CC BY
19DOI 10.24412/cl-37136-2023-1-96-101
BIO-IMAGING USING NOISE: APPLICATION OF LASER SPECKLES FOR DEEP TISSUE
BLOOD FLOW IMAGING
MURALI K1, RIA PAUL1, SOUMYAJIT SARKAR1 AND HARI M VARMA1
department of Biosciences and Bioengineering, Indian Institute of Technology - Bombay, India
ABSTRACT
We present a novel approach for deep tissue blood flow imaging using laser speckles. Our method utilizes a cost-effective system with low frame rate cameras for diffuse correlation spectroscopy (DCS) measurements. We demonstrate the effectiveness of our system through phantom and in-vivo studies, including stroke measurements in mice and number processing tasks in humans to measure the changes in cerebral blood flow. Additionally, we present our recent work on simulation of speckles using stochastic differential equation with desired statistical properties. Our studies contribute to the development of affordable solutions for high density deep tissue blood flow imaging.
INTRODUCTION
Blood flow is a fundamental physiological parameter that plays a vital role in maintaining the normal functioning of tissues and organs in the human body [1]. Accurate measurement and assessment of blood flow are crucial for understanding various physiological processes, diagnosing medical conditions, and guiding treatment strategies. Several optical imaging techniques have been developed to quantify blood flow non-invasively, including Laser Speckle Contrast Imaging (LSCI), Laser Doppler Flowmetry (LDF), Diffuse Correlation Spectroscopy (DCS), and Diffuse Correlation Tomography (DCT) [2,3].
These techniques exploit the unique properties of laser speckles, which arise from the interference and scattering of coherent light by tissues [4]. Laser speckles, appearing a randomly fluctuating intensity noise, carries valuable information about the underlying blood flow dynamics, which can be analyzed to extract meaningful flow-related parameters [5,6].
While LSCI and LDF have proven effective in assessing blood flow in superficial tissues, the measurement of deep tissue blood flow remains challenging [3]. DCS and DCT have emerged as promising approaches for non-invasively probing deep tissue blood flow by harnessing the speckle properties of scattered light. These techniques utilize the inherent noise present in laser speckles to derive quantitative information about blood flow dynamics and perfusion. DCS, in particular, utilizes intensity autocorrelation measurements at multiple distances from the source to quantify blood flow. However, it has limitations in terms of confined detection sites and the requirement for expensive multiple detectors [7].
To overcome these limitations, one alternative approach is to explore the use of array detectors in DCS. While array detectors are not commonly used in DCS, they offer potential solutions to the challenges associated with confined detection sites and the requirement for expensive multiple detectors. However, implementing array detectors for DCS requires high frame rate detectors with reasonable signal-to-noise ratio (SNR) at low exposure time, which are currently not readily available and tend to be more expensive [7,8]. Nevertheless, in light of these challenges, speckle contrast-based methods like SCOS [9], DSCA [10], SCOT, scDCT [11] and their variants [12] have been proposed as alternative techniques to enhance flow quantification in DCS. Speckle
contrast, which represents the ratio of the standard deviation to the mean intensity, serves as a key parameter that relates to the integrated intensity autocorrelation over the exposure time [2].
In this paper, we present an overview of our novel algorithm and a cost-effective system that utilizes low frame rate CCD \or CMOS cameras for DCS measurements. Our approach exploits the fact that multi-exposure speckle contrast data contains information on the intensity autocorrelation [13]. The algorithm employs a multistep Volterra integral method (MVIM) to recover the full auto-correlation function from the multi-exposure speckle contrast data. We demonstrate the effectiveness of our system through experiments conducted on tissue-mimicking phantoms and human subjects, including hand-cuff occlusion and voluntary tasks such as apnea and number processing. Furthermore, we validate our system by measuring stroke in mice using a new small animal platform.
Additionally, we establish the equivalence between laser speckle contrast-based methods and DCS, supported by the Volterra integral equation theory [7, 13]. We emphasize the importance of regularized fitting in multi-exposure speckle contrast imaging to accurately recover the auto-correlation function. Moreover, we introduce M-DCT [14], a high-density DCT system that incorporates a spatially weighted filter to improve depth localization and eliminate unwanted surface artefacts. The iterative use of autocorrelation measurements at multiple delay times enhances the reconstruction results, which are validated through simulations, phantom experiments, and in-vivo human studies.
Lastly, we present our recently published novel approach to simulating laser speckles using a stochastic differential equation [15]. This method enables the generation of speckles with desired statistical properties, including different blood flow profiles and realistic noise models. The simulations encompass both superficial and diffuse speckles, making them applicable to deep tissue blood flow imaging. The validity of our simulation model is confirmed through comparisons with in-vivo studies conducted on mice and healthy human subjects.
METHODS
M-DCS algorithm:
The M-DCS algorithm utilizes the multi-step Volterra integral method (MVIM) to recover the field autocorrelation function. The relationship between speckle contrast (k) and the normalized electric field autocorrelation function (gx) is represented by the equation
which is a Volterra integral equation of the first kind. To solve this equation, it is discretized using the trapezoidal rule and expressed in matrix form. The resulting matrix equation is then solved using Tikhonov regularized least square minimization, where the cost function is minimized to obtain the best estimate of g1. The algorithm incorporates the selection of important parameters such as correlation delay time (t) and exposure time (T) to ensure accurate recovery. Furthermore, an iterative scheme is implemented to update the prior information (x0) at each iteration, enhancing the accuracy of the recovered gt. Detailed steps of the algorithm can be found in Algorithm (Fig 1(b)), and further information is available in reference [7].
(1),
Figure 1: (a) Schematic of the M-DCS / M-DCT system; The system consists of a focused laser source (LD- Laser diode; AL- Aspheric lens; AM- Anamorphic prism; AP- Aperture; FL- Focusing lens; GM- Galvo mirror) illuminated on the sample/ Phantom. The scattered light is captured to camera via objective lens (Obj). (b) A pseudocode of the M-DCS algorithm to recover g1. (c) Photograph of the system.
Figure 2: Schematic of the human head for illustrating the M-DCT system; The idea is that short SDs that has information from extracerebral layers whereas the long SDs contain information from extracerebral as
well as deep layers of brain. We design a filter based on short SD and use it to remove artefacts and
extracerebral interferences from long SDs.
M-DCS system:
The M-DCS system used in this study employs a low frame rate camera, specifically the Basler 640-120-um camera for phantom and small animal experiments, and the Photometries Prime BSI camera for human studies. For deep tissue blood flow measurements, a pointed source illumination with a wavelength of 785 nm (Thorlabs L7850P90) laser is used, while uniform illumination is employed for surface blood flow measurements. The system configuration is illustrated in Figure 1(a) and includes the camera, laser source, and appropriate optical components. The system enables the measurement of multi-exposure speckle contrast at a specified source-detector separation.
High Density M-DCT system:
To overcome challenges associated with extracerebral interferences in diffuse correlation tomography (DCT) measurements, a high-density system is proposed. This system utilizes an array of sources and detectors, modeled as multi-speckle DCT (M-DCT), and incorporates multiple delay-times in an iterative reconstruction approach [14]. The goal is to improve depth localization and accurately measure blood flow in deep tissues. The modified Born approximation is utilized, where a filter design based on short source-detector separation is implemented to enhance discrimination between deep tissue blood flow signals and surface effects, as depicted in Fig (2).
The reconstructed filtered autocorrelation function,
di'F(,rs>rd>T) = —02rUsk° \ / tGf(rd,r,r)GF(r,rs,T)W(r)Dgdr , is computed using the proposed algorithm.
S F
Here gx' is the filtered autocorrelation and W(r) is the weight function designed to address the biased sensitivity of the reconstruction towards shallower region. In addition, by implementing our previously proposed algorithm [16], which can eliminate the requirement for inverting the Jacobian matrix, and could reduce the computational time. All human and animal studies were approved by the Institute ethical committee at Indian Institute of Technology - Bombay and APT research center, Pune.
RESULTS AND DISCUSSION:
Phantom and in-vivo studies:
Here, we present two representative figures illustrating the capability of the M-DCS algorithm and system to recover the autocorrelation function using a low frame rate camera. Figure 3(a) displays the results of g1 obtained from multi-exposure speckle contrast at two different flow conditions. Figure 3(b) demonstrates the relative cerebral blood flow (rCBF) acquired during a number processing task performed by a given subject (n=3 trials). With an SD separation of 2 cm, it can be observed that blood flow increases during the task and decreases after completion, thereby validating the effectiveness of the M-DCS system and algorithm. Further details can be found in Ref [7,8,14].
in S Time (s)
Figure 3: (a) g1 recovered from multi exposure speckle contrast using M-DCS algorithm for two different flow. (b) in-vivo blood flow changes quantified as rCBF during a number processing task;
Animal studies:
To validate our algorithm in pre-clinical studies, we developed a portable modular small animal imaging platform (details in Ref [17]). Using this platform, we measured blood flow in different tissue types of the mouse brain, including arteries, veins, and parenchyma. Figure 4(c) illustrates the measurements obtained from our proposed M-DCS system in both the alive and post-sacrifice conditions. Furthermore, we present a 3D tomographic reconstruction of a blood flow changes associated with stroke in the left hemisphere of mice induced by photo-thrombosis in Figure 4(d).
(a) (b) (c)
Figure 4: A custom-built modular portable animal imaging platform is depicted. (b) An anesthetized animal placed in a stereotaxic frame is shown. (c) The results obtained from the M-DCS algorithm reveal distinct flow patterns in the artery (R1-L), vein (R2-L), and parenchyma (R3-L) regions, both when the animal was alive (indicated by suffix L) and after sacrifice (indicated by suffix D). (d) A tomographic reconstruction demonstrates blood flow during stroke in the left hemisphere induced by photo-thrombosis. Simulation of speckles using SDE:
All the above-mentioned speckle-based blood flow imaging methods requires testing with calibrating phantoms before translation. There are many different ways to simulate speckles in the literature most of which rely upon either the Fourier-based methods or statistical tools. We present a novel method for simulating laser speckles in blood flow imaging using stochastic differential equations (SDE) [15]. This method allows us to generate speckles with predefined probability density functions and temporal auto-correlation, enabling the modelling of different blood flow profiles and the simulation of both superficial and deep tissue speckles. We validated our simulation by comparing the results with in-vivo studies conducted on mice and healthy human subjects. Our method provides a valuable tool for the analysis and development of laser speckle-based imaging techniques. The algorithm, shown in Fig 5(a), utilizes the solution to the SDE based on the Milstein scheme, In+1 = In + a(/n)At + b(In)AWn + 0.5bOn)b'On)[(AWn)2 - At] (2),
where I(t) represent the intensity of the speckles. The parameters 'a' and 'b' are determined by the optical and dynamic properties of the tissue, and further details can be found in Ref [15]. The representative figure of the speckles generated using our proposed method is shown in Fig 5(b), along with their validation using autocorrelation and speckle contrast in Fig 5(c) and 5(d) respectively.
Figure 5: Speckle simulation tool using SDE. (a) The algorithm used to simulate speckles for mimicking deep tissue blood flow is shown. The parameters p and a~ contain information on tissue optical and dynamic properties, which are fed into the SDE algorithm in equation (2). The intensity speckles (as shown in (b)) that
follow an exponential probability density function and the autocorrelation based on the blood flow are generated. Speckle noise is added based on the detector. The algorithm is validated by quantifying either the autocorrelation (as shown in (c)) or the speckle contrast (as shown in (d)).
REFERENCES
[1] Zauner A, Daugherty WP, Bullock MR, Warner DS. Brain oxygenation and energy metabolism: part I -biological function and pathophysiology. Neurosurgery. 2002;51(2):289-302.
[2] Boas DA, Dunn AK. Laser speckle contrast imaging in biomedical optics. J Biomed Opt. 2010; 15(1):011109
[3] Durduran T, Choe R, Baker W, Yodh AG. Diffuse optics for tissue monitoring and tomography. Rep Prog Phys. 2010;73(7):076701.
[4] Goodman JW. Speckle Phenomena in Optics: Theory and Applications. Roberts and Company Publishers; 2007.
[5] Dainty JC. Laser Speckle and Related Phenomena. Vol. 9. Springer Science & Business Media; 2013.
[6] Herranz Olazabal J, Wieringa F, Hermeling E, Van Hoof C. Camera-Derived Photoplethysmography (rPPG) and Speckle Plethysmography (rSPG): Comparing Reflective and Transmissive Mode at Various Integration Times Using LEDs and Lasers. Sensors. 2022 Aug 13;22(16):6059.
[7] Murali K, Nandakumaran AK, Durduran T, Varma HM. Recovery of the diffuse correlation spectroscopy data-type from speckle contrast measurements: towards low-cost, deep-tissue blood flow measurements. Biomed Opt Express. 2019;10(10):5395-5413.
[8] Murali K, Varma HM. Multi-speckle diffuse correlation spectroscopy to measure cerebral blood flow. Biomed Opt Express. 2020;11(11):6699-6709.
[9] Valdes CP, Varma HM, Kristoffersen AK, Dragojevic T, Culver JP, Durduran T. Speckle contrast optical spectroscopy, a non-invasive, diffuse optical method for measuring microvascular blood flow in tissue. Biomed Opt Express. 2014;5(8):2769-2784.
[10] Bi R, Dong J, Lee K. Deep tissue flowmetry based on diffuse speckle contrast analysis. Opt Lett. 2013;38(9):1401-1403.
[11] Huang C, Irwin D, Lin Y, Shang Y, He L, Kong W, Luo J, Yu G. Speckle contrast diffuse correlation tomography of complex turbid medium flow. Med Phys. 2015;42(7):4000-4006.
[12] Seong M, Oh Y, Lee K, Kim JG. Blood flow estimation via numerical integration of temporal autocorrelation function in diffuse correlation spectroscopy. Computer Methods and Programs in Biomedicine. 2022 Jul 1;222:106933.
[13] Murali K, Nandakumaran AK, Varma HM. On the equivalence of speckle contrast-based and diffuse correlation spectroscopy methods in measuring in vivo blood flow. Optics Letters. 2020 Jul 15;45(14):3993-6.
[14] Paul R, Murali K, Varma HM. High-density diffuse correlation tomography with enhanced depth localization and minimal surface artefacts. Biomed Opt Express. 2022;13(11):6081-6099.
[15] Murali K, Varma HM. Laser speckle simulation tool based on stochastic differential equations for bio imaging applications. Biomed Opt Express. 2022;13(12):6745-6762.
[16] Paul R, Murali K, Chetia S, Varma HM. A simple algorithm for diffuse optical tomography without Jacobian inversion. Biomed Phys Eng Express. 2022;8(4):045001.
[17] Paul R, Sarkar S, Marathe SD, Murali K, Das S, Abraham NM, Varma HM. Functional imaging of olfactory bulb and somatosensory cortex in mice using small-animal blood flow imaging platform. InDynamics and Fluctuations in Biomedical Photonics XX 2023 Mar 7 (Vol. 12378, pp. 45-48). SPIE.
[18] Murali K, Varma HM. Exploring different source configurations for laser speckle-based blood flow measurement system. InEuropean Conference on Biomedical Optics 2021 Jun 20 (pp. EM1A-23). Optica Publishing Group.
