Ultrasound velocity is one of the key acoustic parameters for noninvasive diagnosis of osteoporosis. Ultrasound phase velocity can be uniquely measured from the phase of the ultrasound signal at a specified frequency. Many previous studies used fast Fourier transform (FFT) to determine the phase velocity, which may cause errors due to the limitations of FFT. The new phase tracking technique applied an adaptive tracking algorithm to detect the time dependent phase and amplitude of the ultrasound signal at a specified frequency. This overcame the disadvantages of FFT to ensure the accuracy of the ultrasound phase velocity. As a result, the new method exhibited high accuracy in the measurement of ultrasound phase velocity of two phantom blocks with the error less than 0.4%. 41 cubic trabecular samples from sheep femoral condyles were used in the study. The phase velocity of the samples using the new method had significantly high correlation to the bulk stiffness of the samples (r = 0.84) compared to the phase velocity measured using fast Fourier transform FFT (r = 0.14). In conclusion, the new method provided an accurate measurement of the ultrasound phase velocity in bone.     

Feasibility study of using the dispersion of surface acoustic wave impulse for viscoelasticity characterization in tissue mimicking phantoms

The aim of this study was to investigate the feasibility of utilizing the phase velocity dispersion of impulse surface acoustic wave (SAW) for viscoelasticity characterization of soft materials. The focused ultrasound transducer and the phase‐sensitive optical coherence tomography were applied as the impulse SAW inducer and tracker, respectively. Three types of liquid‐paraffin‐based cream‐in‐agar phantoms were tested. Phase velocity dispersion curve was extracted using a Fourier transform‐based phase velocity analysis algorithm. Viscoelastic parameters were obtained by fitting the dispersion curve of SAW into Rayleigh wave dispersion equation. The estimated viscoelasticity was compared with that from spherical indenter, ramp‐hold relaxation testing for validation. Both results show an increasing trend in the elasticity and decreasing trend in the viscosity with the concentration of liquid‐paraffin‐based cream increasing in the samples. The proposed method has the capability of evaluating the viscoelastic properties of homogeneous soft tissue. By combining viscoelastic parameters estimated from the proposed method, the dispersive SAW‐impulse‐based viscosity‐compensated elastography could be further developed.      

An ultrasonic technique for the measurement of the elastic moduli of human cornea

In the hopes of reducing the unpredictability associated with refractive surgical procedures and ultimately improving surgical techniques, many investigators have attempted to determine the elastic moduli of the cornea. Techniques such as stress-strain tests of corneal strips and the measurement of mercury drop displacement in a whole eye under increasing pressure have resulted in a range of values for Young's modulus from 10⁵ to 10⁷ N m⁻². Both of these methods are limited because these mechanical tests cannot be performed in the physiological state and because of the large amount of force applied during testing. We used an ultrasonic technique to determine the elastic moduli of the human cornea. Two groups of six corneas prepared under different conditions (in saline and in dextran) were examined separately and the shear waves were generated and detected in these 12 human eye bank eyes. All the waveforms were digitized and saved in files of binary format. Fast Fourier transformation (FFT) was applied to calculate the speed and attenuation of the shear wave. Using the resulting wave speeds and attenuation coefficients, the Young's moduli of the corneal samples were calculated as (5.3±1.1)×10⁶ N m⁻² and (2.0±1.0)×10⁷ N m⁻² for cornea samples prepared in saline and in dextran at 2.25 MHz, respectively.     

Phase dual‐slopes in frequency‐domain near‐infrared spectroscopy for enhanced sensitivity to brain tissue: First applications to human subjects

We present a first in vivo application of phase dual‐slopes (DS?), measured with frequency‐domain near‐infrared spectroscopy on four healthy human subjects, to demonstrate their enhanced sensitivity to cerebral hemodynamics. During arterial blood pressure oscillations elicited at a frequency of 0.1 Hz, we compare three different ways to analyze either intensity (I) or phase (?) data collected on the subject's forehead at multiple source‐detector distances: Single‐distance, single‐slope and DS. Theoretical calculations based on diffusion theory show that the method with the deepest maximal sensitivity (at about 11 mm) is DS?. The in vivo results indicate a qualitative difference of phase data (especially DS?) and intensity data (especially single‐distance intensity [SDI]), which we assign to stronger contributions from scalp hemodynamics to SDI and from cortical hemodynamics to DS?. Our findings suggest that scalp hemodynamic oscillations may be dominated by blood volume dynamics, whereas cortical hemodynamics may be dominated by blood flow velocity dynamics.     

Hydraulic input impedance measurements in physical models of the arterial wall

A white noise method was used to measure the hydraulic input impedance and transmission characteristics in physical models of an arterial system made of single, unbranched latex tubes. The experimentally obtained impedance curves show a rise in modulus and a positive phase at high frequencies in the absence of wave reflections. Using the impedance moduli in the presence of wave reflections, wave velocity and attenuation were calculated. The influence of wall nonlinearity on hydraulic impedance was also examined. It is concluded that, in the model used neither wave reflections nor wall nonlinearity can account for the deviations of the experimental impedance curves from the theoretically predicted ones. Impedance moduli in the presence of reflections may be used to study transmission characteristics (wave velocity and attenuation) of the model.     

Viscoelastic shear properties of the corneal stroma

The cornea is a highly specialized transparent tissue which covers the front of the eye. It is a tough tissue responsible for refracting the light and protecting the sensitive internal contents of the eye. The biomechanical properties of the cornea are primarily derived from its extracellular matrix, the stroma. The majority of previous studies have used strip tensile and pressure inflation testing methods to determine material parameters of the corneal stroma. Since these techniques do not allow measurements of the shear properties, there is little information available on transverse shear modulus of the cornea. The primary objectives of the present study were to determine the viscoelastic behavior of the corneal stroma in shear and to investigate the effects of the compressive strain. A thorough knowledge of the shear properties is required for developing better material models for corneal biomechanics. In the present study, torsional shear experiments were conducted at different levels of compressive strain (0–30%) on porcine corneal buttons. First, the range of linear viscoelasticity was determined from strain sweep experiments. Then, frequency sweep experiments with a shear strain amplitude of 0.2% (which was within the region of linear viscoelasticity) were performed. The corneal stroma exhibited viscoelastic properties in shear. The shear storage modulus, G′, and shear loss modulus, G″, were reported as a function of tissue compression. It was found that although both of these parameters were dependent on frequency, shear strain amplitude, and compressive strain, the average shear storage and loss moduli varied from 2 to 8 kPa, and 0.3 to 1.2 kPa, respectively. Therefore, it can be concluded that the transverse shear modulus is of the same order of magnitude as the out-of-plane Young's modulus and is about three orders of magnitude lower than the in-plane Young's modulus.     

Evaluation of a three point pressure method for the determination of arterial transmission characteristics

The mathematical expressions required to analyse wave transmission characteristics (frequency dependent phase velocity, attenuation, and reflection) in arteries, under in vivo conditions, are summarized. In addition, a three point pressure method, which theoretically permits experimental determination of the propagation constant (phase velocity and attenuation), was tested under in vitro conditions. It is found to be a potentially powerful tool for in vivo studies if used with the appropriate constraints.     

In vivo sensing of rabbit cornea by terahertz technology

A Novel scalable approach using Terahertz (THz) waves together with the electromagnetic field simulation was applied to investigate four rabbits of eight rabbit corneas in vivo. One eye of each rabbits’ corneas was edema induced; the other eye of the corneas served as the control. The simulation revealed the propagation of THz waves at a certain distance along the sub-surface of the cornea. THz spectra have been collected close to the corneal surface by deviating the direct reflection of the THz beam for the edema cornea, the reflected wave intensity for edema corneas is generally larger compared with the control cornea. Upon edema becomes severe at the end of the observation, the reflected wave intensities obtained by detector corresponding to the corneal deep stroma layer approach to the same value for all observed corneas. Good correlation is observed between central corneal thickness measurements and THz wave reflection signal intensities. Our results demonstrated that THz spectroscopy technique could obtain the information from different corneal sublayers.     

Combining particle tracking microrheology and viscometry for the study of DNA aqueous solutions

We use video particle tracking microrheology (VPTMR) in order to investigate the viscoelasticity of salmon DNA and correlate it to its steady-flow shear-thinning viscosity. Aqueous solutions of DNA are tested in a wide concentration range from the dilute to the semidilute unentangled concentration regime. The observed mean squared displacement shows power-law scaling with lag-time which is equivalent to power-law behavior of the complex modulus as a function of frequency that is, |G^*(ω)| = S ∙ ω ^α . The relaxation exponent α changes abruptly with concentration in the semidilute regime from about 1 to about 0.5 which is the exponent predicted by the Rouse model. The quasi-property S follows the scaling of viscosity for uncharged polymers near θ-conditions in the semidilute regime that is, with ν_eff = 0.50 − 0.51 . The shear-thinning exponent observed by viscometry increases gradually towards the value of 0.5 which has been predicted for Rouse chains under flow. Our findings are in agreement with recent studies of DNA solutions where DNA is treated as a model polymer and addresses the low-molar mass regime of DNA viscoelasticity. This work demonstrates that the combination of passive particle tracking with viscometry can provide a complete picture on the viscoelasticity of DNA-based biopolymer materials.     

Periodic flow of a viscous liquid in a thick-walled elastic tube

Arterial blood flow is analyzed on the basis of a realistic model consisting of a viscous liquid contained in a thick-walled viscoelastic tube. Approximate forms of the Navier-Stokes and continuity equations are derived for this model and solved in conjunction with the equations of motion of an elastic solid. Expressions are found for the displacement of the tube wall, velocity distribution, volume flow rate and phase velocity of the pressure wave. Changes in the shape of the pressure wave caused by damping and dispersion are determined, and the effect of viscoelasticity is assessed. Numerical results are presented which correspond to observed parameters of the circulatory systems of living animals.     

Assessment of the influence of viscoelasticity of cornea in animal ex vivo model using air‐puff optical coherence tomography and corneal hysteresis

Application of the air‐puff swept source optical coherence tomography (SS‐OCT) instrument to determine the influence of viscoelasticity on the relation between overall the air‐puff force and corneal apex displacement of porcine corneas ex vivo is demonstrated. Simultaneous recording of time‐evolution of the tissue displacement and air pulse stimulus allows obtaining valuable information related in part to the mechanical properties of the cornea. A novel approach based on quantitative analysis of the corneal hysteresis of OCT data is presented. The corneal response to the air pulse is assessed for different well‐controlled intraocular pressure (IOP) levels and for the progression of cross‐linking‐induced stiffness of the cornea. Micrometer resolution, fast acquisition and noncontact character of the air‐puff SS‐OCT measurements have potential to improve the in vivo assessment of mechanical properties of the human corneas.      

Enhanced spatial resolution for snapshot hyperspectral imaging of blood perfusion and melanin information within human tissue

We report a reconstruction method to achieve high spatial resolution for hyperspectral imaging of chromophore features in skin in vivo. The method utilizes an established structure‐adaptive normalized convolution algorithm to reconstruct high spatial resolution of hyperspectral images from snapshot low‐resolution hyperspectral image sequences captured by a snapshot spectral camera. The reconstructed images at chromophore‐sensitive wavebands are used to map the skin features of interest. We demonstrate the method experimentally by mapping the blood perfusion and melanin features (moles) on the facial skin. The method relaxes the constrains of the relatively low spatial resolution in the snapshot hyperspectral camera, making it more usable in imaging applications.     

Periodic flow of a viscous liquid in a thick-walled elastic tube

Arterial blood flow is analyzed on the basis of a realistic model consisting of a viscous liquid contained in a thick-walled viscoelastic tube. Approximate forms of the Navier-Stokes and continuity equations are derived for this model and solved in conjunction with the equations of motion of an elastic solid. Expressions are found for the displacement of the tube wall, velocity distribution, volume flow rate and phase velocity of the pressure wave. Changes in the shape of the pressure wave caused by damping and dispersion are determined, and the effect of viscoelasticity is assessed. Numerical results are presented which correspond to observed parameters of the circulatory systems of living animals. This research was partially supported by the National Science Foundation; it was done in part by D. K. Whirlow in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Carnegie Institute of Technology.     

An Approach to Quantifying the Multi‐Channel EEG Spatial‐Temporal Feature

Investigation of spatial characteristics in the multi‐channel EEG (electroencephalogram) has been of great importance to the fundamental and clinical medicine. Conventional methods are mostly based on the coherence and correlation analysis in time and frequency domain. The authors present the method of quantifying the global waveform complexity in EEG by analyzing the high‐dimensional state‐space trajectory constructed from the multi‐channel EEG. The resulting average complexity index ( ) is well distinct between the background (4.0 ∼ 4.5) and event (3.0 ∼ 3.5 for the focal‐sharp‐wave transient) in the 5‐channel case study. In addition, the running measurement for different electrode arrays, for a fixed number of state‐space dimension (n = 5), reveals the EEG spatial characteristic. An array composed of nearby channels with similar EEG activities tends to have a small . On the other hand, the computed increases as the array consists of electrode sites with spatially incorrelated EEG activities. Thus the method is capable of quantifying the spatial‐temporal feature of the multi‐channel EEG.     

Noninvasive detection of nanoscale structural changes in cornea associated with cross‐linking treatment

Corneal cross‐linking (CXL) using ultraviolet‐A (UVA) irradiation with a riboflavin photosensitizer has grown from an interesting concept to a practical clinical treatment for corneal ectatic diseases globally, such as keratoconus. To characterize the corneal structural changes, existing methods such as X‐ray microscopy, transmission electron microscopy, histology and optical coherence tomography (OCT) have been used. However, these methods have various drawbacks such as invasive detection, the impossibility for in vivo measurement, or limited resolution and sensitivity to structural alterations. Here, we report the application of oversampling nanosensitive OCT for probing the corneal structural alterations. The results indicate that the spatial period increases slightly after 30 minutes riboflavin instillation but decreases significantly after 30 minutes UVA irradiation following the Dresden protocol. The proposed noninvasive method can be implemented using existing OCT systems, without any additional components, for detecting nanoscale changes with the potential to assist diagnostic assessment during CXL treatment, and possibly to be a real‐time monitoring tool in clinics.     

THE LOCOMOTION OF LIMAX : I. TEMPERATURE COEFFICIENT OF PEDAL ACTIVITY.

Pedal progression of the slug Limax maximus was studied to obtain relations between wave velocity on the sole of the foot, wave frequency, the advance due to a single wave, and the velocity of vertically upward creeping. Each of the first three quantities is directly proportional to the simultaneous velocity of progression. Under comparable conditions, that is when work is done at a constant rate, the frequency of pedal waves is influenced by the temperature according to the equation of Arrhenius, with µ = 10,700 (Q ₁₀ for 11° to 21° = 2.1). The velocity of a single wave must have very nearly the same "temperature characteristic," which is found also in another case of nerve net transmission (in Renilla).     

Dynamic response of immature bovine articular cartilage in tension and compression, and nonlinear viscoelastic modeling of the tensile response

Very limited information is currently available on the constitutive modeling of the tensile response of articular cartilage and its dynamic modulus at various loading frequencies. The objectives of this study were to (1) formulate and experimentally validate a constitutive model for the intrinsic viscoelasticity of cartilage in tension, (2) confirm the hypothesis that energy dissipation in tension is less than in compression at various loading frequencies, and (3) test the hypothesis that the dynamic modulus of cartilage in unconfined compression is dependent upon the dynamic tensile modulus. Experiment 1: Immature bovine articular cartilage samples were tested in tensile stress relaxation and cyclical loading. A proposed reduced relaxation function was fitted to the stress-relaxation response and the resulting material coefficients were used to predict the response to cyclical loading. Adjoining tissue samples were tested in unconfined compression stress relaxation and cyclical loading. Experiment 2: Tensile stress relaxation experiments were performed at varying strains to explore the strain-dependence of the viscoelastic response. The proposed relaxation function successfully fit the experimental tensile stress-relaxation response, with R2 = 0.970+/-0.019 at 1% strain and R2 = 0.992+/-0.007 at 2% strain. The predicted cyclical response agreed well with experimental measurements, particularly for the dynamic modulus at various frequencies. The relaxation function, measured from 2% to 10% strain, was found to be strain dependent, indicating that cartilage is nonlinearly viscoelastic in tension. Under dynamic loading, the tensile modulus at 10 Hz was approximately 2.3 times the value of the equilibrium modulus. In contrast, the dynamic stiffening ratio in unconfined compression was approximately 24. The energy dissipation in tension was found to be significantly smaller than in compression (dynamic phase angle of 16.7+/-7.4 deg versus 53.5+/-12.8 deg at 10(-3) Hz). A very strong linear correlation was observed between the dynamic tensile and dynamic compressive moduli at various frequencies (R2 = 0.908+/-0.100). The tensile response of cartilage is nonlinearly viscoelastic, with the relaxation response varying with strain. A proposed constitutive relation for the tensile response was successfully validated. The frequency response of the tensile modulus of cartilage was reported for the first time. Results emphasize that fluid-flow dependent viscoelasticity dominates the compressive response of cartilage, whereas intrinsic solid matrix viscoelasticity dominates the tensile response. Yet the dynamic compressive modulus of cartilage is critically dependent upon elevated values of the dynamic tensile modulus.