the technical details of the arfem system used in this study have been described in detail previously . briefly , the system essentially is comprised of three core components , a femtosecond laser , a dual element ultrasound transducer , and a sample chamber . santa clara , ca , usa ) that produces 130 fs pulses at a wavelength of 800 nm . the ultrasound transducer has two elements , an outer low frequency , high intensity force - generating element , and in an inner low intensity , high frequency tracking , or a - scan element . the outer force - generating , or pushing , element has a central frequency of 1.5 mhz and a spatial peak , pulse average intensity ( isppa ) of 125 watts / cm . the a - scan element is driven by a commercial pulser - receiver ( panametrics model 5072pr , waltham , ma , usa ) at a pulse repetition frequency of 5 khz . the pushing element is driven by an arbitrary function generator ( model 3314a ; agilent technologies , palo alto , ca , usa ) feeding into a 50 db amplifier ( eni model 240l ; mks instruments , wilmingtom , ma , usa ) . the focal point of the laser is fixed in space , while the ultrasound transducer can be moved in three dimensions . to ensure that the optical and ultrasonic elements are confocal , the a - scan signal from a laser - created bubble was maximized by adjusting the alignment of the ultrasonic transducer . the 3-d sample stage then is moved independently of the optical and ultrasonic components , which are focused to the same location . the corneal sample is embedded in gelatin within the sample chamber , while the rest of the chamber is filled with degassed , distilled water for acoustic coupling . the chamber itself is mounted to a 3-d microstage , allowing for the placement of the microbubble anywhere within the cornea . the laser is focused through a 0.3 na objective creating a microbubble ( d = 22  2 m ) within the cornea with a single pulse . once the bubble has been created and confirmed via a - scan , the measurement sequence is initiated manually and the outer element of the ultrasound transducer generates an acoustic radiation force chirp 2 ms in duration . the acoustic force displaces the microbubble within the cornea , while the displacement of the bubble is tracked by the inner ultrasound element with an a - scan at a pulse repetition frequency of 5 khz . thus , the position / movement of the bubble in response the acoustic radiation force is measured every 200 s . the elastic modulus is inversely proportional to the bubble displacement and is calculated using : 
 where  i  is the acoustic intensity ,  a  is the bubble radius , the acoustic intensity and bubble radius are calibrated before the experiment , while maximum bubble displacement is measured experimentally with an a - scan . the raw a - scan rf data are filtered using a 10 mhz high pass filter , and then processed using 1-d cross - correlation between a reference bubble a - scan and the remaining pulse - echoes . the speed of sound m / s ) was used in all calculations in place of the speed of sound in cornea for convenience . six human cadaver eyes from three donors were obtained from the san diego eye bank . samples were refrigerated and measurements were performed within 3 days of death on average , but no later than 5 days . basic donor data are provided in the table . before the experiment , corneas were thinned to a physiologic thickness of 500 to 570 m by inflating the intact globe with 20% dextran solution at 20 mm hg iop . the samples were placed into a suction holder whereby the posterior portion of the globe created a seal with the holder allowing a mild suction force to hold the sample in place . the sample was oriented such that the central corneal surface was orthogonal to the ultrasonic tip of the pachymeter ( reichert , inc . , the cornea then was excised , leaving a 2-mm scleral rim , and embedded in a 7.5% gelatin gel within the sample chamber . experiments were performed only when the corneal thickness was in the physiologic 500 to 570 m range . we obtained arfem measurements in the central cornea ( 0 mm ) , at 2.5 mm ( mid ) , and at 5 mm ( peripheral ) toward the limbus . at each of these locations , the cornea was placed on the gelatin surface in such a way that half of the cornea was flat against the gelatin surface , with the other half curving upward . this was necessary due to the fact that the corneal surface must be perpendicular to the laser beam for optimal bubble creation . laying the half cornea flat against the gel allowed measurements to be made in the central and peripheral regions without having to reorient the cornea . during the measurements , the cornea was oriented so that the acoustic force and resultant microbubble displacements were perpendicular to the corneal surface . corneal orientation and arfem measurement locations . measurements are made at 0 ( center ) , 2.5 ( mid ) , and 5 ( peripheral ) mm . at each radial position , the sample is flattened against the surface of the gel so that measurements can be made at multiple locations without having to reposition the cornea . the technical details of the arfem system used in this study have been described in detail previously . briefly , the system essentially is comprised of three core components , a femtosecond laser , a dual element ultrasound transducer , and a sample chamber . santa clara , ca , usa ) that produces 130 fs pulses at a wavelength of 800 nm . the ultrasound transducer has two elements , an outer low frequency , high intensity force - generating element , and in an inner low intensity , high frequency tracking , or a - scan element . the outer force - generating , or pushing , element has a central frequency of 1.5 mhz and a spatial peak , pulse average intensity ( isppa ) of 125 watts / cm . the a - scan element is driven by a commercial pulser - receiver ( panametrics model 5072pr , waltham , ma , usa ) at a pulse repetition frequency of 5 khz . the pushing element is driven by an arbitrary function generator ( model 3314a ; agilent technologies , palo alto , ca , usa ) feeding into a 50 db amplifier ( eni model 240l ; mks instruments , wilmingtom , ma , usa ) . the focal point of the laser is fixed in space , while the ultrasound transducer can be moved in three dimensions . to ensure that the optical and ultrasonic elements are confocal , the a - scan signal from a laser - created bubble was maximized by adjusting the alignment of the ultrasonic transducer . the 3-d sample stage then is moved independently of the optical and ultrasonic components , which are focused to the same location . the corneal sample is embedded in gelatin within the sample chamber , while the rest of the chamber is filled with degassed , distilled water for acoustic coupling . the chamber itself is mounted to a 3-d microstage , allowing for the placement of the microbubble anywhere within the cornea . the laser is focused through a 0.3 na objective creating a microbubble ( d = 22  2 m ) within the cornea with a single pulse . once the bubble has been created and confirmed via a - scan , the measurement sequence is initiated manually and the outer element of the ultrasound transducer generates an acoustic radiation force chirp 2 ms in duration . the acoustic force displaces the microbubble within the cornea , while the displacement of the bubble is tracked by the inner ultrasound element with an a - scan at a pulse repetition frequency of 5 khz . thus , the position / movement of the bubble in response the acoustic radiation force is measured every 200 s . the elastic modulus is inversely proportional to the bubble displacement and is calculated using : 
 where  i  is the acoustic intensity ,  a  is the bubble radius , the acoustic intensity and bubble radius are calibrated before the experiment , while maximum bubble displacement is measured experimentally with an a - scan . the raw a - scan rf data are filtered using a 10 mhz high pass filter , and then processed using 1-d cross - correlation between a reference bubble a - scan and the remaining pulse - echoes . the speed of sound m / s ) was used in all calculations in place of the speed of sound in cornea for convenience . 
  arfem experimental setup . six human cadaver eyes from three donors were obtained from the san diego eye bank . samples were refrigerated and measurements were performed within 3 days of death on average , but no later than 5 days . basic donor data are provided in the table . before the experiment , corneas were thinned to a physiologic thickness of 500 to 570 m by inflating the intact globe with 20% dextran solution at 20 mm hg iop . the samples were placed into a suction holder whereby the posterior portion of the globe created a seal with the holder allowing a mild suction force to hold the sample in place . the sample was oriented such that the central corneal surface was orthogonal to the ultrasonic tip of the pachymeter ( reichert , inc . , the cornea then was excised , leaving a 2-mm scleral rim , and embedded in a 7.5% gelatin gel within the sample chamber . experiments were performed only when the corneal thickness was in the physiologic 500 to 570 m range . we obtained arfem measurements in the central cornea ( 0 mm ) , at 2.5 mm ( mid ) , and at 5 mm ( peripheral ) toward the limbus . at each of these locations , the cornea was placed on the gelatin surface in such a way that half of the cornea was flat against the gelatin surface , with the other half curving upward . this was necessary due to the fact that the corneal surface must be perpendicular to the laser beam for optimal bubble creation . laying the half cornea flat against the gel allowed measurements to be made in the central and peripheral regions without having to reorient the cornea . during the measurements , the cornea was oriented so that the acoustic force and resultant microbubble displacements were perpendicular to the corneal surface . measurements are made at 0 ( center ) , 2.5 ( mid ) , and 5 ( peripheral ) mm . at each radial position , the sample is flattened against the surface of the gel so that measurements can be made at multiple locations without having to reposition the cornea . the mean elastic moduli were 4.2  1.2 , 3.4  0.7 , and 1.9  0.7 kpa in the central , mid , and peripheral regions , respectively . the mean elastic moduli were 2.3  0.7 , 1.6  0.3 , and 2.9  1.2 kpa in central , mid , and peripheral regions , respectively . while the anterior cornea was approximately twice as stiff as the posterior cornea in the central and mid cornea , the anterior elastic modulus decreased with respect to the posterior elastic modulus in the peripheral cornea . multiple comparisons were performed using anova in matlab ( mathworks , natick , ma , usa ) to determine which location - specific elastic moduli means were different from the others . statistically significant differences in elasticity could be established between the following regions : the central anterior cornea is stiffer than any other region ( p = 0.05 ) ; the mid anterior cornea is stiffer than the mid posterior , central posterior , and peripheral anterior cornea ( p = 0.05 ) ; and the peripheral posterior cornea is stiffer than the central posterior , mid posterior , and peripheral anterior cornea ( p = 0.05 ) . no statistically significant differences could be established when comparing arfem elasticity measurements in between all other regions . elastic modulus in the anterior 150 m of cornea from the center to the periphery . elastic modulus in the posterior 150 m of cornea from the center to the periphery . the arfem technique used in this study has the significant limitation of being unable to measure the elasticity distribution in the mechanically - loaded cornea and intact globe . given the nature of the current arfem device , the cornea must be excised from the globe and placed between the laser objective and ultrasound . additionally , the cornea is laid flat against the gelatin surface in such a way that half of the cornea curves unnaturally upward . the mechanical effect of this curvature is assumed to be negligible based on previous measurements of the central cornea with the natural radius of curvature preserved showing the same 2:1 ratio in elasticity between the anterior and posterior regions . we found the elasticity in the central anterior cornea to be nearly twice the elasticity in the central posterior cornea . similar results were found using needle indentation , which revealed the same 2:1 ratio in elastic modulus between the anterior and posterior central cornea . likewise , the mid anterior cornea was twice as stiff as the mid posterior cornea . structurally , the anterior cornea possesses highly interwoven collagen structure compared to the relative homogeneity in the posterior . despite this apparent correlation between microstructure and elasticity in the central and mid cornea the peripheral anterior cornea was approximately half as stiff as the central anterior , while the peripheral posterior cornea was approximately 30% stiffer than the central posterior cornea . it is interesting to note that interlamellar cohesive strength in the stroma is twice as strong in the periphery as it is centrally . though arfem does not measure interlamellar cohesive strength , both results suggest a biomechanical change in the peripheral cornea . furthermore , the peripheral anterior elasticity is approximately 2/3 that of the peripheral posterior cornea . it appears as though in the periphery , the anterior and posterior corneas nearly reverse elastic moduli relative to each other . structural data in the literature anterior collagen interweaving , as measured by collagen lamellae angle relative to the corneal surface using nonlinear optical high resolution macroscopy ( nlo - hrmac ) , did not detect a significant difference between the central and peripheral cornea . the wrinkles on the posterior surface in figure 6a are artifacts from the mounting of the sample . figures 6b to 6d show that the anterior interweaving relative to posterior collagen orientation is preserved from the center to the periphery . structural differences in the periphery of the cornea may be masked by the shifting orientation of lamellae from central to peripheral . structurally , the cornea is changing as it nears the limbus , with collagen fibers adopting a more tangential ( circumferential ) orientation in the periphery , as imaged by wide angle x - ray scattering . collagen fibers in this orientation would not have been detected in the previous work by nlo hrmac , as the technique does not image en face collagen fibers . while the posterior lamellae continue uninterrupted into the sclera , the anterior interwoven region seems to end abruptly at the limbus . ( b  d ) center , middle , and peripheral measurement locations , respectively . recently , micro focus x - ray scattering data were used to determine the inclination angles of lamellae relative to the corneal surface as a measure of lamellar interweaving . as expected , inclination angles in the central anterior cornea were the greatest . the same study found that inclination angles in the posterior peripheral cornea were high when compared to the posterior central cornea , suggesting more interweaving in the posterior peripheral cornea . this finding seems to support our observation of an increasing elastic modulus in the peripheral posterior cornea . the effect of increasing inclination angle in the peripheral stroma along with the effect of tangentially oriented collagen fibers on local elasticity is unknown . as the lamellae exit the biomechanical effects of the transition or insertion of collagen lamellae into the sclera also are unknown . furthermore , the periphery may be subject to different swelling conditions because the peripheral edge of the sample is exposed directly to the gelatin medium . the cornea is , indeed , thicker in the periphery and hydration differences between the anterior and posterior could be exacerbated to the proximity of the measurements to the edge of the sample . in addition to collagen microstructure , proteoglycan ( pg ) distribution throughout the cornea also may have an effect on local elasticity as measured by arfem . specifically , it is pertinent to explore any differences in pg distribution between the anterior and posterior cornea , centrally and peripherally . a pg consists of a core protein with one or more covalently attached glycosaminoglycans ( gag ) . the gag is highly polar , negatively charged , and , as such , binds water . the concentration of keratan sulfate , the most prominent pg in the cornea , increases from anterior to posterior in the central cornea . furthermore , stromal swelling is caused almost entirely by the gel pressure ( swelling pressure ) generated by negatively charged proteoglycans . when these findings are considered along with the highly interwoven structure of the anterior cornea , it seems reasonable that the anterior cornea is resistant to edema compared to the posterior cornea . our results also indicated that the peripheral anterior corneal elasticity is approximately half that of the central anterior cornea . with studies showing conflicting accounts of the amount of interweaving in the periphery , , it would be interesting to know the trend in pg distribution in the peripheral cornea . it is possible that local pg concentration and the resultant swelling pressure have an effect on local elasticity as measured by arfem . unfortunately , the literature does not reveal many telling details about the differences in pg concentration between the central and peripheral cornea . one study looked at total soluble protein concentration between the anterior and posterior cornea , traversing across the cornea from the limbus to the central cornea . they found that total soluble protein concentration in the peripheral anterior cornea was nearly twice that of the central anterior cornea . though it may appear that this result corroborates our findings between central and peripheral elasticity , the correlation could be entirely coincidental since they were not specifically measuring pg distribution . to truly resolve this issue , a specific measurement of the axial pg gradient in the peripheral cornea would need to be performed . we found that there is a unique distribution of elasticity axially and radially throughout the cornea . while arfem results in the central cornea are in reasonable agreement with other techniques , including needle indentation and torsional rheometry , lack of mechanical data in the peripheral cornea makes comparisons difficult . however , it is clear that the full picture of corneal biomechanics is quite broad , from complex and inhomogenous collagen microstructure to varying concentration of pg throughout the cornea . a better understanding of these variables along with elasticity measurements , especially in the peripheral cornea , would certainly help in completing the picture . future modifications of arfem to automate the measurement procedure , specifically the movement of the sample with respect to the confocal volume , will result in an elasticity map with greater spatial density and may help provide this information .
purposethe biomechanical properties of the cornea have an important role in determining the shape of the cornea and visual acuity . 
 since the cornea is a nonhomogeneous tissue , it is thought that the elastic properties vary throughout the cornea . 
 we aim to measure a map of corneal elasticity across the cornea.methodsan acoustic radiation force elasticity microscope ( arfem ) was used to create a map of corneal elasticity in the human cornea . 
 this arfem uses a low frequency , high intensity acoustic force to displace a femtosecond laser - generated microbubble , while using a high frequency , low intensity ultrasound to monitor the position of the microbubble within the cornea . from the displacement of the bubble and the magnitude of the acoustic radiation force 
 , the local value of corneal elasticity is calculated in the direction of the displacement . 
 measurements were conducted at 6 locations , ranging from the central to peripheral cornea at anterior and posterior depths.resultsthe mean anterior elastic moduli were 4.2  1.2 , 3.4  0.7 , and 1.9  0.7 kpa in the central , mid , and peripheral regions , respectively , while the posterior elastic moduli were 2.3  0.7 , 1.6  0.3 , and 2.9  1.2 kpa in the same radial locations.conclusionswe found that there is a unique distribution of elasticity axially and radially throughout the cornea .