Measurement of the complex refractive index of tissue-mimicking phantoms and biotissue by extended differential total reflection method

Tutorial on the Use of the Photon Diffusion Approximation for Fast Calculation of Tissue Optical Properties

Computer simulations, which are performed at a single wavelength at a time, have been traditionally used to estimate the optical properties of tissues. The results of these simulations need to be interpolated. For a broadband estimation of tissue optical properties, the use of computer simulations becomes time consuming and computer demanding. When spectral measurements are available for a tissue, the use of the photon diffusion approximation can be done to perform simple and direct calculations to obtain the broadband spectra of some optical properties. The additional estimation of the reduced scattering coefficient at a small number of discrete wavelengths allows to perform further calculations to obtain the spectra of other optical properties. This study used spectral measurements from the heart muscle to explain the calculation pipeline to obtain a complete set of the spectral optical properties and to show its versatility for use with other tissues for various biophotonics applications.

Model-based prediction of optogenetic sound encoding in the human cochlea by future optical cochlear implants

When hearing fails, electrical cochlear implants (eCIs) partially restore hearing by direct stimulation of spiral ganglion neurons (SGNs). As light can be better confined in space than electrical current, optical CIs (oCIs) provide more spectral information promising a fundamental improvement of hearing restoration by cochlear implants. Here, we turned to computer modelling for predicting the outcome of optogenetic hearing restoration by future oCIs in humans. We combined three-dimensional reconstruction of the human cochlea with ray-tracing simulation of emission from LED or laser-coupled waveguide emitters of the oCI. Irradiance was read out at the somata of SGNs. The irradiance values reached with waveguides were about 14 times higher than with LEDs, at the same radiant flux of the emitter. Moreover, waveguides outperformed LEDs regarding spectral selectivity. oCIs with either emitter type showed greater spectral selectivity when compared to eCI. In addition, modeling the effects of the source-to-SGN distance, orientation of the sources and impact of scar tissue further informs the development of optogenetic hearing restoration.

Immersion optical clearing of adipose tissue in rats: ex vivo and in vivo studies

Optical clearing (OC) of adipose tissue has not been studied enough, although it can be promising in medical applications, including surgery and cosmetology, for example, to visualize blood vessels or increase the permeability of tissues to laser beams. The main objective of this work is to develop technology for OC of abdominal adipose tissue in vivo using hyperosmotic optical clearing agents (OCAs). The maximum OC effect (77%) was observed for ex vivo rat adipose tissue samples exposed to OCA on fructose basis for 90 minutes. For in vivo studies, the maximum effect of OC (65%) was observed when using OCA based on diatrizoic acid and dimethylsulfoxide for 120 minutes. Histological analysis showed that in vivo application of OCAs may induce a limited local necrosis of fat cells. The efficiency of OC correlated with local tissue damage through cell necrosis due to accompanied cell lipolysis.

Multimodal quantitative optical elastography of the crystalline lens with optical coherence elastography and Brillouin microscopy

Assessing the biomechanical properties of the crystalline lens can provide crucial information for diagnosing disease and guiding precision therapeutic interventions. Existing noninvasive methods have been limited to global measurements. Here, we demonstrate the quantitative assessment of the elasticity of crystalline lens with a multimodal optical elastography technique, which combines dynamic wave-based optical coherence elastography (OCE) and Brillouin microscopy to overcome the drawbacks of individual modalities. OCE can provide direct measurements of tissue elasticity rapidly and quantitatively, but it is a challenge to image transparent samples such as the lens because this technique relies on backscattered light. On the other hand, Brillouin microscopy can map the longitudinal modulus with micro-scale resolution in transparent samples. However, the relationship between Brillouin-deduced modulus and Young's modulus is not straightforward and sample dependent. By combining these two techniques, we can calibrate Brillouin measurements with OCE, based on the same sample, allowing us to completely map the Young's modulus of the crystalline lens. The combined system was first validated with tissue-mimicking gelatin phantoms of varying elasticities (N = 9). The OCE data was used to calibrate the Brillouin shift measurements and subsequently map the Young's modulus of the phantoms. After validation, OCE and Brillouin measurements were performed on ex-vivo porcine lenses (N = 6), and the Young's modulus of the lenses was spatially mapped. The results show a strong correlation between Young's moduli measured by OCE and longitudinal moduli measured by Brillouin microscopy. The correlation coefficient R was 0.98 for the phantoms and 0.94 for the lenses, respectively. The mean Young's modulus of the anterior and posterior lens was 1.98 ± 0.74 kPa and 2.93 ± 1.13 kPa, respectively, and the Young's modulus of the lens nucleus was 11.90 ± 2.94 kPa. The results presented in this manuscript open a new way for truly quantitative biomechanical mapping of optically transparent (or low scattering) tissues in 3D.

Complex Refractive Index Dispersion of Strong Absorbing Material Determined Using Internal Reflectance Spectra Measurement

Complex refractive index dispersion (CRID) of offset inks is an important spectral property that affects the quality of printing. Due to the strong absorption of offset inks, great difficulty exists when measuring their CRID. In this study, a recently proposed apparatus that can detect the internal reflectance spectra was used to measure the CRID of three strong absorbing offset inks (magenta, yellow, and cyan). Both anomalous dispersion curve and extinction coefficient curve were well determined over the spectral range of 400-750 nm. This study experimentally proves that the apparatus and related method are feasible for the CRID measurement of strong absorbing materials and could serve as a powerful measuring tool for optical parameters.

Refractive index of adipose tissue and lipid droplet measured in wide spectral and temperature ranges

This study presents refractive index measurements of human and porcine adipose tissues and lipid droplet content in the visible and near-infrared. The coefficients of the Sellmeier formula were calculated for approximation of tissue dispersion. For the first time, to the best of our knowledge, the phase transition temperatures and temperature increments dn/dT of adipose tissue were quantified for a wide wavelength range from 480 to 1550 nm and from room temperature up to 50°C. For human abdominal adipose tissue, the refractive index increment averaged across all wavelengths is dn/dT=-(3.54±0.15)×10^-4°C^-1, for porcine tissue dn/dT=-7.92(0.74)×10^-4°C^-1, and for porcine lipid droplet dn/dT=-6.01(0.29)×10^-4°C^-1. Data available in literature for refractive indices of adipose tissues measured by different techniques are summarized and compared with the received data.

Spectral refractive index assessment of turbid samples by combining spatial frequency near-infrared spectroscopy with Kramers-Kronig analysis

A practical algorithm for estimating the wavelength-dependent refractive index (RI) of a turbid sample in the spatial frequency domain with the aid of Kramers-Kronig (KK) relations is presented. In it, phase-shifted sinusoidal patterns (structured illumination) are serially projected at a high spatial frequency onto the sample surface (mouse scalp) at different near-infrared wavelengths while a camera mounted normally to the sample surface captures the reflected diffuse light. In the offline analysis pipeline, recorded images at each wavelength are converted to spatial absorption maps by logarithmic function, and once the absorption coefficient information is obtained, the imaginary part (k) of the complex RI (CRI), based on Maxell's equations, can be calculated. Using the data represented by k, the real part of the CRI (n) is then resolved by KK analysis. The wavelength dependence of n  (  λ  )   is then fitted separately using four standard dispersion models: Cornu, Cauchy, Conrady, and Sellmeier. In addition, three-dimensional surface-profile distribution of n is provided based on phase profilometry principles and a phase-unwrapping-based phase-derivative-variance algorithm. Experimental results demonstrate the capability of the proposed idea for sample's determination of a biological sample's RI value.

Monitoring of temperature-mediated phase transitions of adipose tissue by combined optical coherence tomography and Abbe refractometry

Observation of temperature-mediated phase transitions between lipid components of the adipose tissues has been performed by combined use of the Abbe refractometry and optical coherence tomography. The phase transitions of the lipid components were clearly observed in the range of temperatures from 24°C to 60°C, and assessed by quantitatively monitoring the changes of the refractive index of 1- to 2-mm-thick porcine fat tissue slices. The developed approach has a great potential as an alternative method for obtaining accurate information on the processes occurring during thermal lipolysis.

Simple multimodal optical technique for evaluation of free/bound water and dispersion of human liver tissue

The optical dispersion and water content of human liver were experimentally studied to estimate the optical dispersions of tissue scatterers and dry matter. Using temporal measurements of collimated transmittance [Tc(t)] of liver samples under treatment at different glycerol concentrations, free water and diffusion coefficient (Dgl) of glycerol in liver were found as 60.0% and 8.2×10-7  cm2/s, respectively. Bound water was calculated as the difference between the reported total water of 74.5% and found free water. The optical dispersion of liver was calculated from the measurements of refractive index (RI) of tissue samples made for different wavelengths between 400 and 1000 nm. Using liver and water optical dispersions at 20°C and the free and total water, the dispersions for liver scatterers and dry matter were calculated. The estimated dispersions present a decreasing behavior with wavelength. The dry matter dispersion shows higher RI values than liver scatterers, as expected. Considering 600 nm, dry matter has an RI of 1.508, whereas scatterers have an RI of 1.444. These dispersions are useful to characterize the RI matching mechanism in optical clearing treatments, provided that [Tc(t)] and thickness measurements are performed during treatment. The knowledge of Dgl is also important for living tissue cryoprotection applications.

Determination of the complex refractive index segments of turbid sample with multispectral spatially modulated structured light and models approximation

Spectral data enabling the derivation of a biological tissue sample's complex refractive index (CRI) can provide a range of valuable information in the clinical and research contexts. Specifically, changes in the CRI reflect alterations in tissue morphology and chemical composition, enabling its use as an optical marker during diagnosis and treatment. In the present work, we report a method for estimating the real and imaginary parts of the CRI of a biological sample using Kramers-Kronig (KK) relations in the spatial frequency domain. In this method, phase-shifted sinusoidal patterns at single high spatial frequency are serially projected onto the sample surface at different near-infrared wavelengths while a camera mounted normal to the sample surface acquires the reflected diffuse light. In the offline analysis pipeline, recorded images at each wavelength are converted to spatial phase maps using KK analysis and are then calibrated against phase-models derived from diffusion approximation. The amplitude of the reflected light, together with phase data, is then introduced into Fresnel equations to resolve both real and imaginary segments of the CRI at each wavelength. The technique was validated in tissue-mimicking phantoms with known optical parameters and in mouse models of ischemic injury and heat stress. Experimental data obtained indicate variations in the CRI among brain tissue suffering from injury. CRI fluctuations correlated with alterations in the scattering and absorption coefficients of the injured tissue are demonstrated. This technique for deriving dynamic changes in the CRI of tissue may be further developed as a clinical diagnostic tool and for biomedical research applications. To the best of our knowledge, this is the first report of the estimation of the spectral CRI of a mouse head following injury obtained in the spatial frequency domain.

Determination of continuous complex refractive index dispersion of biotissue based on internal reflection

The complex refractive index dispersion (CRID), which contains the information on the refractive index dispersion and extinction coefficient spectra, is an important optical parameter of biotissue. However, it is hard to perform the CRID measurement on biotissues due to their high scattering property. Continuous CRID measurement based on internal reflection (CCRIDM-IR) is introduced. By using a lab-made apparatus, internal reflectance spectra of biotissue samples at multiple incident angles were detected, from which the continuous CRIDs were calculated based on the Fresnel formula. Results showed that in 400- to 750-nm range, hemoglobin solution has complicated dispersion and extinction coefficient spectra, while other biotissues have normal dispersion properties, and their extinction coefficients do not vary much with different wavelengths. The normal dispersion can be accurately described by several coefficients of dispersion equations (Cauchy equation, Cornu equation, and Conrady equation). To our knowledge, this is the first time that the continuous CRID of scattering biotissue over a continuous spectral region is measured, and we hereby have proven that CCRIDM-IR is a good method for continuous CRID research of biotissue.

Analysis of reflectance curve of turbid media and determination of the non-surface complex refractive index

Based on the theory of Goos-Hänchen shift and its continuity near the critical angle, we introduce the concept of penetration depth below the critical angle, and obtain the general formula of reflectance using the gradient complex refractive index multilayered model. Compared with the fitting curve with Fresnel's Formula, our calculated results are more consistent with experimental results of Intralipid solution and the suspension of rutile TiO(2) powder. Combining the change of penetration depth near the critical angle with our model, we also reveal the essence of a simple method used to obtain the non-surface complex refractive index of turbid media.

Measurement of the refractive index of hemoglobin solutions for a continuous spectral region

Determination of the refractive index of hemoglobin solutions over a wide wavelength range remains challenging. A famous detour approach is the Kramers-Kronig (KK) analysis which can resolve the real part of complex refractive index from the imaginary part. However, KK analysis is limited by the contradiction between the requirement of semi-infinite frequency range and limited measured range. In this paper, based on the Multi-curve fitting method (MFM), continuous refractive index dispersion (CRID) of oxygenated and deoxygenated hemoglobin solutions are measured using a homemade symmetrical arm-linked apparatus in the continuous wavelength range with spectral resolution of about 0.259nm. A novel method to obtain the CRID is proposed.

Continuous refractive index dispersion measurement based on derivative total reflection method

Traditionally, continuous refractive index dispersion (CRID) measurement of materials with scattering is hard to realize. In this paper, CRID measurement based on the derivative total reflection method (CRIDM-DTRM) is proposed to measure the CRID of both absorption and scattering materials. It effectively determined the CRID of K9 glass, concentrated milk, and 0.5% methyl red solution in the 400-750 nm range with the spectral resolution of about 0.259 nm. For the first time, CRID of a scattering material is measured. CRIDM-DTRM is a useful technique in the field of RID measurement, especially for biotissues and anomalous dispersion materials.

Effect of the gradient of complex refractive index at boundary of turbid media on total internal reflection

We analyze the existence of non-uniformity at the boundary of turbid media, and develop a gradient complex refractive index multilayered model in terms of this fact. Our model reveals the physics mechanism of the discrepancies between experimental data above the critical angle and the fitting curve with Fresnel's Formula. Also, from the perspective of the energy flow, reflectance R is obtained by the simplified models. We get complex refractive indexes and reflectance curves by fitting experimental data of 20% and 30% Intralipid solutions and rutile TiO₂ powder suspension with two different methods. Compared with Fresnel's Formula, our model can fit experimental data better.

Two-dimensional scanning focused refractive-index microscopy and applications to refractive-index profiling of optical fibers

The refractive-index profile (RIP) of optical fibers is of fundamental significance in determining critical fiber properties. Here, we present the application of a two-dimensional (2-D) scanning focused refractive-index microscopy (SFRIM) to accurately obtain the 2-D RIP of a graded-index optical fiber. Some modifications are made to SFRIM for better 2-D measurement. Quantitative RIP of the fiber is obtained with derivative total reflection method. The refractive-index accuracy is 0.002. The measured result is in good agreement with theoretical expectation. This method is straightforward, simple, repeatable, and free from signal distortion. This technique is suitable for symmetric and asymmetric optical fibers. The results indicate that this technique can be applied to obtain the RIPs of a wide range of materials and has broad application prospect in many fields.

Study on the refractive index matching effect of ultrasound on optical clearing of bio-tissues based on the derivative total reflection method

In recent years, the tissue optical clearing (OC) technique in the biomedicine field has drawn lots of attention. Various physical and chemical methods have been introduced to improve the efficacy of OC. In this study, the effect of the combination of glycerol and ultrasound treatment on OC of in vitro porcine muscle tissues has been investigated. The refractive index (RI) matching mechanism of OC was directly observed based on the derivative total reflection method. A theoretical model was used to simulate the proportion of tissue fluid in the illuminated area. Moreover, the total transmittance spectra have been obtained by a spectrometer over the range from 450 nm to 700 nm. The administration of glycerol and ultrasound has led to an increase of the RI of background medium and a more RI matching environment was achieved. The experimental results support the validity of the ultrasound treatment for OC. The RI matching mechanism has been firstly quantitatively analyzed based on the derivative total reflection method.

Refractive index measurement of turbid media by transmission of backscattered light near the critical angle

We investigate experimentally the determination of the effective refractive index (RI) of a turbid particle suspension from the angle dependence of light scattered by the particles and then transmitted into a transparent prism of higher RI. We assembled a versatile experimental device that may be recognized as an Abbe-type refractometer in which the sample is illuminated from the prism side and use it to measure the intensity profile of diffuse light refracted into the prism around the critical angle. By fitting a recently proposed theoretical model we extract the complex RI of turbid suspensions of particles from the measured intensity profiles. We show that the real part of the effective RI is readily obtained with good precision regardless of how the sample is illuminated, whereas obtaining the imaginary part is done with less precision but nevertheless useful measurements can be obtained. The effective RI obtained with this method compares very well with the so-called van de Hulst effective RI and the one derived from Keller's model of the effective propagation constant.

Note: refractive index sensing of turbid media by differentiation of the reflectance profile: does error-correction work?

A widely used method for determining refractive index postulates that the derivative of the angular profile for light reflected from the sample is maximum at the critical angle for total internal reflection (TIR). It is well-known that in turbid media this "differentiation method" yields errors in refractive index. Unexplained anomalies in previous error-calculations are eliminated if one uses a recent model of TIR which departs from traditional Fresnel theory. However we find that, in practical situations, the refractive index obtained by differentiation even after error-correction is significantly different from the best estimate for the refractive index obtained by curve-fitting the reflectance data. Thus the differentiation method lacks scientific validity in turbid media.

Effect of tissue fluid on accurate determination of the complex refractive index of animal tissue

We investigate the effect of tissue fluid on the measurement of complex refractive index (RI) of animal tissue. A new model is proposed and verified through experimental results of simulation samples made of glycerol and methyl-red-doped poly(methyl methacrylate). Coupled with polarized optical reflectance measurements performed on several kinds of animal muscle tissues, RIs were resolved using the new model. We find that the tissue fluid existing at the prism-sample interface is unavoidable. We also find that with a change of proportion of the tissue fluid, the RI of muscle tissue can still be measured using the new model.