Ultrasound in Med. & Biol., Vol. -, No. -, pp. 1–9, 2013Copyright � 2013 World Federation for Ultrasound in Medicine & Biology

Printed in the USA. All rights reserved0301-5629/$ - see front matter

/j.ultrasmedbio.2013.11.009

http://dx.doi.org/10.1016

d Original Contribution

MEASUREMENT OF CORNEAL ELASTICITY WITH AN ACOUSTIC RADIATIONFORCE ELASTICITY MICROSCOPE

ERIC MIKULA,* KYLE HOLLMAN,yz DONGYUL CHAI,x JAMES V. JESTER,*x and TIBOR JUHASZ*x

*Department of Biomedical Engineering, University of California, Irvine, Irvine, California, USA; yDepartment of BiomedicalEngineering, University of Michigan, Ann Arbor, Michigan, USA; zSoundsight Research, Livonia, Michigan, USA; and xGavin

Herbert Eye Institute, University of California, Irvine, Irvine, California, USA

(Received 1 April 2013; revised 5 November 2013; in final form 6 November 2013)

AIrvine,

Abstract—To investigate the role of collagen structure in corneal biomechanics, measurement of localized cornealelasticity with minimal destruction to the tissue is necessary. We adopted the recently developed acoustic radiationforce elastic microscopy (ARFEM) technique to measure localize biomechanical properties of the human cornea.In ARFEM, a low-frequency, high-intensity acoustic force is used to displace a femtosecond laser-generatedmicro-bubble, while high-frequency, low-intensity ultrasound is used to monitor the position of the microbubble withinthe cornea. Two ex vivo human corneas from a single donor were dehydrated to physiologic thickness, embedded ingelatin and then evaluated using the ARFEM technique. In the direction perpendicular to the corneal surface, AR-FEM measurements provided elasticity values of E 5 1.39 ± 0.28 kPa for the central anterior cornea andE 5 0.71 ± 0.21 kPa for the central posterior cornea in pilot studies. The increased value of corneal elasticity inthe anterior cornea correlates with the higher density of interweaving lamellae in this region. (E-mail:emikula@uci.edu) � 2013 World Federation for Ultrasound in Medicine & Biology.

Key Words: Cornea, Biomechanics, Elasticity, Elastic modulus, Ultrasound, High-intensity focused ultrasound.

INTRODUCTION

Corneal biomechanics plays an important role in deter-mining the shape of the corneal surface and, thus, affectsthe quality of vision. The air-anterior cornea boundary ac-counts for nearly two-thirds of the eye’s refractive power,and even slight alterations on this surface can cause sig-nificant optical aberrations and reduce the quality ofvision. Abnormal biomechanical properties have impli-cations in a variety of corneal disorders such as keratoco-nus, post-LASIK ectasia, astigmatism, myopia andhyperopia.

It has been found that there is significant inter-weaving of stromal lamellae in the anterior cornea,whereas the posterior cornea has markedly less inter-weaving (Jester et al. 2010; Komai and Ushiki 1991;Radner and Mallinger 2002; Radner et al. 1998).Furthermore, lamellar interweaving markedly increasesinterlamellar cohesive strength (Smolek 1993; Smolekand McCarey 1990) and protects the anterior region ofthe cornea against extreme swelling (Muller et al. 2001).This non-uniform structure and varying mechanical

ddress correspondence to: Eric Mikula, 118 Medical Surge I,CA 92697-4375, USA. E-mail: emikula@uci.edu

1

behavior suggest an inhomogeneous spatial distributionof corneal elasticity across the corneal thickness. Thegoal of the study described here was to establish a mini-mally invasive technique for measurement of corneal elas-ticity that allows determination of localized cornealelasticity values that can be compared with corneal micro-structure at the same location. This would contribute toour understanding of how corneal elasticity and shapeare dependent on microstructure and provide insight intobiomechanical disorders such keratoconus and cornealastigmatism.

In earlier measurements of corneal elasticity, striptesting and globe inflation methods were used (Hjortdal1995, 1996; Hoeltzel et al. 1992; Jue and Maurice1986; Nyquist 1968; Shin et al. 1997; Woo et al. 1972;Zeng et al. 2001). Strip testing involves removing arectangular-shaped sample from the cornea and then me-chanically stretching the strip with increasing force tocalculate stress-strain curves. Recently, uniaxial striptesting has been used to evaluate the effect of ultravioletcollagen cross-linking on elasticity (Schumacher et al.2011). Strip testing was also used to correlate mechanicalbehavior of the cornea to stromal structure by subjectingcorneal strips to uniaxial tension along different direc-tions (Elsheikh and Alhasso 2009). Strip testing lacks

2 Ultrasound in Medicine and Biology Volume -, Number -, 2013

the ability to measure the spatial distribution of elasticproperties without physically sectioning the cornea intostrips from varying regions. Globe inflation assesses elas-ticity by measuring the displacements of external markerson the corneal surface in response to varying intraocularpressure (IOP). Although globe inflation measures amean elastic modulus for the entire cornea, or potentialelasticity variations across the corneal surface, it clearlylacks the capability to measure the depth dependence ofcorneal elasticity (Elsheikh et al. 2007; Hjortdal 1996).

Atomic force microscopy has been used to measurethe depth dependence of the elastic modulus in thesectioned cornea (Last et al. 2012). In a different study,measurement of the transverse shear modulus at varyingdepths using torsional rheometry was described (Petscheet al. 2012). However, both of these methods involvephysical sectioning of the corneal sample to access thedifferent layers and also have limitations in depth andlateral resolution. The Ocular Response Analyzer (Reich-ert, Buffalo, NY, USA) measures the deformation of thecornea in response to a brief puff of air and returnscorneal hysteresis and corneal resistance instead ofelastic modulus (Luce et al. 2005). Corneal hysteresis isa measure of the viscous dampening of the cornea inresponse to the air puff, and corneal resistance is derivedfrom corneal hysteresis (Bayoumi et al. 2010). Becausethis method does not require corneal sectioning, it hasgained limited use in clinical practice.

Various ultrasonic methods have also been devel-oped for probing the elastic properties of tissues. Shearwave elasticity imaging uses a focused acoustic radiationforce to generate shear waves within a tissue. The trans-verse strain generated by the shear waves is imaged andrelated to the shear elasticity of the tissue (Sarvazyanet al. 1998). Supersonic shear imaging also uses focusedacoustic radiation force to generate shear waves within atissue, which are imaged and related to elasticity (Bercoffet al. 2004). Supersonic shear imaging has been usedto evaluate the efficacy of photodynamic riboflavin/ultra-violet (UVA)-induced corneal collagen cross-linking(Tanter et al. 2009). Surface wave elastometry measuresthe speed of acoustic surface waves traveling parallel tothe orientation of corneal collagen fibers and relates thepropagation velocity to elasticity (Dupps et al. 2007).Similarly, optical coherence tomography has been usedto measured shear wave speed in the cornea in responseto mechanical perturbation of the corneal surface by awire (Manapuram et al. 2012). In a variation of thismethod, an acoustic radiation force was used to perturbthe tissue while imaging the tissue vibration with opticalcoherence tomography (Qi et al. 2012). In acoustic radi-ation force impulse imaging, high-intensity focused ultra-sound pulses are used to directly induce a displacement inthe tissue. The displacement of the tissue is tracked using

pulse echoes and is related to the mechanical properties ofthe tissue (Nightingale et al. 2003). In a similar method,corneal strain induced by a metal plate is imaged withan ultrasound elasticity microscope (Hollman et al.2002, 2013). The ultrasound elasticity imagingtechniques described above rely on speckle trackingmethods to create the strain images. Elastic propertiesare calculated from the complex displacement field.

In acoustic radiation force elastic microscopy (AR-FEM), a low-frequency, high-intensity acoustic force isused to displace a femtosecond laser-generated micro-bubble, and high-frequency, low-intensity ultrasound isused to monitor the position of the microbubble withinthe tissue (Erpelding et al. 2005). The elastic modulusis related to the displacement of the microbubble withinthe tissue rather than tissue strain. ARFEM has the advan-tage of improved depth resolution over other ultrasonicmethods. Additionally, elasticity is simply related to bub-ble displacement as opposed to a complex strain image.The location of the elasticity measurement dependssolely on the location of the bubble, which can be createdanywhere without the need to section the cornea.

To develop a method that can measure the 3-D dis-tribution of elastic properties throughout the cornea, weused ARFEM to measure corneal elasticity in the anteriorand posterior central cornea. The ARFEM measurementis similar to the needle indentation method, where asmall-area needle is pushed against the corneal surface,and the displacement of the surface is measured to char-acterize tissue elasticity on the surface (McKee et al.2011). The clear advantage of ARFEM is that it can mea-sure not only surface location dependence, but alsodependence of corneal elasticity on the depth across theentire thickness of the tissue without tissue sectioning.Thus, a 3-D elasticity map of the cornea can be createdand compared with local collagen lamellae structure.Because interweaving collagen fibers are especiallyabundant in the anterior regions of the cornea and theirdensity markedly decreases in the posterior region, themeasurement of localized corneal elasticity as a functionof depth across the entire thickness of the tissue is impor-tant. ARFEM was chosen because it can provide data onthe depth dependence of the corneal elasticity obtainedwith minimally invasive experiments.

METHODS

ARFEM theoryMost ultrasonic radiation force techniques rely on

tissue absorption and reflection of ultrasound energy toinduce tissue strain and generate strain images, respec-tively. Unfortunately, the cornea is neither an efficientabsorber nor an efficient reflector of ultrasound. Howev-er, the boundary between an aqueous medium, such as the

Fig. 1. Experimental setup. The corneal sample and acoustictank are placed on a 3-D positioning stage that can move inde-

pendently of the laser and transducer.

Measurement of corneal elasticity d E. MIKULA et al. 3

cornea, and a gaseous bubble is nearly a perfect reflector.The reflection coefficient between the aqueous mediumand a gaseous bubble is given by

R5

�Z22Z1

Z21Z1

�2

; (1)

where R is the reflection coefficient at the boundary, andZ1 and Z2 are the acoustic impedances of the two mate-rials (412 and 1.50 3 106 Pa$s/m for air and cornea,respectively). This results in a reflection coefficient of0.999 for the acoustic wave reaching the bubble withinthe cornea. For a sound wave traveling in an aqueous me-dium such as the cornea, nearly 100% of the incoming ul-trasound energy incident on a bubble is reflected becauseof the high acoustic impedance mismatch betweenaqueous tissue and gas in the bubble. This makes gener-ation of acoustic radiation force twice as efficient asthat for a perfect absorber, because the acoustic wave isfirst stopped and then reversed. In the experimentdescribed in this article, a bubble created in the corneawith a femtosecond laser pulse is pushed by high-intensity focused ultrasound (HIFU) in the directionperpendicular to the corneal surface, referred to as theaxial direction, and the axial displacement of the bubbleis monitored with a separate low-intensity, high-fre-quency A-scan ultrasound. The bubble is tens of micronsin diameter and vanishes within 1 min.

The elastic modulus of a viscoelastic material can becalculated from the displacement of an embedded micro-bubble in response to an acoustic radiation force using

E5Ia

2cxmax

(2)

where I is acoustic intensity, a is bubble radius, c is speedof sound in the cornea and xmax is maximum bubbledisplacement (Ilinskii et al. 2005). The intensity, I, is cali-brated before the experiment, whereas bubble radius andmaximum displacement are measured experimentally.The speed of sound, c, in water (1500 m/s) was used inall calculations in place of the speed of sound in corneafor convenience. The acoustic intensity is generated bythe HIFU element of the transducer in the form of a2-ms chirped acoustic force pulse. A chirped acousticforce pulse differs from a single-frequency tone burst inthat the frequency of the ultrasound wave is swept from1.4 to 1.7 MHz. This is done to reduce the effect of stand-ing waves in the sample chamber (Erpelding et al. 2007).The intensity of the force pulse was measured using acalibrated needle hydrophone with an active elementdiameter of 200 mm (Precision Acoustics, Dorchester,Dorset, UK). The central 500 mm of the force beamprofile at the focal plane was found to be uniform.Thus, it is reasonable to assume that the bubble, though

considerably smaller in diameter than the active elementof the hydrophone, was experiencing the same intensityas measured by the hydrophone. The spatial peak, pulseaverage intensity (Isppa) in the uniform, central area ofthe focus of the transducer was calculated from the re-corded radiofrequency (RF) signal as defined by

Isppa 5

ðt2t1

v2ðtÞdt104rcM2

LðfcÞPD; (3)

where v is the signal voltage from the hydrophone (V),r is the density of water (kg/m3), c is the speed ofsound in water (m/s), ML is the hydrophone sensitivity(V/Pa) and PD is the force pulse duration (AmericanInstitute of Ultrasound in Medicine/National ElectricalManufacturers Association [AIUM/NEMA] 2004). Thenumerical integral is calculated using the trapezoidmethod for numeric integration. Bubble radius ismeasured directly using a light microscope. It wasassumed that bubble deformation was negligible duringARFEM measurement because the bubble displacementswere less than one and a half times the bubble radius(Ilinskii et al. 2005). With eqns (1) to (3), the elasticmodulus of the cornea in the vicinity of a bubblecan be calculated by measuring the maximum displace-ment of the bubble in response to the acoustic radiationforce.

ARFEM setupFigure 1 is a schematic of the ARFEM system. A

femtosecond laser is focused into the focal volume of adual-element, confocal ultrasound transducer. A singlelaser pulse creates a bubble at a desired location in thecornea. Next, focused ultrasound from the force-generating element pushes on the bubble while the inner

Fig. 2. Electronic synchronization wiring diagram. All equipment is synchronized to a 10-MHz master clock.The digitizing board samples the radiofrequency (RF) signal at 100 MHz.

4 Ultrasound in Medicine and Biology Volume -, Number -, 2013

tracking element monitors the axial position of the bubblewith an A-scan. The sample chamber is mounted to a 3-Dmicro-stage enabling precise positioning of the bubblewithin the cornea. The laser and ultrasound foci remainfixed and aligned with each other.

A commercial Ti:sapphire femtosecond laser(Coherent, Santa Clara, CA, USA) is used to create mi-crobubbles in the samples. The laser produces 130-fspulses at 800-nm wavelength. The beam is focusedthrough a 0.3 NA objective with a working distance of40 mm. A pulse energy of 80 mJ is used for bubble crea-tion. The ultrasound transducer used to probe the micro-bubble was custom built to our specifications by theNational Institutes of Health Resource Center for Ultra-sonic Transducer Technology at the University of South-ern California. The transducer consists of two confocalelements. The bubble tracking element (inner) is a 1–3PZT crystal with a diameter of 15 mm and has a centerfrequency of 17 MHz with an f-number of 2.9. TheHIFU acoustic radiation force-generating element (outer)is a PZT-4 crystal with a 30-mm diameter and has a centerfrequency of 1.5 MHz with an f-number of 1.4. Both havea focal length of 41 mm. The Isppa of the force-generatingelement is 125 W/cm2.

Figure 2 is a schematic of thewiring for synchroniza-tion of inner and outer ultrasound elements, as well as thedigitizing board. Synchronization between the forceelement, imaging element and digitizing board is neces-sary to ensure that the position of the bubble is measuredexactly when the force is turned off. The tracking elementis driven by a commercial pulser-receiver (Model 5072PR, Panametrics, Waltham, MA, USA) at a pulse repeti-tion frequency of 5 kHz, giving one A-scan every 200ms. The pushing element is driven by an arbitrary function

generator (Model 3314a, Agilent Technologies, Palo Alto,CA, USA) feeding a 50-dB amplifier (ENI Model 240 L,MKS Instruments, Wilmington, MA, USA). The chirpedacoustic force pulse waveform is created in MATLAB(The MathWorks, Natick, MA, USA) and exported tothe function generator. The waveform consists of a trainof 10 force pulses, each 160 ms in duration and swept infrequency from 1.4 to 1.7 MHz, with a 40-ms delay be-tween force pulses (2 ms total). Thus, the strong forcepulse, which is a source of noise, is turned off when the re-flected tracking pulse reaches the transducer. RF signalsfrom the tracking element are captured by a digitizingboard (Agilent Technologies) on a PC sampling at 100MS/s. All components are synchronized to a 10-MHzmas-ter clock. Furthermore, the A-scan tracking pulses are syn-chronized with an additional tunable delay to ensure thatthey are triggered during the 40-ms delay between forcepulses. This drastically reduces noise in the A-scan and en-ables tracking of the bubble while it is being displaced. InFigure 3 is the A-scan, HIFU synchronization scheme.

Sample preparationTwo human cadaver eyes from the same donor were

obtained from the San Diego Eye Bank. The eyes werepreserved within 24 h of death and stored no longer than5 d. Before the experiment, corneas were thinned to aphysiologic thickness of 500–570 mm by inflating theintact globe with 20% Dextran solution at 20 mm HgIOP. Central corneal thickness was monitored using aReichert IOPAC pachymeter (Reichert, Depew, NY,USA). The cornea was then excised, leaving a 2-mmscleral rim, and embedded in a 7.5% gelatin gel withinthe acoustic chamber. To avoid any effect of corneal hy-dration on the experiments, corneal thickness was also

Fig. 3. Imaging pulses are delayed to coincide with notches between chirped force pulses to remove noise from theA-scans.

Measurement of corneal elasticity d E. MIKULA et al. 5

monitored during the ARFEM studies by the echoes of thetracking pulse from the anterior and posterior corneal sur-faces. Experiments were performed only when the cornealthickness was in the physiologic range 500 to 570 mm.

Gelatin phantomsAcoustic radiation force elasticmicroscopymeasure-

ments were conducted in gelatin phantoms and comparedagainst needle indentation measurements in the samephantoms. In this method, a flat-ended cylinder connectedto a load cell is used to indent the sample. The elasticmodulus is calculated based on the recorded stress-strainrelationship and the geometry of the indenting cylinder(McKee et al. 2011). Measurements were made in gelswith concentrations of 5%, 7.5% and 10% by weight.

Fig. 4. Sample M-scan from a swollen porcine cornea illus-trating the position (y-axis) of the bubble as a function of time(x-axis), as well as the force pulse (vertical band). The y-axisspans about 2 mm, and the x-axis, 9 ms. The sample 1-D slicerepresents just one of the A-scans at 7-ms time delay taken

from the 2-D image.

Data acquisition and analysisThe raw 1-DRF data are sectioned and stacked into a

2-D array, where each column represents a single A-scan.The pulser-receiver triggers the A-scan at a 5-kHz pulserepetition frequency, resulting in a 1-D image of thecornea and bubble in every 200 ms. Thus, the resultingM-scan describes the time evolution of the bubble move-ment in 200-ms steps. A typical M-scan measurement isillustrated in Figure 4. This figure was derived from aporcine eye and is used here solely for visualization ofthe actual measurement. The porcine cornea is far thickerand softer than the human cornea, allowing for easierdistinction of the anterior, posterior and bubble surfaces.The vertical checkered band is the saturated acousticradiation force pulse as detected by the tracking element.This image was obtained without notched force pulseA-scan synchronization for the purpose of illustratingthe force pulse during the measurement. With the notchedsynchronization, the saturated acoustic band is not presentin the data. The figure indicates the position of the ante-rior/posterior corneal surfaces and microbubble before,during and after the chirped force pulse. The small inset

figure is one sample A-scan taken from the 2-D image.The bubble is displaced in the direction of the acousticforce and returns to its original position once the forcepulse is turned off.

In Figure 4 the vertical acoustic radiation force bandis masking the position of the bubblewhile the force pulseis on. A high-pass (10-MHz) filter is applied to the data inpost-processing to remove the low-frequency data con-tained in the vertical band. Additionally, a 1-MHz high-pass hardware filter on the pulser-receiver is used tofurther reduce the noise caused by the force pulse. Thehigh-pass filtering along with the notched acoustic forcepulse waveform described earlier removes nearly all ofthe acoustic force pulse signal and noise from theA-scan. As result, bubble position can be measured dur-ing the force pulse. Figure 5 illustrates the value of usingthe notched force pulse waveform. Figure 5a illustratesthe data pre-processed with only the high-pass filter,and Figure 5b, the high-pass filtered data collected usingthe notched force pulse waveform approach.

Bubble displacement is calculated from the RF datausing a 1-D cross-correlation method between a reference

Fig. 5. (a) Noise leakage from the high-intensity focused ultra-sound element into the A-scan, obscuring the position of thebubble during the force chirp. (b) Removal of this noise by syn-

chronization of the A-scan with a notched force pulse.

6 Ultrasound in Medicine and Biology Volume -, Number -, 2013

bubble A-scan and the remaining A-scans. The cross-correlation algorithm computes the time lag between sub-sequent A-scans of the bubble and compares them withthe reference A-scan (original bubble position). To ac-count for movement of the cornea as a whole within thegel in response to the acoustic force pulse, the displace-ment of the corneal surface is subtracted from thedisplacement of the bubble when calculating themaximum bubble displacement.

Fig. 6. Elastic moduli of 5%, 7.5% and 10% gels as measuredand needle indentation. Solid lines r

RESULTS

Figure 6 compares ARFEM and needle indentationelasticity measurements in gels of varying concentration.ARFEM measured elastic moduli of 0.82 6 0.09,1.09 6 0.04 and 1.59 6 0.16 kPa in the 5%, 7.5% and10% gels, respectively. The indentationmethod measured1.116 0.03, 2.286 0.08 and 3.456 0.12 kPa for the 5%,7.5% and 10% gels. Both methods indicate a linear in-crease in stiffness with concentration.

Figure 7 illustrates the averaged displacement path of10 bubbles in the axial direction as a function of time inthe anterior 100 mm of the central region of the twohuman cadaver corneas. The mean bubble diameter wasmeasured to be 226 2 mm. The average bubble displace-ment and elastic modulus in the anterior region of the twocorneas were 3.46 0.60 mm and 1.396 0.28 kPa, respec-tively. The anterior elastic modulus was 1.42 6 0.30 kPain eye 1 and 1.36 6 0.30 kPa in eye 2. For comparison,measurements were also made 150 mm from the posteriorsurface of the central region in the same corneas. Theaverage bubble displacement and elastic modulus in theposterior region of the two corneas were 6.9 6 1.7 mmand 0.71 6 0.21 kPa, respectively. The posterior elasticmodulus was 0.70 6 0.21 kPa in eye 1 and0.72 6 0.24 kPa in eye 2.

DISCUSSION

It is interesting to compare elasticity values obtainedin this experiment with values generated from othermethods. Recently, articles describing measurementswith needle indentation techniques on corneal flaps

by acoustic radiation force elastic microscopy (ARFEM)epresent linear fits to the data.

Fig. 7. Averaged displacement path of 10 bubbles as a functionof time in the central anterior of the two human cadaver corneas.The high-intensity focused ultrasound element (HIFU) force isturned on between the 1- and 3-ms marks. The mean displace-ment was 3.4 6 0.6 mm, corresponding to an elastic modulus

of E 5 1.39 6 0.28 kPa.

Measurement of corneal elasticity d E. MIKULA et al. 7

(Winkler et al. 2011) and with atomic force microscopy(Last et al. 2012) have reported elastic moduli rangingfrom roughly 0.5 kPa to .100 kPa. Winkler et al. re-ported average corneal elasticity values in the axial direc-tion from roughly 0.75 kPa in the posterior cornea to1.75 kPa in the anterior region using the needle indenta-tion method. These results are in good agreement withelasticity values obtained with ARFEM. Additionally,both techniques indicate that the stiffness of the anteriorcornea is approximately twice of that of the posteriorsegment. This observation is consistent with the signifi-cant increase in interweaving fibrils present in the ante-rior cornea (Jester et al. 2010; Komai and Ushiki 1991;Radner and Mallinger 2002; Radner et al. 1998).

Acoustic radiation force elastic microscopy and nee-dle indentation data for gelatin phantoms were alsosimilar. Although there are some small discrepancies inthe absolute values, both needle indentation and ARFEMreveal the same linear dependence of elasticity on gelatinconcentration. The small discrepancies in absolute valuemay be explained by the fact that needle indentation mea-surements are performed on the surface of the gel,whereas ARFEM measurements are bulk measurementsinside the material.

It is rather difficult to compare ARFEM data with re-sults obtained with other elastometry methods. Forexample, torsional rheometry (Petsche et al. 2012) mea-sures the transverse shear modulus, which is considerablydifferent than the axial direction measured by ARFEM.Well-established methods such as strip testing and globeinflation measure elasticity along the direction of thecorneal lamellae, where tensile strength is high, and arenot comparable to ARFEM. Likewise, ultrasonic shear

wave imaging and surface wave elastometry measurepropagation along the axis parallel to corneal lamellae.However, ARFEM data are in reasonable agreementwith results obtained with elastometry methods testingthe same axial component of corneal elasticity, such asneedle indentation.

One technical challenge with ARFEM measure-ments is the inconsistent bubble displacements intro-duced by standing acoustic waves. Standing wavesoccur when incoming acoustic waves interfere withearlier waves reflected from the chamber bottom. Theincoming waves can either constructively or destructivelyinterfere to cause standing positive and negative pressurepeaks, respectively. In addition to sweeping the frequencyof the force pulse, we used a long-working-distancefocusing objective. The long focal length enabled the tis-sue sample to be mounted far above the optical window atthe bottom of the acoustic chamber. Thus, the divergingreflected acoustic waves were too sparse to significantlyinterfere with incoming waves in the sample plane. Thesetwo improvements, along with the notched acousticforce/tracking pulse synchronization, allowed for predict-able bubble displacement, as well as clear imaging of thebubble trajectory. The bubble response in the cornea us-ing ARFEM was similar in shape to the response pre-dicted by the classic Voigt model, with relaxation of thedisplacements following an exponential path (Walkeret al. 2000).

Another technical challenge with the ARFEM tech-nique is the measurement of transverse elasticity in the di-rection of the corneal lamellae parallel to the cornealsurface. With the current technique, elasticity can bemeasured only in the axial direction, orthogonal to thecorneal surface. To accommodate measurements in thetransverse direction along the corneal lamellae, the trans-ducer would need to be set to a non-orthogonal angle.This will allow measurements of an angled bubbledisplacement, which can be broken down into compo-nents, giving the axial and transverse elastic moduli.

In vivo applications are prevented with the currentsetup because the laser beam and ultrasound are posi-tioned on opposing sides of the sample. However, rede-sign and rearrangement of the ultrasound transducerand focusing optics to the same side of the tissue mayallow for in vivo applications. Because the current setupprevented us from measuring full globes, the effect ofphysiologic IOP levels on elasticity could not be investi-gated. However, conclusions are drawn from relativevalues of elasticity at different locations, which may notbe influenced by a lack of IOP.

Although current measurements were performed oncadaver corneas, after the redesign mentioned in the pre-vious paragraph, the ARFEM system has potential forclinical applications if ultrasound and laser intensity

8 Ultrasound in Medicine and Biology Volume -, Number -, 2013

values are within tolerable limits. Toward this end, wecompared our intensity values with U.S. Food and DrugAdministration safety guidelines. Although the femto-second laser beam intensity used in the experiment isbelow the 0.5-W safety limit, the spatial peak, pulseaverage intensity of the ultrasonic push pulse is approxi-mately four times the Food and Drug Administrationlimit of 28 W/cm2. We believe that further optimizationof the ARFEM technique will result in a substantialdecrease in the required push pulse intensity, as well asthe applied laser power, allowing for potential clinical ap-plications. For example, in the current experimentalsetup, a pulse energy of 80 mJ was used to create the mi-crobubble, whereas typically, pulse energies of just a fewmicro-joules are sufficient to create optical breakdown inthe cornea. The increase in the laser energy required maybe explained by the fact that the laser was focusedthrough 4 cm of gelatin before entering the cornea.Because the gelatin surface does not have a controlled op-tical quality, considerable wavefront distortions are intro-duced into the beam. This may result in increases in thedimensions of the focal spot, hence the need for higherpulse energies to reliably create microbubbles. Therefore,engineering a beam coupling interface with good opticalquality will allow a considerable decrease in the appliedlaser power.

CONCLUSIONS

We have illustrated that ARFEM can measure local-ized axial elastic modulus in the human cornea withoutconsiderably disturbing its mechanical structure. Thetechnique has high lateral and axial resolution that willallow mapping of elasticity throughout the cornea. Addi-tionally, ARFEM may be re-engineered to measure elas-ticity in vivo, allowing potential future clinicalapplications in the early diagnosis of mechanicallycompromised corneas, such as those with keratoconusor corneal ectasia after LASIK surgery.

Acknowledgments—This research was supported by National Institutesof Health Grant R01 EY014163 and Research to Prevent Blindness, Inc.

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