OF BACKSCATTEKED SPECKLE PATTERN ^' S

IN LASER SPECKLE RHEOLOGY OF BIOLOGICAL FLUIDS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority from atsd benefit of U.S. Provisional Patent

Application Nos. 61/701,819 titled "Compensation for Multiple Scattering in Laser Speckle Rheoiogy of Biological Fluids" and filed on September 17, 2012 and 61 / 738,808 title "Evaluation and Correction for optical Scattering Variations in Laser Speckle Rheoiogy of Biological Fluids" and filed December 18, 2012. The disclosure of each of the above-mentioned provisional applications is incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[ΘΘ02] This invention was made with government support under Grants Numbers R2, 1 HL 088306,

R21 HL 088306-02S1, and U54 EB 015408-01-8416 awarded by the Nffl. The government has certain rights in the invention,

TECHNICAL FIELD

[CI883] The present invention relates to optical systems and methods for the measurement and monitoring of the material properties of biological fluids and, in particular, to a means for compensation for multiple scattering and or absorption in laser speckle rheoiogy (LSR) of the biological fluids during such monitoring.

BACKGROUND

[0ΘΘ4] Typically, the progression of a disease in the biological tissue is accompanied by changes in tissue mechanical properties. Therefore, the availability of the modality' effectuating the measurement of the mechanical properties of tissue in situ, in its native state, would provide critical diagnostic information, laser Speckle Rheoiogy (LSR) is an optical approach that enables non-contact probing of tissue viscoelasticity. In LSR, tissue is illuminated by a mono-chromatic laser source and a high-speed CMOS camera is used to capture temporal intensity fluctuations of back-scattered laser speckle patterns. The temporal speckle intensity fluctuations are exquisitely sensitive to the displacements of light scattering centers undergoing Browman motion, and the extent of this thermal motion reflects the viscoeiastic properties of the surrounding medium. Speckle frames acquired by the high-speed camera are analyzed to obtain She speckle intensity temporal autocorrelation curve, g ₂ (t). The gift) curve is a measure of the rate of temporal speckle intensity ilucttiations and is closely related to the extent and time scales of particle motion, and in turn mechanical properties of the medium, defined by the viscoelastic modulus, G*fco) = G'fco) + i 0"(ω), which defines the mechanical behavior of materials. Traditionally, G*(e>) is measured using a mechanical rheometer, by evaluating the ratio of an applied oscillatory stress to the corresponding induced strain in the specimen, over a limited oscillation frequency range. Using the LSR, the viscoelastic modulus, θ*(ω), can be assessed in a non-contact manner, by analyzing the gif) and retrieving displacement of scattering particles, often quantified by the mean square displacement (MSD), denoted as <Ai?(t)>. The generalized Stokes-Einstein relation (G ^' SER) is then used to extract the viscoelastic modulus, G* a>), from the measured MSD. For relatively soft materials, the Brownian movements of scattering particles are fast and MSD increases quickly with time, eliciting rapid speckle fluctuations. In contrast, for mechanically rigid materials, scattering particles exhibit confined morions around a fixed position, which lead to restrained growth of MSD and slow variation of speckle patterns.

[0ΘΘ6] The primary challenge in extracting the viscoelastic modulus of tissue from speckle frame series lies in assessing the MSD from the measured gift) curve(s), partly because the rate of temporal speckle fluctuations depends not only on the Brownian displacement of scattering centers but also on the optical properties of the tissue - such as absorption and scattering coefficients and scattering amsofropy factor (μ _α , /„ and g) - that determine the transport of light within the illuminated volume, Accordingly, in order to accurately measure sample mechanical properties using LSR, it is required to isolate the influence of optical absorption and scattering from the g ₂ t) measurements to accurately describe tire MSD.

|08O7] Traditionally, diffusing wave spectroscopy (DWS) formalism is used to describe the relationship between the measured gift) and MSD for strongly scattering media with negligible absorption, in such media, light transport is often assumed to be diffusive. The majority of biological fluids and tissue, however, exhibit considerable absorption (μ _α > 0), and highly anisotropic scattering (g~ 0.9), and back- scatter light rays with sub-diffusive characteristics. In this case, the simple DWS formalism is modified to incorporate the knowledge of optical properties of the tissue to better explain the relationship between gift) and MSD. To compensate for shortcomings of the DWS, which assumes diffusive light transport an analytical solution termed the "telegrapher equation" has been proposed. The telegrapher approach shares the ease and simplicity of the DWS expression but aims to incorporate the attributes of strong absorption, scattering anisotropy, and non-diffusive propagation of rays wiihin short source-detector distances in a modified photon-transport equation. Alternatively, a Monte-Carlo ray tracing (MCRT) algorithm may be used to simulate the propagation of light in a medium of known optical properties and derive a numerical solution for speckle intensity temporal autocorrelation curve as a function of particle Brownian displacement. [8008] A new polarisation-sensitive correlation transfer (PSCl)-MCRT algorithm was proposed for describing light propagation in purely scattering media and accounting for the fluctuations of scattered light. (See Z. Hajjarian and S. K. Nadkami, "Evaluation and Correction for Optical Scattering Variations in Laser Speckle Rheolog of Biological Fluids," PLoS ONE 8, e650!4, 2013). The performance of PSCT-MCRT in estimating the MSD of Browniars particles in purely scattering media showed improved accuracy of estimating sample mechanical properties compared to the DWS approach [3]. Most biological tissues, however, in addition have light absorbing characteristics that are typically not taken into account in devising the MSD.

[0009] Fluid biological tissues - biological fluids (also referred herein as biofluids) - such as cerebrospinal fluid (CSF), mucus, synovial fluid, and vitreous humorous function as shock-absorbents, allergen and bacteria trappers, and lubricants in different organs and organ systems. Biofluids have distinct theological characteristics and exhibit both solid-like and fluid-like behavior over different loading conditions and size scales. As the evidence of correlation between viscodasric properties of bio&ids and initiation and progression of various bodily maladies becomes available, there arises a need in development of a methodology that would allow the user to evaluate mechanical properties of biological fluids in situ under native conditions to advance clinical disease diagnosis and treatment monitoring.

SUMMARY OF THE INVENTION

[0010] Embodiments of the invention provide a method for determining a viscoelastic modulus of an optically scattering tissue sample with she use of laser speckle rheology (LSR). The tnethod comprises (i) acquiring, with an optical detector, data sets representing time evolution of speckle associated with the sample irradiated with light from a light source; (ii) determining an optical property of the optically scattering tissue sample based at least on a radial profile of flux determined from the acquired data sets; and (iii) calculating a mean square displacement (MSD) value based on intensity decorrelation function describing the time evolution of speckle based on the determined optical property,

[0011] Embodiments of the invention additionally provide a method for determining a viscoelastic modulus of an optically scattering biological fluid with the use of laser speckle rheology (LSR), which includes acquiring, with an optical detector, data sets representing time evolution of speckle associated with the biological fluid irradiated with laser light and calculating an intensity decorrelation function based on the acquired data sets. The method additionally includes determining parameters of a fitting curve, for the intensity decorrelation function, based on the Laplace transform of a momentum transfer distribution associated with photon scattering by the biological fluid and calculated based on at least a reduced scattering coefficient characterizing distribution of optical scatterers in the biological fluid. A method further includes deriving a value of the vtscoelastic modulus based on a closed algebraic form of the fitting curve.

|θβΙ2] Embodiments of the invention further provide an article of manufacture including a computer program product that enables a computer processor to effectuate computational steps of the method of an embodiment of the invention. Embodiments of the invention further provide a measurement system including a system configured to perform laser speckle rheological measurements of a sample of optically scattering liquid and a computational sub-system adapted to perform calculations associated to an embodiment of the method of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The invention will be more fully understood by referring to the following Detailed

Description in conjunction with the Drawings, of which:

Fig. 1 is a diagram illustrating measurement of intensity fluctuations of light that has interacted with a biological fluid sample;

Fig, 2A is an embodiment of a laser-speckle-based imaging system configured to operate n a backscattering regime, in accord with an embodiment of the invention;

Fig. 2B is a block-scheme representing an embodiment of the PSCT-MCRT algorithm according to the invention;

Fig. 3 is a plot presenting decorreiation curves, for aqueous glycerol mixtures of different viscosities and containing a small percentage of light-scattering particles, obtained with the use of an embodiment of the invention;

Fig. 4 is a plot presenting decorreiation curves, for an aqueous glycerol mixture containing light scattering particles in different concentrations, obtained with tlie use of an embodiment of the invention;

Fig, 5 is a plot presenting raw MSD-values for light-scattering particles in mixtures of Fig. 4 under the assumption of diffusion approximation;

Fig. 6 is a plot presenting raw, uncorrected data for viscoelastic moduli for the mixtures of Fig. 4, calculates with the use of generalized Stokes-Einsiein equation from the MSD values of Fig. 5;

Fig. 7A is a plot presenting the radial flux profiles for die samples of Fig.4;

Fig. 7B is a plot presenting the results of theoretical and empirical determination for the reduced scattering coefficient according to an embodiment of the invention;

Fig. 8A is plot presenting tlie results of determination of the compensated MSD, corresponding to the scattering particles in tlie samples of Fig. 4, obtained with the PSCT-MCRT ray tracing according to an embodiment of the invention; Fig. 8B is a plot presenting the results of detemunation of the values of compensated complex viscoelastic moduli, corresponding to the samples of Fig. 4, obtained the PSCT-MCRT ray tracing according to an embodiment of the invention;

Figs. 9A and 9B are plots of speckle decorrelation functions the bovine synovial fluid and the vitreous humor with different concentrations of scattering particles of TiO?. obtained according to an embodiment of the invention;

Figs. 1 OA and I OB are plots providing comparison between the values of complex viscoelastic moduli obtained based on the mechanical rheological measurements, those based on the LSR measurements under the assumption of diffusion theory, and those based on the LSR measurements and corrected using an embodiment of the method of the invention;

Fig. 11 presents speckle intensity temporal autocorrelation curves for aqueous glycerol suspensions of varying μ . The speckle fluctuations speed up with increasing μ', and accelerate the decay trend otgrft) curves;

Figs, 12A, 12B, I2C are plots of viscoelastic moduli, G*(co)\ calculated based on data from gi(i) curves of Fig. 1, based on the DWS equation, the Telegrapher equation, and the PSCT-MCRT of the invention, respectively. The viscoelastic modulus measured using a conventional rheometer is shown as a black dashed curve.

Fig. 3 shows speckle intensity temporal autocorrelation curves for aqueous glycerol suspensions of varying absorption coefficient. As μ _α increases, speckle fluctuations decelerate, and g t) curves decay slower.

FIG. 14A, 14B, 3.4C: Viscoelastic modulus, \G*( )\, derived from g ₂ (t) curves of Fig. 13, using the DWS equation, the Telegrapher equation, and the PSCT-MCRT algorithm, respectively, for glycerol suspensions of identical mechanical properties, similar reduced scattering coefficient, μ , but varying absorption coefficient, The viscoelastic modulus measured using a conventional rheometer is shown as a black dashed curve, it is clear that DWS and telegrapher approaches are capable of correcting for the influence of variations in μ _α . PSCT- MCRT performs well for any arbitrary set of optical properties.

FIGs. 15 A, 15B show speckle intensity temporal autocorrelation curves, g t) for samples of varying μ' ₅ and μ _α . Fig, 15 A: samples with higher ί', have a smaller μ„, Fig. 15B; μ' _ε and μ _α are proportional

FIGs. 16A, 16B, I6C: Viscoelastic modulus, \G*(m)\, derived from g ₂ (t) curves of Fig. 15A, using the DWS equation, the Telegrapher equation, and the PSCT-MCRT algorithm, respectively, for glycerol suspensions of identical mechanical properties and varying μ and μ _α . The viscoelastic modulus measured using a conventional rheometer is shown as a black dashed curve. [G*(co)j derived from speckle fluctuations, using DWS equation exhibit an unexpected close agreement with conventional rheoiogy even in the case of weak scattering and strong absorption. In con trast, telegrapher equation fails, whenever strong absorption accompanies highly anisotropic scattering, PSCT-MCRT agrees well with rheometry results in most cases, but slightly over-estimates the modulus in weakly scattering samples of strong absorption.

FXGs. I7A, 17B, 17C : Viscoelastic modulus, \0*(ω)\, obtained ftam grfl) curves of Fig. i 6B using the DWS equation, the Telegrapher equation, and the PSCT-MCRT, respectively. The viscoelastic modulus measured using a conventional rheometer is shown as a black dashed curve. DWS and telegrapher equations match the results of conventional rheometry for samples with non-negligible μ _β . The PSCT-MCRT results are in close agreement with conventional theology for any arbitrary set of optical properties.

DETAILED DESCRIPTION

[0014] The idea of this invention addresses the role of optical absorption and/or scattering in modulating temporal speckle intensity fluctuations using test, phantom samples thai cover a wide range of optical properties pertinent to biological tissues. In accordance with embodiments of the present invention, the problem of non-invasive assessment of the viscoelasitc modulus of a biological fluid having varying optical and mechanical characteristics is solved by devising an algorithm for extracting the data representing such modulus from the biological-fluid-related speckle fluctuation information (that has been obtained with the LSR-based measurements) while decoupling the contribution (to the LSI. speckle fluctuation data) introduced by multiple scattering and/or absorption and displacement of particles of the biological fluid, in particular, the application of DWS, telegrapher, and PSCT-MCRT approaches in describing and correcting for the influence of varying absorption and scattering properties on the measured MSD from speckle intensity fluctuations are presented, and the accuracy of each of the three approaches in measuring the mechanical properties in phantom samples covering the range of optical properties relevant to tissue is assessed.

{0015j The presented empirical results suggest the prominent role of optical properties in modulating temporal speckle fluctuations and establish that the isolation and correction of optical properties is needed for precise interpretation of LSR measurements of the mechanical properties of a sample. It is shown that the PSCT-MCRT provides the most accurate estimation of sample viscoelastic properties via the MSD with samples possessing not only scattering characteristics but also absorption characteristics. The comparison among the different methods demonstrates that even for sampies with non-negligible absorption , DWS exhibits accurate results and performs similarly to the PSCT-MCRT approach in its capability to measure MSD and retrieve the viscoelastic modulus. On the other hand, fee telegrapher equation does not provide a significant improvement over DWS formalism and fails in the presence of strong absorption and anisotropic scattering. These findings provide a definitive affirmation that the LSR methodology can be used as a diagnostic tool for evaluating the mechanical properties of biological materials with any, substantially arbitrary, set of optical properties.

| 016] In related art, the mechanical behavior of a medium is sometimes described using the DLS approach with the purpose of demonstration that the mechanical properties of homogenous medium (such as complex fluids) can be examiner with the use of exogenous light scattering mieroparricles introduced to such medium. According to the DLS principle, lime- varying fluctuations of light intensity are measured at a single spot of the medium, and averaging over several cross-correlation functions that evolve in time is required to obtain the intensity correlation function, g ₂ (i). Since in DLS g?(t) is measured over a single spot, the required data-acquisition time (on the order of several minutes to hours) is orders of magnitude larger than the typical time scale of laser-speckle intensity fluctuations, thereby attesting to impraclicality of the use of the DLS for analysis of tissue in situ.

[00171 ^m contradistinction with fee DLS, as previously demonstrated, the LSR successfully Sends itself to the in situ analysis. See, for example, Characterization of atherosclerotic plaques by laser speckle imaging, Nadkami et al, in Gradation 112: 885-892, 2005; Measurement of fibrous cap thickness in atherosclerotic plaques by spatiotemporal analysis of laser speckle images; Nadkami et al, in J Biomed Opt. 11 : 21006, 2006; Laser speckle imaging of atherosclerotic plaques through optical fiber bundles; Nadkami et al., in J. Biomed. Opt. 13: 054016, 2008; intravascular laser speckle imaging catheter for the mechanical evaluation of the arterial wail, Hajjarian et al., in. i. Biomed. Opt. 16: 026005, 201 3 ; and Evaluating the viscoeiastic properties of tissue from laser speckle fluctuations, Hajjarian ei al, in Set. Rep. 2: 316. However, the analysis of even a single gj(t) curve, obtained with the use of LSR, generates plethora of information representing various relaxation times, which complicates the examination of speckle dynamics and reduces the accuracy of results. According to embodiments of the invention, the LSR methodology is hereby extended with the use of an opticai-seattering-and-absorption compensation algorithm to increase the accuracy of the assessment of mechanical properties of Suids or, in general, a material (such as a tissue, for example) that has a clearly recognized scattering and/or absorption characteristics. The proposed algorithm is adapted to process the LSR-nieasuremeni data representing viscoeiastic moduli of either a liquid phantom or biological fluid the optical and or mechanic properties of which can be, generally speaking, substantially arbitrary. In particular, embodiments of a polarization-sensitive correlation transfer Monte-Carlo ray tracing (P8CT-MCRT) algorithm, discussed in this disclosure, are used to assess the contribution of optical properties to evolution of the LSR-acquired speckle (in particular, speckle intensit fluctuation) for a chosen concentration of scatterers in a fluid of interest. |0 3 j In particular, in order to measure accurately viscoelasticity of the biofiuid using the LSR, the dependence of viscoelasticity on light scattering an&/or absorption properties should be decoupled from that on the mechanical properties of the biofiuid.

[001 ] According to the idea of the invention, the accuracy of the LSR methodology in determination of the mechanical characteristics of biofluids is increased by compensating for variations of optical scattering and/or absorption characteristics in samples with varying optical and mechanical properties. To this end, optical properties of a sample are calculated from time-averaged speckle data, and a polarization sensitive correlation transfer Monte-Carlo ray tracing (PSCT-MCRT) algorithm is implemented to characterize and correct for the contribution of optical scattering in evaluation of MSD. Using this approach, complex viscoeiastic moduli of test phantoms and biological fluid samples are evaluated and compared with reference-standard mechanical measurements obtained using a rheometer.

[0020] Fig. 1 shows a diagram schematically illustrating the principle of measurement of laser speckle intensity fluctuation caused by a sample. Depending on a particular configuration, incident polarized highly coherent light 110 is reflected by and'or transmitted trough the sample 128 having numerous intrinsic light-scattering elements. Upon interaction with the sample 120, light is detected (in a reflection arm - as beam 124, and/or in a transmission arm - as beam 128) by an appropriate detector system {134, 138) to acquire image data representing image of laser speckle pattern produced by light scattered by the sample 120 as a function of time and to acquire and store, on tangible non-transient computer-readable medium, the acquired data. Such interferometric image data are further processed to detennine detected light intensity fluctuations 144, 148 associated with the illuminated sample 120.

Image Acquisition and Analysis.

[0821] Fig. 2 provides an example of an embodiment 200 of the experimental set up configured to operate in reflection (faaekseattering regime). The embodiment 2ΘΘ includes a laser source 210 (such as a He-Ne laser, with output of about 20-30 mW at 633 ran; JDSU 1145) producing light 110 that, upon passing through an optical train including a linear polarizer 214 and a beam expander (10: 1) 218, was focused into an approximately 50 micron spot onto the biofiuid sample 128 through an optical system 22© including a lens 222 and a beam splitter 224. in a related implementation, where the working di tance between the lens 222 and the sample 120 is varied, depth-resolved mapping of the sample 120 can be realized. Optionally, light 110 was transmitted through a single-mode fiber (SMF) 226 prior to traversing the polarize 214. Time series of images of the sample 120 in light 228 backscattered by the sample 120 were acquired through a polarizer 230 (arranged in cross orientation with the polarizer 214, to reduce the unwanted acquisition of specularly reflected light) with a Mgh-speed CMOS camera 232 (such as PixelLIN PL-761F, Ottawa, Canada) through a lens with adjustable focal length (such as, for example, a focusing lens system MLH-lOx by Computer, Comniack, NY). The use of CMOS camera 232 to acquire laser speckle patterns from the sample 120 in a 180 degree backscattering geometry enhances the statistical accuracy in measuring ¾(ί) by simultaneous enseinble averaging of multiple speckle spots, which significantly reduces data acquisition time. The acquired imaging data were stored and processed with the use of a pre-programmed data-processing electronic circuitry (such as a computer processor) 236, and optionally displayed for visualization in a required format on a display (not shown). The acquisition of imaging data representing the sample 120 in backscattered light 228 was conducted at a predetermined rate (for phantom samples: at about 490 frames- per-second, fps, and for tissxje samples: at about 840 ips to ensure that last sample dynamics is appropriately detected) during the acquisition time periods of about 2 seconds. The acquired sequences of speckle patterns were optionally additionally processed to obtain temporally-averaged intensity (a diffuse reflectance profile) for ROI of about 296-by-296 pixels, which corresponded to the field -of-view (FOV) of about 1 mm ² . It is appreciated that an embodiment related to that of Fig. 2 can be adapted to operate in transmission (or forward scattering regime).

[0022] Data representing the interaction of light with various media were acquired, with the use of the embodiments of LSR measurement set-up of Fig. 2 A, in a form of series of speckle data frames and appropriately processed with the use of cross-correlation analysis of the first data frame with the subsequent frames, required spatial and temporal averaging (over multiple data points) for different phantom samples and biofluid samples. The speckle size - to- CCD pixel ratio was set to at least four to maintain sufficient spatial sampling and speckle contrast. The speckle intensity temporal autocorrelation curve, gtfi), was calculated by measuring the correlation between pixel intensities in the first speckle image and subsequent images. Spatial averaging was performed over the entire frame of pixels, the g i) curves evolving in time were averaged to

[ΘΘ24] where &nd I(l+t ₀ ) refer to the speckle intensity at times ¾ and t+t ₀ , and < and <

>,() indicate spatial and temporal averaging over all the pixels in the images and for entire imaging duration (for example ~ 2 sec), respectively.

MSB Evaluation With th Use ofDLS and DIP'S Formulisms.

[0825] For single or strong multiply-scattering media, DLS and DWS theories, respectively, have expressed the measured gift) (eqn. (1)) as a function of MSD as follows:

[ΘΘ29] Here k ₀ is the wave number, n is the refractive index of the sample, and γ is an experimental parameter that reflects the ratio of long diffuse path lengths to short non-diffusive ones. It is used to expand the theoretical limitations of DWS in back-scattering geometry and is generally assumed to be y = 5/3. The DLS formalism is not valid for the moderate to strongly scattering samples used in this work

[8030] in a specific case, when fee absorption properties of the biofiuidic sample are taken into account, and based on the diffusion approximation, the relationship between gj(t) and MSD in the back- scattering geometry is as follows;

where μ' ₃ = μ,ίΐ-g) is the reduced scattering coefficient. The second term in the exponents is related to optical properties of the sample and accounts for attenuation of long paths due to absorption. For strongly scattering media, this term reduces to zero (see Eq. (3)).

MSB Evaluation With the Use of the Telegrapher Formalism,

f0833] The telegrapher equation, which is a modification of die DWS equation, results in the following final expression to describe the g ₂ (i) and MSD relation (see, for example, P. A. Lemieux et al., "Diffissiiig-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering," Phys Rev E 57, 4498-4515 (1998):

[0835] Here, Do = 1/3 is the normalized photon diffusion coefficient, and z _e ^:::: 2/3 is related to boundary conditions and sample wail reflectivity, x™ kiri<Ar ^! {f)> + 3 ( _a (u' _s and is the same as the argument in the exponent of Eq. (4), and g refers to the scattering anisotropy parameter. The telegrapher eqisation models the scattering anisotropy by introducing a void in the concentration of diffused photons at the vicinity of the light source, to emulate the impact of forwardly directed anisotropic scattering on the photon concentration profile. Moreover, this equation provides a distinct treatment of photon migration at different length scales, and provides an alternative closed- form solution to derive the MSD from the g _? (¾> curve in both transmission and back-scattering geometries for turbid media with strong absorption properties and anisotropic scattering.

[0036] An embodiment of the PSCT-MCRT algorithm according to the invention (Fig. 2B, Box 3) was employed to simulate gl ^iCRT (i) curves and to derive a modified relationship between MSD rid g t), for samples with arbitrary optical properties, The PSCT-MCRT model incorporated all experimental LSR parameters, for a focused Gaussian beam (50μιη) illuminating the sample placed in a cuvette (10 mm light path, 1.5 ml) with μ _α and μ measured as above. A total of 10 ⁵ photons were tracked from the source to the receiver (FOV of 2 mm). The temporal speckle fluctuations were modified by the polarization state of detected light. As a result, the embodiment of the PSCT-MCRT algorithm incorporated attributes of the polarization state by tracking the Stokes' vector, [I Q U VJ, with respect to the corresponding reference frame. Euler equations were used to modify the Stokes' vector upon scattering and transport within the medium. At the receiver site, a final rotation was applied (with the polarizer P2) to redefine the Stokes' vector in the receiver coordinates system and since LSR setup captured the rapidly evolving speckle pattern of the cross-polarized channel, only the cross-polarized component of intensity was retained. To account for the momentum transfer (causing Doppler shift) at each scattering event, the scattering wave vector q-=2k in(8/2) was tracked, as well. Here Θ is the polar angle of scattering. The total momentum transfer, defined as with the summation over all scattering events involved in that path, represented the reduction of speckle intensity temporal autocorrelation due to all scattering events involved in each path. Consequently, g2 ^1CRT (t) was obtained by integrating the field temporal autocorrelation curves of all received rays, weighted by the corresponding momentum transfer distribution, P(Y), as:

[0037] From Eq. (5), it is noted that the term h brackets is simply the

Laplace transform of P{¥), L (P(Y)} evaluated at I/3k _i} ² ^<Ar ² (t)>. L {P(¥)} is equivalent to speckle field autocorrelation, g> ^MLR* (t), in turn related to speckle intensity autocorrelation carve, gi ^MCRT (0, through the Siegert relation as: PSCT-MCRT only provided the statistical histogram of photons' Pff) and generated a numerical solution for L {P(Y)j (= g/ ^* '(OX a^d consequently ,g (t). To simplify Eq. (5), a parametric function was fitted to L {POO} as follows;

[G038] L {P(Y)} ^ e- ^r(3S} (6) [0839] where S was the argument of the transform (complex frequency). The parameters y and ζ were derived from PSCT-MCRT simulation by numerical calculation of the total momentum transfer distribution P(Y), based on the experimentally evaluated values for/i _a and μ' ₃ and Mie theory calculations of g for each individual sample. Consequently, the following expression was derived fo g/ ^{i K} ¾) as a function of

[8Θ41] The account for light propagation in turbid tissue, expressed as Eq. (7), provides an alternative numerical approach to describe the gift) and MSD relationship and implements a polarization- sensitive correlation transfer PSCT-MCRT algorithm. The PSCT-MCRT approach incorporates parameters of the illumination and collection setup, sample geometry and optical properties (μ _α , ¾, g) to track the scattering wave vector, defined as q 2k ₀ sin(O/2), at each photon-particle collision event. The total momentum transfer of each photon (light path), provides a superior descriptio of correlation decay induced by ail scattering events involved in each path. For a fixed choice of illumination/ collection setup and sample geometry, the parameters y and ζϋι Eq. (7) depend only on the optica! properties, namely μ _α &ηάμ' ₅ =μ (1-g).

|0042| As discussed below, the MSD was derived from speckle intensity fluctuations using each of the three approaches (DWS, telegrapher, and PSCT-MCRT) and compared by substituting gift) in the corresponding equations with the experimentally values gf ^l '(t) of Eq. (1) measured based on the time- varying laser speckle patterns. Finally, \G*fco)\ was derived by substituting the derived MSD values in the generalized Stokes-Einstem relation (GSER) as

100 3] G * (ω) = ^ _T . _{r 7} ^sl . ₍₈₎ πα{ τ ^ι ( )Γ(1 + flr( ) Li _/fii

[0044] Here Kg is the Boltzman constant (1 ,38* IG ^"23 ), T= 297 (room temperature) is the absolute temperature (degrees Kelvin), a is the scattering / absorbing particle's radius (in rnn, based on product specifications), ω=1Η is the loading frequency, /'represents the gamma function, and a(t)^-d log <Ar(l)>/3 log t corresponds to the logarithmic derivative of MSD.

Example 1: laflaesce of Optical Scattering on LSR Measurements

[0045] Aqueous glycerol mixtures with different glycerol-bio-fkid ratios were prepared to test the applicability of the LSR. methodology to evaluating of the viscoclastic properties of liquid samples. |0046] Particles of Ti02 (in the form of Anatase powder, diameter of about 400 sm, by Acres

Organics, Geel, Belgium) were added to tlie mixtures in various concentrations (from about 0.04% to about 2% of volume fractions, corresponding to experimentally evaluated reduced scattering coefficients, μ , ; 1.3 - 84,8 mm ^" '; total of N=l 8 different concentrations). The correspondence between the volume fractions (VF) of Ti02 pariicSes and reduced scattering coefficients in summarized in Tables 1 A, IB, which is appiicable to the Figures (7 A and 7B) referred to below in Example 1 and related portions of the discussion:

Table 1A

Table IB

[0047] The resulting solutions were vortexed extensively to assure that scattering particles were totally disintegrated and evenly disseminated throughout the solutions. About 1.5 ml of a so prepared liquid sample were placed in a sealed spectroscopic couvette for the LSR measurements and about 2 ml were used to fill the gap of a parallel plate stainless steel geometry of 40 mm diameter for a conventional mechanical rheology testing, fa this Example 1, the extrinsically added TiC¾ particles were utilized purely for the purpose of validating our approach over a large range of optical scattering concentrations relevant to the tissue sample [0048] Fig. 3 is a plot showing an intensity decorrelation function, g2(t), for aqueous glycerol mixtures of various concentrations (defined as 60% glycerol-40% water, 70%~30%, 80%~2Q%, 90%- 10%, and 100%, respectively) with mixed in Ti<¾ scattering particles (of about 400 nm in diameter) mixed in the amount of about 0,1 weight-%. Values of viscosity (in units of [η]= Pa S), corresponding to each of the measured mixtures, are also indicated. Due to similar optical properties of the samples of Fig. 3, the direct comparison of speckle dynamics is possible, which enables the relative assessment of viscosity values. As shown, a gi(t) curves corresponding to a liquid with higher viscosity decays slower than a g ₂ (t) curve corresponding to a liquid of the same nature but of lower viscosity.

|Q049| However, the variation in concentrations of scattering particles in the fluids of the same nature is expected to modify speckle dynamics, regardless of viscoelastic properties of the fluids. To illustrate this fact. Fig, 4 shows a plot with g ₂ (t) curves calculated based on empirically acquired speckle data for phantom solutions containing 90% glycerol and 10% water (volume fraction), to which with Ti{¾ particles were mixed in different concentrations. The TiQ ₂ concentrations, represented by N=l 8 samples, ranged from about 0,04% (labeled as "a") to about 0.06% (labeled as '¾") and so on, to about 1% (labeled as "<g"), to about 2% (labeled as "r"). Also displayed in Fig. 4, for comparison with the empirical results, are die theoretical curves I and II for g ₂ (t) obtained according to the DLS and DWS methodologies, respectively, under the assumption of a radius of 0.3 μιη for a T1O ₂ particle. For this purpose, the theoretical particle diffusion constant of the corresponding glycerol solution was used in equations for DLS and DSW. Based on direct comparison of the curves a, b, ,.p ,q, and r with the curves II it is evident that speckle dynamics of the above-defined glycerol- water-Ti0 ₂ mixes deviate from predictions of DLS and DWS methodologies. The decorrelation curves fail somewhere between she DLS and DWS curves for most of the values of concentration of scattering particles. Put differently, by changing the TiOi concentration in the glycerol water mix from 0.04% to 2%, g ₂ (t) curves sweep the gap of operational values between the two dieoretical limits, thereby demonstrating a dramatic change in speckle fluctuation rate. Consequently, while viscosities of all phantom samples used for the purposes of Fig. 4 are substantially the same, large deviation is observed in speckle dynamics. A skilled artisan would readily conclude that the use of either of the DLS and DWS formalisms for interpreting specHe dynamics and extracting mean square displacements (MSD) of scattering particles is improper as such used results in erroneous estimation of a decorrelation curve and a corresponding complex viscoelastic modulus.

[8QS0] Fig. 5 is a plot demonstrating the MSD values for Ti(¾ scattering particles estimated based on respectively-corresponding g ₂ (i) curves of Fig. 4 with the use of the DWS formalism for backscattering geometry. Such formalism is discussed, for example, by Cardinaux F. et al. (in

Microrheology of Giant-Micelle Solutions, Europhysics Letters 57: 7, 2002). In deriving the results presented in Fig. 5, it was assumed that the diffusion approximation was valid for all considered concentrations of scattering particles. A iarge variation is observed among the curves of Fig. 5, which supports the conclusion that if raw MSD curves are not compensated for variations in optical properties, the complex viscoelastic modulus derived in reliance on such data will he biased due to variations in scattering concentrations.

[8051] When performing the measurements with a conventional mechanical rheometer, the AR-

G2 rheometer (TA instruments. New Castle, DE) was used. A 40 mm diameter stainless steel parallel plate geometry was employed and the frequency sweep oscillation procedure was carried out to evaluate G G", and G ^* over the frequency range from about 0. i Hz to about 100 Hz. For aqueous glycerol mixtures, such tests were carried out in the room temperature, 25°C, and the strain percentage was controlled to be 2% thorough the procedure. (Similar procedures were performed on synovial fluid and vitreous humorous, as discussed below, except that the strain percentage was set to about 1% and the synovial fluid samples were evaluated at about 37° C.)

[00S2] Fig. 6 is a plot presenting the estimated frequency-dependent complex viscoelastic modulus, G*(w), calculated by substituting the raw MSD curves of Fig. 5 in the generalized Stokes Einstein Eq. (8) .

[1)053] A person of skill in the art would appreciate that G*(e>) data of Fig. 6 calculated from raw

MSD values do not match the results of conventional mechanical testing (as shown by most of the curves in Fig. 6). In particular, G*(<B) is overestimated, especially at lower concentrations of scattering particles due to slower decorrelation of speckle intensity. From the presented results it appears that is only at Ti<¾ concentration of about 2% {sample q) that strong multiple scattering dominates, and the values of G*(«B) substantially converge to the results obtained with mechanical rheometry. it may be concluded, therefore, that, while for a substantially optically dense phantom sample the diffusion theory may be used to model transport of photons and account for correlation transfer of the received light, such theory is substantially improper for the enablement of accurate estimation of G*((o) of samples of arbitrary optical properties. Accordingly, the accurate determination of G*(w) requires the use of an alternati ve model of light propagation and correlation transfer.

[0054] Unlike the DLS and DWS methodologies, which measure temporal statistical parameters associated with intensity of light scatted by tracer particles of known sizes and concentrations, the LSR evaluates speckle fluctuations originated from specimens of arbitrary and a priori unknown optical properties. Therefore, the simplifying assumpdons of diffusion approximation, and central limit theorem are not applicable for analysis of the LSR measurements and speckle dynamics critically depend on optical properties of the sample (such as, for example, absorption and scattering coefficients and asymmetry parameter (μ _β , μ _¾ g),the latter defining transport of light in the medium)s. The calculation of g _∑ (t) curves of phantom samples, displayed in Figs. 3 and 4, substantiates that impetuous use of the diffusion approximation for extracting the MSD date from the g ₂ (t) data leads to underestimation of MSD, as illustrated in Fig. 5. Consequently, the resulting 0*(ω) values are erroneously biased by concentrations of scattering particles (Fig, 6).

[ 0SS] The diffusion approximation describes transport of light ibr samples characterized by strong multiple scattering and minimal absorption. The above results indicate that the DWS formalism leads to inaccurate estimation of both the MSD and complex viscoeiastic moduli for samples with optical scattering properties of intermediate (no too weak and not too significant) strength,

Example 1 : Correction for Optical Scattering Variations in LSR According to the PSCT-MCRT Embodiment of Invention

| 0S6| Since obtaining an analytical closed form for gz(t) (as a function of optical and mechanical properties of a medium) is not trivial, a parametric model is developed to correct for the effects of optical scattering in determining the MSD from gj(t) and to extract the complex viscoeiastic modulus, as outlined in a flow-chart of Fig, 2a, for arbitrary concentration of optical scatterers in the biofluidie sample.

|O0S7] In one implementation, flux measurements were performed over an extended region of interest (ROI) of the sample 120 of Fig. 1 to evaluate the optical diffusion constant and the effective scattering coefficient and to determine absorption and scattering coefficients, in estimating optical properties from speckle frame series, a larger ROI is considered and pixels close to illumination center (a point in an image space representing a point at which the focused beam 110 is incident onto the sample 120) were abandoned.

fOOSSj Figs. 7A and 7B demonstrate the validity of an embodiment of the invention for evaluating the optical properties of phantom glycerol samples from time-averaged speckle images. The diffuse light remittance profile (DRP) curves are shown in Fig. 7A for the fluid samples discussed in reference to Fig, 4, and are in partial agreement with the predictions of diffusion theory, especially further away the inumination center. In Fig. 7 A, a distance from the illumination center is denoted as ρ. The diffusion approximation is substantially improper for processing speckle d>¾amics and second order intensity tatistics, due to smaller Oi of speckle dynamics acquisition, high frame rate (i.e. small exposure time), and a need to account for pixels close to iuumination center (due to higher signal-to-noise ratio and contrast associated with such pixels). In Fig, 7A the number of remitted photons per unit area (photon flux) intensified at higher concentration and the inset of curves increased while slope of the photon flux profil e became steeper.

|00S9] Absorption and reduced scattering coefficients (μ _α , μ' ₃ = μ$*(1· )) _> & ^{e aiier} lotted in Fig.

7B, are evaluated from the photon flux profile of Fig. 7A obtained from temporally averaged speckle image series. Here, to assess the optical properties of a chosen medium, the data of Fig. 7A were processed to determine the radial pro file of photon current (or flux based on camera responsibly (of about 28.1

DN/(nj/ ^' em ^'! )) and photon energy (E=hv, MPlank's constant, v= optical frequency). Accordingly, each digital number (which relates to a value representing intensity registered by a single pixel of the camera) corresponded to ~ 1 million photon per mm ² . This number was further corrected by taking into account the contributions of camera gain (of about 12.04 dB) and exposure time. The radial profile of flux was then fitted to the diffusion theory model assuming an isotropic point source located at a position (0, ¾) in an infinite medium and cylindrical coordinates: ψ{ρ, ζ ₀ ) =—

fOS6S>l ^{4Λυ r} > (9) fiMMSIj where D-{3[ _B +(l-g) μ ₆ ]) ^* ' is the photos diffusion constant, μ ₈ ]) is the effective attenuation coefficient, and , where ?<> ~ f , which is the reduced scattering coefficient). As a result, for each medium sample, the values of ₃ and p _s ' were detennined.

[C5062J The reduced scattering coefficient, μ , measured using this method is in close agreement with theoretical calculations particularly at low and intermediate scattering concentrations (See tables 1 A and J B). Deviations at higher concentrations were likely caused by clumping (larger particles, larger g) and sedimentation of TiQ _? . particles (given the density of 4,23 g cm ³ for Ti(¾ relative to <L26 g/cm ³ for glycerol mixture) which often resulted in Sower μ', compared to ie predictions. Moreover, at higher Ti<¾ concentrations close proximity of adjacent particles could also lead to interactions of near-field radiation and reduce the baekseattering efficiency, which influenced ihe measured/^ values. For predominantly scattering samples, used in this Example 1, results were solely focused on the influence οίμ' ₃ variations on the speckle dynamics and the role of absorption was not studied, (it is appreciated, nonetheless, that optical absorption is expected to eliminate rays with longest optical paths, corresponding to a large number of scattering events, and decelerate g t) curves). In the received back-scattered signal, attributes of scattering angular distribution were extensively washed off by multiple scattering. As a result experimental evaluation of phase function and g was not trivial and instead theoretical Mie calculations were used to predict these parameters which resulted in g=0.6 for TiG ₂ particles suspended in glycerol suspensions. Thus, in the current study, the effect of scattering anisotropy was not addressed in experiments. The resulting radial profiles of flux and assessed optical properties (specifically, scattering coefficients depicted in Fig. 7B) reveal close agreement 0.96, p<0.0001) with theoretical calculations, especially at lower concentrations of scattering particles. At higher concentrations of scattering particles, the experimentally estimated reduced scattering coefficient appears to deviate from the theoretically determined one, which is explained by imperfections of an experimental set-up. For example, clamping of panicles and sedimentation give rise to lower values of empiricaliy-determined reduced scattering coefficient. Moreover, limited djuamie range of CMOS camera (59 dB) somewhat distort photon current profile at high concentrations. According to Brown (Dynamic light scattering : the method and some applications, Oxford: Clarendon Press, xvi, 735 .p, 1993), it is likely thai the inter-particle structure and interaction are also partly responsible to erroneous estimation of scattering mean free path.

[0063] Phantom samples: Fig. 8A, plots the MSD of particle dynamics in glycerol suspensions of

90%G-1G%W, measured by employing the PSCT-MCRT based optical scattering correction algorithm. The variability between MSD curves over the range of scattering concentrations (0.04%-2%), was significantly reduced compared to the results of Fig. 5 (which employed the DWS formalism). The impact of corrections was more pronounced in the intermediate times and residual small deviations were still observed at very early or long times, corresponding to initial decay and final plateau of gf ^¥ (t). These mismatches were most likely due to certain experimental factors, as discussed later. Fig. 8B showed the LSR evaluation of \G*(<a)\ for the 90%G-iO%W samples measured by employing optical scattering compensation compared with the corresponding rheometer measurements (dashed line). Compared to Fig.6, the optical, scattering dependence οΐ\ΰ*(ω)\ curves was significantly reduced by employing the compensation algorithm. Moreover, the scattering compensated moduli corresponding to all scattering concentrations closely corresponded with the measurements of mechanical rheometer. These results demonstrate that while differences in optical properties dramatically modulated the g2(t) curves, a significant improvement was achieved in the LSR evaluation of viscoelastic moduli when optical scattering variations were compensated for with an embodiment of the algorithm of the invention, as opposed to the direct application of DWS formalism in the estimation of MSD, and calculation of the \G*(o))\.

[0064J Biological Fluids: In the following discussion, the reference is made to Figs. 9A and 9B that present plots of speckle decorrelation functions the bovine synovial fluid and the vitreous humor with different concentrations of scattering particles of TiOj , respectively. The concentrations are indicated in. plot insets.

|0065] The biofluid samples were prepared as follows: the frozen bovine synovial fluid and vitreous humorous (Animal Technologies, Tyler, TX) were warmed up to the body temperature (of about 37° C) in a water bath prior to the LSR imaging. The Ti02 particles were added to these fluids in various concentrations (synovial fluid: 0.08%, 0.1%, 0.15%, and 0.2%, N=4; vitreous humor: 0.08%, 0.1%, 0.15%, N=3) to create scattering signal. n a fashion similar to that described in reference to the phantom samples above, about 1.5 ml of the samples were placed in clear plastic couvettes and about 2 ml were used for measurements with the use of mechanical rheology.

[0066] Figs. 9A and 9B show gf ^p (t) curves measured based on time-varying speckle images of synovial fluid and vitreous humor, respectively. Similar to the glycerol samples, tbs g2 (t) decay accelerated with increased scattering in both cases. Since g ^ft) decayed slower for synovial fluid compared to vitreous humor, it was expected that synovial fluid would have a relatively higher modulus. However, it was necessary to correct for the contribution of optical scattering prior to comparing absolute mechanical moduli.

[0067] Just like for phantom samples discussed above, for biofluids it was also observed that g t) curves decay faster for samples corresponding to higher concentrations of scattering particles. It is recognized, however, that because both the synovial fluid and the vitreous humor possess a somewhat low viscoelastic modulus, both the LSR-based evaluation and the conventional mechanical rheology based characterization of these samples are rather challenging. On one hand, the conventional mechanical testing of the samples is possible only at relatively low oscillation frequencies (for instance, at less than about 5 to 10 Hz), because at higher frequencies (in excess of 10 Hz or so) the stirring rod inertia produces unreliable data. Accordingly, it may be justified to omit the data acquired with a mechanical rheorneter at higher frequencies. On the oilier hand, the LSR-based determinations are somewhat involved at low frequencies due to rapid speckle evolution, which leads to blurring of images and reduction of speckle contrast. Accordingly, only the initial decay of ga(t) curves (corresponding to high, frequency modulus values) are chosen for representation of viscoelastic behavior, and long-time decorrelation of speckle intensity smears out by artificial raising of the plateau, especially at higher concentrations of scatterers (i.e., for turbid samples approaching the DWS limit such as samples q and r). To partially correct the plateau level, additional processing is performed to restore the contrast through subiracdng the background signal, for calculating the g ₂ (t) function. Consequently, LSR results (curves b of Figs. 10A and Ϊ0Β) demonstrate close correspondence with the results of conventional, mechanical rheomeiric measurement (curves of Figs. I OA, lOB) of G*(<u) over a limited range at low oscillation frequencies, for the same biofluids. Curves b are obtained based on the LSR measurement data with the use of the PSCT-MCRT algorithm of the invention, while curves c represent the results obtained from the LSR measurement data with the use of the diffusion approximadon. The overlapping region (i.e. the region of frequencies within which the results of conventional mechanical rheology substantially equal to the results obtained with the LSR) is smaller for biological fluids as compared to phantom samples. This is partly due to small complex modulus of biofluids, which inhibits accurate conventional testing of the samples at high frequencies. Moreover, during the measurements performed with the use of con ventional mechanical rheology, the strain percentage for biological samples is set to about 1%, as opposed to about 2% for phantom glycerol samples, to eliminate the possibility of damaging the micro- structure and changing the mechanical properties. The smaller strain percentage reduces the capability of rheorneter in correcting for inertia of the rod at higher frequencies. On the other hand, the LSR methodolog is capable of evaluating the modulus over more than three decades. This range can even be extended further by using a higher frame rate and longer acquisition time to increase both low and high frequency limits of the estimated modulus. Figs. I OA, 10B show the LSR results for synovial fluid and vitreous humor, respectively, measured with and without optical scattering eon"ection. The red diamonds represent average G*(w)\ values of synovial fluid and vitreous humor samples of Figs. 9A, 9B, estimated using LSR based on the DWS expression of Eq. (3), which did not take into account optical scattering variations. The purple squares correspond to me moduli resulted from corrected MSD values, using the modified expression of Eq, (7) derived from the compensation algorithm of the invention. The red and purple error bars stand for the standard error. Also depicted in this figure are the \G*(m)\ values measured using a conventional rheometer (black solid line, round markers). It was evident that in the case of LSR with optical scattering correction, \G*(a>)\ exhibited a close correspondence with conventional mechanical testing. Moreover, \G*(a>)\ measured using DWS approximation resulted in an offset of about one decade relative to conventional meometric testing results. This was due to slower decay of speckle intensity temporal autocorrelation curve, caused by relatively low concentration of Ti0 ₂ particles as discussed later. From the results of Figs. 10A, 10B it was clear that synovial fluid had a slightly higher viscoelastic modulus, which was consistent with our initial observation of speckle fluctuations and with standard reference mechanical rheometry. The non-Newtonian behavior of these bio-fiuids, reflected in smaller slope of \G*(a>)\ and lower frequency dependence compared to viscous glycerol solutions, pointed to the complex viscoelastic behavior of bio-fluids relative to glycerol samples. These results established the critical need of compensating for optical scattering properties to enable accurate measurement of viscoelastic moduli from laser speckle patterns and demonstrated the potential of LSR for evaluating the viscoelastic properties of biological fluids.

[00683 Optical transparency and clarity of the synovial fluid and the vitreous humor enable changing the optical properties of the samples of these biofluids and facilitated examination of samples with different concentrations of scattering particles. This provided better understanding of optical and mechanical cumulative effects on modulating the speckle dynamics. While the intensity of light scattering at such semitransparent materials, in their native state, and as detected by a photodeteetor, is rather low, in an embodiment related to that of Fig. 2 higher illumination power and more sensitive detection schemes may enable measurements of samples close to the DLS limit (i.e., samples with low concentration of scatterers) without ihe intentional manipulating the optical properties of the samples.

|0869| The Ti(¾ tracer particles, used to evaluate biofluids according to the embodiments of the invention, were exogenous scattering centers of known dimension. Thus, the estimation of G*(«J) from MSD using the generalize Stokes-Einsiein relationship was relatively straightforward. To enable the assessment of viscoelastic parameters of semi-dilute or substantially opaque biological samples (such as, blood, lymph, and mucus, for example) it is important to define a mechanism for estimating the particle size distribution and take into account the poly-dispersed nature of these biofluids.

[8870] For the following examples, the aqueous glycerol phantoms were used Ihe properties of which are summarized in Table 2.

[00 1] As discussed below, ail three approaches (the DWS, the telegrapher approach, and the

PSCT-MCRT of the present invention) were used to devise the MSD and the resultant viscoelastic modulus, \G*(m)\, from the LSR measurements, and the results were compared with those acquired from the reference standard mechanical rheometery (AR-G2, TA Instruments, MA). AH prepared samples (Table 2) were evaluated using the mechanical rheometer, as follows: a sample (2 mi) was placed within the rheometer tool and top plate of 40 mm dia. exerted an oscillatory shear stress upon the sample, with oscillation frequency sweeping the 0.1-100 Hz range to obtain the frequency dependent visco-eiastic modulus. Mechanical testing was carried out at 25°C, and 2% strain was applied on the samples. Example 2: Influence of Optical Scattering on LSR Measurements

[8072J Fig. 1 1 displays g t) curves of aqueous glycerol suspensions with identical viscosities but varying concentration of Ti<¾ scattering particles (0,05% - 2%), corresponding to the first column of Table 2. For these samples, μ', : 3.2-129 mm ^"1 a d /ia ~ 0 (negligible absorption), In Fig. 11 the dotted and dashed curves corresponds to theoretical g (t) curve predicted by Dynamic Light Scattering (DLS) and the DWS formalism for single (μ', very small) and rich multiple scattering (/¾ /<', = 0) scenarios, respectively. Similarly to the results of Example 1 , it is observed that the experimental gj(t) curves for varying scattering properties span the gap between the theoretical limits of single and strong multiple scattering with samples of larger μ ' _χ decaying faster. Still, even for μΊ = 129.8 mm ^" ', gz(t) decays slower than the predictions of diffusion equation for primarily scattering material. This may be related to the shortcomings of the DWS equation in describing the sub-diffusive behavior of back-scattered intensity, as discussed later. The plots of Fig. 11 are similar to our earlier observations (Fig. 4) that the variations in scattering properties modify speckle fluctuations, independent of sample mechanical properties. More specifically, for glycerol suspension of identical viscosities, and consequently similar MSD, the increase ϊ μ leads to faster temporal speckle fluctuations. As a result, g ₂ (t) curves of samples with identical mechanical properties exhibit a range of decay rates, tuned purely by scattering properties.

0073| Next, performances of the three approaches, DWS, telegrapher, and PSCT-MCRT in isolating sample mechanics from the influence of varying scattering properties are reported, in the following analysis of the application of DWS, telegrapher, and PSCT-MCRT to isolating sample mechanics from the influence of varying scattering propertie is presented. The MSD is deduced from the experimentally evaluated g;(t) curves of Fig. 11 with the use of dependencies of Eqs. (4), (5), and (7) and substituted in Eq. (8) to calculate the frequency-dependent viscoelastic moduli, \0*{ω)\, that are displayed in Figs. 12A, 12B, 12C. The results of the standard mechanical rheometry measurement (denoted as Rheo) are also shown for comparison with the LSR results, in a dashed black curve. For these primarily scattering samples of negligible absorption, both DWS and telegrapher equations (Figs, 12 A, 12B) fail to yield an accurate estimate of viscoelastic properties. In contrast, PSCT-MCRT (Fig. 12C) successfully derives the moduli from speckle intensity temporal autocorrelation curves of Fig, 1 1 ,

[0074] Clearly. \ G*(w)\ curves obtained from both DWS and telegrapher equations (Figs. 12 A,

12B, respectively) present a considerable deviation from conventional rheology. The failure in accurate extraction of ! G*(eo) \ , is drastically aggravated for samples of low to moderate μ ' _s values. In this case, the relatively slower speckle fluctuations, generated by a smaller number of light scattering events, erroneously result in an over-estimation of the viscoelastic modulus, it is only for highly scattering samples (yellow and orange open circles) that the LSR measurements, derived by both DWS (Fig, 12A) and telegrapher equations (Fig, \ 28) converge to the results of standard mechanical rheology. Given the comparable performance of the two techniques, it seems that the telegrapher equation fails to improve upon DWS formalism in the backseattering geometry. In stark contradistinction, the PSCT-MCRT approach of the invention succeeds in sufficiently isolating optical scattering contributions to estimate moduli for any arbitrary μ', value (Fig. 12C). The measured \G*( )\ curves corresponding to weakly, moderately, and strongly scattering sampies show close correspondence with the results of conventional rheology, especially at intermediate frequencies, At low and high frequency limits, a slight deviation of \G*((o)\ curves is observed between LSR and mechanical rheometry potentially caused by speckle contrast artifacts and rheometer inertia limitations, respectively, as discussed later.

Example 3: Itifitoerace of Absorption on LSR Measarerneirts

|0Θ75] in this Example 3, She optical absorption characteristic of a sample is varied, while scattering properties are maintained constant to assess the collective effects on speckle fluctuations. Fig. 13 displays gi(t) curves of samples with identical mechanical properties and identical concentration of TiOj scattering particles (0.5%) mixed with different concentrations of carbon light absorbing nano- powder (0%-0.4%) (the row corresponding to the concentration of Ti02 of 0.5% in Table 2).

ΪΘ076] It is observed that the variation of absorption properties greatly influences the gift) curve.

As absorption coefficient increases, temporal speckle intensity fluctuations slow down, likely due to elimination of longer optical paths, which involve a larger number of scattering events. Figs. 14A, 14B, 14C display the resulting \G*(o))\, obtained from the gift) curves of Fig. 11 according to the procedure described in Example 2.

fiS0?7) Results of Figs. 14A through 14C indicate that both DWS and telegrapher formalisms are capable of accounting for changes in speckle intensity fluctuations, caused b variation in absorption properties. As compared to Figs. 12A through 12C, which clearly display the errors induced in estimated values by scattering variations, with the addition of absorbing particles it appears that both DWS and telegrapher formalisms ar e fairly resilient to abso tion-ind ced adjustment of speckle intensity fluctuations, in cases when μ _α is non-negligible. However, in both Figs. 14A and 14B, the \G*((o)\ estimated from LSR measurements for the sample with μ' ₃ = 32.4 mm ^' ' and μ _α ~ 0 exhibits a significant deviation from the rheology measurements. The capability of the DWS and telegrapher algorithms in extracting the MSD and consequently the j G*(a>) , in the presence of non-negligible absorption stems from the fact that both Eqs, (4) and (5) incorporate the influence of absorption in the term μ _<ν ^ι μ' ₅ and predict that for a fixed μ , increase in μ _α , leads to slower speckle intensity temporal fluctuations. The telegrapher algorithm does not present a tangible superiorit upon DWS equation. In Fig. 14C, \G*((o)\ derived via the PSCT-MCRT approach of the invention is displayed, which also effectively compensates tor the attributes of absorption variation from the final \G*{(o)\ curves in all cases. Just as in Figs. i2A through 12C, small deviations are still present at high low frequency limits due to experimental artifacts discussed later.

Example 4: Combined iailtience ef Scattering and Absorption on LSR Measurements

|0Θ78| So far we have separately investigated the influence of scattering and absorption variations on speckle intensity fluctuations, by keeping one of the μ' ₃ and μ _α fixed, and modifying the other. To obtain the results in Figs. 15A and 15 B, both μ , and μ _α are varied simultaneously. At first, in Fig. 15A, we consider the temporal speckle fluctuation adjustments as a consequence of increasing the μ' while reducing the μ _α (μ'Α, Λ) (minor diagonal in Table 2). In the second scenario i Fig. 15B, speckle fluctuations are modified by simultaneously increasing both μ and μ _α (μ ¹ *†, μ _α Χ) (major diagonal in Table 2). In Fig. 15 A, the differences of (μ ' _s , μ _α ) pairs cause a significant variation in the experimentally measured gj(t). For the strongly scattering sample of negligible absorption (μ '„ ~ 129.8 mm ⁴ and μ _α ~0, orange curve), light scatters multiple times before being detected and minute displacements of scattering particles, involved in each light path, accumulate and induce a rapidly decaying gj(i) curve. By gradually adding small amounts of absorbing particles and reducing the scattering concentration, for instance in samples with (μ' ₃ = 64.9 mm ^'1 , μ _β ^~ 0.5 mm ), and {u' _s — 32.4 mrn ,/i ₀ ^™ 1.2 mm ^{" !} ), and (^' _s = 12.8 mm ⁴ , μ _α ~ 2.4 mm ⁴ ), long optical paths are ultimateiy absorbed and grft) curves slow down, proportionally. Notice that for these curves, μ^μ ' _s values are equal to 0.007, 0.037, and 0.187, respectively. Thus, as the exponent in Eq. (4) predicts, by gradual growth οΐμ _σ ^ι μ ratio, g t) shows a proportionate slow down. Finally, for weakly scattering samples of strong absorption, (μ', = 6.1 mm ^"1 , μ _α — 4.9 mm ^"1 ) and (μ - 2.8 mm ^"1 , μ _ύ - 9.8 mm ⁴ ), most rays scatter only a few times, due to the sparse distribution of scattering centers. Besides, strong absorption extensively eliminates long optical paths that propagate through the medium. The collective effects of weak scattering and strong absorption render a low intensit scattered signal of stib-diffusive characteristics. For these samples, the μ^μ ratio rises to 0.8 and 3.5, respectively, indicating that the attributes of absorption dominates that of scattering and the underlying assumptions of both DWS and telegrapher equations are at the verge of breakdown. It is observed that the g t) curves decay even slower than the theoretical limit for optically dilute single-scattering medium. This excessive slow-down behavior is likely due to increase in carbon particles' concentrations, which has a three-fold impact on speckle intensity fluctuations. Firstly, it leads to strong absorption, which eliminates the long optical paths and slows downs the speckle intensity fluctuations. Additionally, since carbon particles are susceptible to clustering and agglomeration at high concentrations, average particle diameter increases and impedes the g ₂ decay accordingly. Finally, the potentially increased average particle size leads to larger scattering anisotropy, as seen in Table 2.

[8079] As opposed to Fig. 15A, in Fig. 15B gtft) curves follow a very similar decay trend, despite considerable difference in optical properties. In this panel, optical properties of samples are chosen so that i * and μ _α vary proportionally. Increasing μ' _β is expected to increase the number of received long optical paths of larger decorrelation. However, simultaneous increase of μ _α trims these light paths and cancels out the influence of larger μ . Thus, the collective influence of increasing both μ and μ„ leads to only small changes in speckle fluctuations, which is reflected by the fact that the parameter μ _α ίμ' ₃ varies miniraally between 0.074 and 0.093, ensuing only minute shifts in g ₂ (i).

[0080] Figs. 16A through 16C display the resulting viscoelastic moduli, extracted from all grft) curves of Fig. 15A, using the DWS and telegrapher equations and the PSCT-MCRT algorithm, respectively. Viscoelastic moduli corresponding to samples of low to moderate μ _α represent close agreement with the results of conventional rheoiogy in ail three cases. However, for weakly scattering samples of strong absorption, \G*(m)\ values derived using DWS, Eq. (4), show the closest agreement with the results of conventional rheoiogy. The | G*((a) j values extracted using PSCT-MCRT exhibit a minor but non-negligible offset with respect to the reference standard rheometry, and the curves obtained using telegrapher equation fail altogether in cases of strong absorption.

[0081] Revisiting Fig. 15 A explains that while excessive slow down of g>(i) curves for samples with highest concentrations of Carbon nano-powder is likely caused by particle agglomerations, the DWS formalism ascribes this entirely to the optical properties and the large μ^μ values. At this limit of strong absorption, the diffusion approximation is no longer valid and Eq. (4) predicts &g t) curve behavior that is unreliably even slower than DLS approximation for single scattering. Nonetheless compensating for speckle stow-down based οη μ _α /μ^ ratio effectively restores the MSD and the consequent \G*(o))\ values to match the results of conventional rheoiogy. The telegrapher equation, on the other hand, is inclined to over-estimate the \G*(o))\ whenever scattering is highly anisotropic. This issue is further aggravated when absorption is strong and modulus is magnified erroneously (Fig. 16B). Finally, in these weakly scattering samples with low TiC¾ concentration, carbon particles aggregation heavily modifies the average particle size. Therefore, while PSCT-MCRT accurately evaluates the particles' MSD, lack of sufficient knowledge on the net increase in particles' radius (Eq. (7)) leads to an over-estimated. \G*(o))\, in this case, as seen in Fig. 16C. The underlying causes of these observations are discussed in more detail below.

[0082] Figs. 17A. T7B, 17C display results of \G*(a>)\ derived from the gift) curves of Fig. 15B, using the same three approaches. Both DWS and telegrapher approaches can successfully isolate the contribution of optical properties in samples, for which μ', and,¾ are non-negligible and proportional, as shown in Fig. 17A, 17B, respectively. Similarly to Figs. 12 A, 12B, 12C, the extracted \G*(m)\ curve exhibits a drastic offset for weakly scattering samples with negligible absorption μ' _χ ~ 3.2 mm ^"1 and μ _α - 0). n contradistinction, the PSCT-MCRT results, shown in Fig. 17C, exhibit a close agreement with conventional rheology in all cases.

Discussion.

[00831 Examples 2 through 4 address the influence of optical absorption and scattering on temporal speckle intensity fluctuations and clarify that alterations in sample optical properties complicate the analysis of the speckle intensity autocorrelation curve, gz(t), for extracting the MSD of light scattering panicles, and induce inaccuracies in the estimated viscoelastic moduli. Results of Figures 1 1, 13, 15 A, 1 SB clearly illustrate that for samples of identical viscosities, gi(t) is still modulated by tuning μ _α and μ',. in particular, Fig. 1 i demonstrates that increasing μ leads to faster speckle decorrelation, for glycerol solutions of identical viscosities. Here, μ _: is raised by increasing scattering particles concentration. This causes a net growth in the number of scattering events within the illuminated volume and renders the speckle pattern more sensitive to even the smallest Brownian displacements of scattering particles. μ may also increase by reducing the anisotropy parameter, g. In this case, larger scattering angles (Doppler shifts) are more likely and speckle fluctuations are more perceptive to the displacement of scattering particles. On the contrary when μ„ is elevated by tuning the carbon nano-powder concentration, longer light paths terminate due to absorption. As a result, rate of speckle fluctuations is reduced, Fig. 13. Therefore, the overall decay trend of the g (i) curves may slow down by either reducing the μ or increasing the μ _α and, as Fig. 15A, 15B indicate, the ratio μ^μ', often sufficiently explains how the ₂ (t) decay trend is adjusted by optical properties. In the current study, Mie theory is exploited to obtain μ _α , μ.„ and g based on the size, and concentration of TiC¼ and carbon particles, as well as their relative refractive indices to that of the background glycerol solution at the source wavelength of 632 nm, In these calculations, the actual particle sizes of TiOi and carbon particles, derived from. DLS-based particle sizing experiment, are used to ensure the accuracy of the resulting optical properties. These properties are indeed responsible for majority of variations between speckle intensity autocorrelation curves seen in Figs. 11 , 13, and 15. At the same time, results of our independent DLS-based particle sizing measurements reveal that carbon panicles are prone to agglomeration at higher concentrations, and give rise to slightly larger average particle sizes. The shifts in average particle size is likely responsible for the excessive slowing down of g ₂ (i) curves even beyond the DLS limit, in weakly scattermg ar d strongly absorbing samples of Fig. 15 A. [§§84| la the current study, sample optical properties are tuned based on the range of values relevant to common bio-fluids. In biological systems, μ' ₃ is related to the size distribution of cellular nuclei and organelles, and the concentrations of connective fibers and collagen, and ½ is primarily dependent on blood perfusion, lipid and water content, and presence of biological pigments such as melanin and bilirubin. For instance, the optical properties of oxygenated blood are μ _$ ~ 64.47 mm ^"3 , /< _a ~ 0.3 mm ^" ', and g=0.982 (@ 633 am), and for bile μ„ ~ 42.5±7.5 mm and,« _a ~ 8.8± 1.9 mm ^"1 , and g=0.92 (@ 410 ran), in order to conduct LSR in tissue, it is necessary to experimentally evaluate optical properties, prior to further analysis of the MSD and subsequently \G*(o))\. Here we demonstrated the potential of extracting both. μ _α and μ', from temporally averaged speckle frames and the total remittance profile of the photons. T o this end. the radial diffuse remittance profile was fitted to a model curve derived from steady state diffusion theory and μ _α and μ were extracted. The results of the current study, however, indicate that independent determination of both parameters may not be necessary and evaluating the parameter μ _α /μ , as a whole adequately simplifies the problem. This ratio is related to transport albedo, given by α -μ' Ί+μ _α ), and μ _α /μΊ = I/a'~l. The transport albedo is in turn closely correlated with the degree of depolarization of back-scattered Sight and a more simplified approach may be sufficient to extract this ratio based on the polarization p roperties of the received speckle signal, in a more realistic scenario, such as in tissue, apart from optical properties, the poly-dispersity of scattering particles influences the speckle fluctuations. Large scattering particles pose slower Brownian displacements, where as smaller particles exhibit faster thermal motions, and modify the decay rate of ^t) curve, accordingly. Moreover interactions between live scattering centers complicate the analysis of speckle intensity fluctuations in biological systems. For more in-depth analysis of scattering features in tissue, additional hardware capabilities may be embedded to incorporate the polarization dependent analysis of diffused back-scattered light or angle-resolved low coherence radiation to more accurately describe particle size distribution within tissue.

[0085] Analysis of the acquired speckle frame series show that variations in optical properties not only adjust the speckle intensity fluctuation rate, but also modify the speckle contrast, which is closely related to the grft) plateau. Here, fast acquisition at 964 fps (exposure time- 1 ms) is used to capture the rapid speckle fluctuations and avoid temporal speckle blurring. However, highly scattering samples with weak absorption exhibit exceedingly rapid speckle fluctuations which restrain the speckle temporal contrast. Moreover, samples with different optical properties pose distinct backscaitered signal level. Since the CMOS sensor bit depth is limited, the spatial speckle contrast reduces as _, «' _r increases due to CMOS pixel saturation, and improves by increasing μ _α . The poor contrast, potentially affects the long time behavior ofgj(t) curves by raising the plateau level. [0086] The current study compares the performance of three approaches used to isolate the influence optical and mechanical properties on speckle intensity temporal fluctuations, to derive particle MSD from g ₂ ft) curves. The extent of particle MSD is in turn related to the sample viscoelastic modulus through the GSER (Eq. (8)), Among the three approaches used here, the DWS formalism provides the simplest and most mathematically tractable expression for speckle intensity fluctuations as shown in Eq (4). The results presented in Figs, 12A through 12C, 14A through 14C, 16A through 16C, and 7A through i 7C demonstrate that for typical biological tissues, wit non-negligible weak to moderate absorption features (μ _α ≠ 0), and highly anisotropic scattering (g ~ 0.9), the simple DWS expression and a partial knowledge of optical properties via μ,- μ'·, ratio enables the accurate evaluation of the MSD and subsequently estimation of \G*(e>)\ via the GSER equation.

[60S7J However, the DWS formalism fails whenever absorption is negligible, since the modifying factor οΐμ _α ίμ'.— » 0. In this case, as shown in Figs, 12A, 14A, and 1.7A, the final \G*( )\ curves derived from the MSD, exhibit a bias with respect to the results of standard mechanical testing. The magnitude of this bias is proportional to the deviation of the optical properties from that of a strongly scattering medium.

In the other extreme, for weakly scattering samples of strong absorption, when μ _α Ιμ ' _s is markedly large, Eq. (4) predicts that the g i) curve would slow down indefinitely. Such behavior is not practically feasible, since the received light has scattered at least once and the g ft) curve is not expected to decay any slower than the function of Eq. (2), which is obtained from the DLS formalism for single- scattered light intensity autocorrelation function. The generally cited criterion for validity of DWS formalism is that the mean free path should be sufficiently smaller than the absorption length, or equivalently μ _α !μ' _χ < 0.1. From Figs, I4A, 16A, and 17A, it is evident thai the DWS formalism provides an accurate description of particle MSD and subsequently the \G*(o))\ in moderately absorbing media. The competency of the DWS equation is explained by the broad distribution of received rays in the back- scattering geometry, which is composed of both sub-diffusive ballistic and snake photons as well as diffusive components. The DWS equation is plausibly accurate in describing the behavior of the diffusive part, equivalent to the early decay of gift). On the other hand, it falls short in describing the long-time decay of the gift), related to shorter path lengths with fewer scattering events. However, the long time plateau of gift) curve is often affected by speckle contrast variability as described above. The early, intermediate, and long time decay of gift) curve translate into high, mid, and low speed particles displacements, MSD, respectively. The MSD at these time scales in turn correspond to \G*fco)\ measured at high, intermediate, and low frequencies, respectively. Thus, it is evident that the DWS formalism permiis a precise account of vsscoeiastic modulus in die range of moderate to high frequencies for highly scattering samples with moderate absorption. |0089] As opposed to DWS approach, the telegrapher equation requires not only the μ, ίμ ' _s ratio, hut also the anisotropy factor, g, to retrieve the particles' MSD from g ₂ fi) as seen ixs Eq. (5). Despite incorporating this extra piece of information, the telegrapher equation does not provide any improvement upon DWS in most cases (Figs, 12A through 12C, 14A through 14C, and 17A, 17B). Comparing the viscoelastic modulus in Figs. 16A, 16B reveals that the telegrapher equation performs worse than DWS in the presence of strong absorption, especially if scattering is highly anisotropic. This is an unexpected observation since the telegrapher equation has been originally proposed to overcome the limitations of the diffusion equation in treating scattering anisotropy and strong absorption. Close examination o£g ^e! ft) in Eq. (5) reveals thai for small χ°$ο ³ Η'<άτ'(ίρ+3μ _α μ' _Λ this equation follows a similar trend to that of Eq. (4). This explains me similarities between estimated viscoelastic modulus derived via the DWS approach and telegrapher equation, in cases when optical scattering is dominant. At intermediate x values (0.5 < x <1), the g ¾i decay rate increases slightly (compared to for large g (anisotropic scattering). Finally for (x > 1), which often corresponds to short optical paths with fewer number of scattering events, gi ^!e! ( breaks down similar to DWS approach. For weakly scattering samples of strong absorption in Fig. 16B, μ _α /μ' ₅ - 0.S and 3.5, respectively, and is large even at initial decay times. Since scattering is highly anisotropic as well, (g=Q,71 , and 0.84, respectively), telegrapher equation predicts that g ₂ (t) is rapidly- decaying function of x. However, in reality elevated μ _α slows down the gift) decay rate. As a result, if telegrapher equation is exploited to analyze the experimentally evaluated g t curves in the presence of both strong absorption and scattering anisotropy, MSD tends to be underestimated and the final \ G*f(o)\ values are over-estimated, as seen in Fig. 16B. Thus, telegrapher equation proves unreliable and tails short of the intent to improve upon DWS.

[0090] The results in Figs. 12A through 12C, 14A through 14C, 16A through 16C and 17C, demonstrate that the use of the embodiment of the PSCT-MC T algorithms of the invention, that takes into account the entire set of experimental geometry, optical properties, and polarization effects provide the most accurate estimate of the MSD and the sample viscoeiasticity for any arbitrary choice of optical properties. The PSCT-MCRT approach, although computationally intensive, accurately tracks photons within the turbid medium of known optical properties and computes the total momentum transfer As a result, in all cases it provides superior accuracy over DWS and telegrapher equations. Figs. 12C, 14C, 16C, and 17C clearly depict the advantage of using this numerical approach in accurate calculation of viscoelastic modulus, \G*f(o for any arbitrary set of optical properties. The only slight exception appears in Fig. 16C, in which PSCT-MCRT approach overestimates the viscoelastic modulus for weakly scattering samples of strong absorption. At these weakly scattering samples with lower TiQ ₂ concentrations and higher carbon nano-powder content, carbon particles dominantly determine the average particle radius. In this case, PSCT-MCRT approach correctly deduces particles MSD from experimentally evaluated gift) curves using Eq, (4). However, lack of sufficient information about the effective particle size, due to particle agglomeration, and substituting the nominal particle radius (200 nra) in Eq. 8 results in a slight offset of the evaluated modulus compared to the standard rheometry measurements. This observation indicates the importance of more robust particle sizing method to improve the accuracy of LSR measurements.

f 0091 J Implementation of the embodiments of the invention demonstrated thai by tuning the sample's optical scattering and absorption, temporal speckle intensity fluctuations are modulated independently from, viscoelastic properties. Therefore, the influence of sample's optical properties needs to be isolated in order to correctly derive the MSD and subsequently estimate the viscoelastic modulus from LSR measurements. These findings indicate that in the presence of moderate optical absorption, the simple DWS formalism based on diffusion theory closely mirrors the more computationally intensive PSCT- CRT approach in extracting the MSD for the typical set of optical properties, and yields accurate estimates of sample viscoelastic moduli. These findings obviate the need for going through a more complex route of Monte-Carlo Ray Tracing, whenever noticeable absorption features exist and the ratio P- pt' _s « 1. While the DWS expression proves adequate for interpreting the LSR measurements in turbid media with typical optical properties of tissue, the DWS formalism fails in the case of low to moderate scattering whenever absorption is negligible. The curren development on correcting for the influence of optical properties helps to significantly improve the performance and accuracy of LSR to measure the mechanical properties of tissue.

[05)92] The following notes are in order. References made throughout this specification to "one embodiment," "an embodiment," "a related embodiment," or similar language mean that a particular feature, structure, or characteristic described in connection with the referred to "embodiment" is included in at least one embodiment of the present invention. Thus, appearances of these phrases and terms may, but do not necessarily, refer to the same implementation. It is to be understood mat no portion of disclosure, taken on its own and in possible connection with a figure, is intended to provide a complete description of all features of the invention.

f0093] In addition, the following disclosure may describe features of the invention with reference to corresponding drawings, in which like numbers represent the same or similar elements wherever possible. It is understood that in the drawings, the depicted structural elements are generally not to scale, and certain components may be enlarged relative to the other components for purposes of emphasis and clarity of understanding. It is also to be understood that no single drawing is intended to support a complete description of all features of the invention. In other words, a given drawing is generally descriptive of only some, and generally not all, features of the invention. A given drawing and an as sociated portion of the disclosure containing a description referencing such drawing do not, generally , contain all elements of a particular view or all features that can be presented is this view, for purposes of simplifying the given drawing and discussion, and to direct the discussion to particular elements that are featured in this drawing. A skilled artisan will recognize that the invention may possibly be practiced without one or more of the specific features, elements, component, structures, details, or characteristics, or with the use of other methods, components, materials, and so forth. Therefore, although a particular detail of an embodiment of the invention may not be necessarily shown in each and every drawing describing such embodiment, ihe presence of this detail irs the drawing may be implied unless the context of the description requires otherwise, in other instances, well known structures, details, materials, or operations may be not shown in a given drawing or described in detail to avoid obscuring aspects of an embodiment of the invention that are being discussed. Furthermore, the described single features, structures, or characteristics of the invention may be combined in any suitable manner in one or more further embodiments.

|Q094] If the schematic logical flo w chart diagram is included, the depicted order and labeled steps of the logical flow are indicative of only one embodiment of the presented method. Other steps and methods may be conceived that are equivalent in function, logic, or effect to one or more steps, or portions thereof, of the illustrated method. Additionally, the format and symbols employed are provided to explain the logical steps of the method and are understood not to limit the scope of the method.

[0095] While the description of the invention is presented through the above examples, those of ordinary skill in the art understand that modifications to, and variations of, the illustrated embodiments may be made without departing from the inventive concepts disclosed herein. Furthermore, disclosed aspects, or portions of these aspects, may be combined in ways not listed above. Overall, embodiments of the invention demonstrate the capabilities of the LSR for non-contact evaluation of the bulk mechanical properties of bioiluids and probing heterogeneities in viscoelastic properties. These capabilities of the LSR can be advantageously exploited, for example, for studying the regionally-varying rheoiogical properties of bioiluids induced by variations in concentration of macromolecuSes (such as collagen and hyaluronic acid) and electrolytes, for instance in a vitreous body. The invention as recited in claims appended to this disclosure is intended to be assessed in light of the disclosure as a whole, including features disclosed in prior art to which reference is made.