Anisotropic photon migration in human skeletal muscle

Energy metabolism design of the striated muscle cell

The design of the energy metabolism system in striated muscle remains a major area of investigation. Here, we review our current understanding and emerging hypotheses regarding the metabolic support of muscle contraction. Maintenance of ATP free energy, so called energy homeostasis, via mitochondrial oxidative phosphorylation is critical to sustained contractile activity, and this major design criterion is the focus of this review. Cell volume invested in mitochondria reduces the space available for generating contractile force, and this spatial balance between mitochondria acontractile elements to meet the varying sustained power demands across muscle types is another important design criterion. This is accomplished with remarkably similar mass-specific mitochondrial protein composition across muscle types, implying that it is the organization of mitochondria within the muscle cell that is critical to supporting sustained muscle function. Beyond the production of ATP, ubiquitous distribution of ATPases throughout the muscle requires rapid distribution of potential energy across these large cells. Distribution of potential energy has long been thought to occur primarily through facilitated metabolite diffusion, but recent analysis has questioned the importance of this process under normal physiological conditions. Recent structural and functional studies have supported the hypothesis that the mitochondrial reticulum provides a rapid energy distribution system via the conduction of the mitochondrial membrane potential to maintain metabolic homeostasis during contractile activity. We extensively review this aspect of the energy metabolism design contrasting it with metabolite diffusion models and how mitochondrial structure can play a role in the delivery of energy in the striated muscle.

Anisotropic light propagation in bovine muscle tissue depends on the initial fiber orientation, muscle type and wavelength

The effects of fiber orientation on vis/NIR light propagation were studied in three bovine muscles: biceps brachii, brachialis and soleus. Broadband light was focused onto the sample and the diffuse reflectance spot was captured using a hyperspectral camera (470-1620 nm), after which rhombuses were fitted to equi-intensity points. In samples with fibers running parallel to the measurement surface, the rhombus' major axis was oriented perpendicular to the fiber direction close to the point of illumination. However, at larger distances from the illumination spot, the major axis orientation aligned with the fiber direction. This phenomenon was found to be muscle dependent. Furthermore, the rhombus orientation was highly dependent on the sample positioning underneath the camera, especially when the muscle fibers ran parallel to the measurement surface. The bias parameter, indicating the deviation from a circular shape, was higher for samples with the fibers running parallel to the measurement surface. Moreover, clear effects of wavelength and distance from the illumination point on this parameter were observed. These results show the importance of fiber orientation when considering optical techniques for measurements on anisotropic, fibrous tissues. Moreover, the prediction of muscle fiber orientation seemed feasible, which can be of interest to the meat industry.

Time-resolved measurements of the optical properties of fibrous media using the anisotropic diffusion equation

Transmittance and reflectance from spruce wood and bovine ligamentum nuchae as two different fibrous media are examined by time-of-flight spectroscopy for varying source detector separations and several orientations of the fibers in the sample. The anisotropic diffusion theory is used to obtain the absorption coefficient and the diffusion coefficients parallel and perpendicular to the fibers. The results are compared to those obtained with the isotropic diffusion theory. It is shown that for increasing source detector separations, the retrieved optical properties change as expected from Monte Carlo simulations performed in a previous study. This confirms that the anisotropic diffusion theory yields useful results for certain experimental conditions.

Observation of anisotropic diffusion of light in compacted granular porous materials

By analyzing spatio-temporal characteristics of short optical pulses diffusively transmitted through compacted granular materials, we reveal that powder compaction can give rise to strongly anisotropic light diffusion. Our disclosure represents a revision of the understanding of optics of powder compacts. Routes to material characterization and investigation of compression-induced structural anisotropy are opened, and the falsification of isotropic models have implications for quantitative spectroscopy of powder compacts (e.g., pharmaceutical tablets).

Imaging scattering orientation with spatial frequency domain imaging

Optical imaging techniques based on multiple light scattering generally have poor sensitivity to the orientation and direction of microscopic light scattering structures. In order to address this limitation, we introduce a spatial frequency domain method for imaging contrast from oriented scattering structures by measuring the angular-dependence of structured light reflectance. The measurement is made by projecting sinusoidal patterns of light intensity on a sample, and measuring the degree to which the patterns are blurred as a function of the projection angle. We derive a spatial Fourier domain solution to an anisotropic diffusion model. This solution predicts the effects of bulk scattering orientation on the amplitude and phase of the projected patterns. We introduce a new contrast function based on a scattering orientation index (SOI) which is sensitive to the degree to which light scattering is directionally dependent. We validate the technique using tissue simulating phantoms, and ex vivo samples of muscle and brain. Our results show that SOI is independent of the overall amount of bulk light scattering and absorption, and that isotropic versus oriented scattering structures can be clearly distinguished. We determine the orientation of subsurface microscopic scattering structures located up to 600 μm beneath highly scattering (μ(') (s) = 1.5 mm(-1)) material.

Effects of anisotropy on the depth of penetration of photons into turbid media

Biomedical applications of near infrared radiation (NIR) techniques (i.e., based on light wavelengths roughly between 400 and 1100 nm) require that a preliminary estimate of the tissue volume being investigated be found. One possible estimate is the depth to which a photon penetrates a tissue before it eventually emerges at a separating plane at a given time. A simple model for this problem can be based on a lattice random walk and was initially analyzed when the associated optical coefficients are isotropic with respect to the geometry. Here we include the effects of anisotropy in the optical coefficients, finding that at long times the statistical properties of the depth of penetration can be accounted for by very simple scaling factors while at short times the anisotropy factors can be quite significant.

Scattering correction by use of a priori information

In this paper we demonstrate how a limited amount of a priori knowledge about spectral variability can be used in extended multiplicative scattering correction (EMSC) to remove disturbing effects such as light scattering variation in visible and near-infrared spectra prior to data modeling. Two different datasets were studied. In the first dataset, pigment concentrations (astaxanthin) were estimated in a model system with different concentrations of the scattering agent intralipid. Different cases were created by including varying levels of intralipid in the calibration set and then applying the models on sample sets with scattering properties both within and outside the calibration range. Including the most accurate estimate of light scattering in the EMSC model gave root mean square errors of prediction (RMSEP) that were similar to a cross-validated global model including all samples, even for extreme extrapolation with regard to scattering properties. Less accurate estimates gave on average RMSEPs half of what could be achieved using EMSC without any a priori knowledge, suggesting that the method also has potential in cases where the accurate light scattering spectrum is difficult to obtain. In the second dataset carbohydrate concentrations (sucrose, fructose, and glucose) were estimated in orange-juice mixtures where unwanted spectral variation was caused by a change in distance between transmittance fiber-optic probes. This caused two different interfering phenomena due to path length variation and saturation in the detection system. The prediction results for a model based on spectra collected at one specific probe distance treated with EMSC with a correction spectrum were comparable to what could be achieved by a global model including spectra collected at three different distances. The corresponding RMSEPs for models using EMSC with no correction term were in the worst cases 4, 22, and 36 times higher for sucrose, fructose, and glucose, respectively.

Rotating linear polarization imaging technique for anisotropic tissues

A novel rotating linear polarization imaging technique is developed to characterize the anisotropic properties of tissues. Differences of orthogonal linear polarization with different incident and detection polarization angles are fitted to an analytical function to retrieve a set of parameters. Experiments with different tissues and Monte Carlo simulations indicate that two of the parameters, G and phi(3)2, are correlated to the anisotropic property and the orientation angle of the fibrous structure in the media. The technique can be used for clinical diagnosis.

Optical anisotropic diffusion: new model systems and theoretical modeling

We have developed several new experimental model systems that demonstrate anisotropic diffusion of light. These systems, consisting of aligned fibers, stretched plastic foam, and stretched plastic frit, have relatively simple microstructures and are easily sliced, making them ideal for testing theoretical models of diffusion. We demonstrate that the solution to the diffusion equation for arbitrary orientation of the diffusion tensor is consistent with experimental measurements. We also show that simple models of microstructure, based on cylindrical and planar scatterers, are consistent with the experimental results. These models provide simple analytical expressions for predicting the degree of alignment of the scatterers from diffuse transmission measurements. The combination of experimental results and theoretical support demonstrates both the power and the limitations of the diffusion model for providing information about microstructure via simple experiments and modeling.

Optical measurement of adipose tissue thickness and comparison with ultrasound, magnetic resonance imging, and callipers

Near-infrared spectroscopy is used to quantify the subcutaneous adipose tissue thickness (ATT) over five muscle groups (vastus medialis, vastus lateralis, gastrocnemius, ventral forearm and biceps brachii muscle) of healthy volunteers (n=20). The optical lipid signal (OLS) was obtained from the second derivative of broad band attenuation spectra and the lipid absorption peak (lambda=930 nm). Ultrasound and MR imaging as well as mechanical calliper readings were taken as reference methods. The data show that the OLS is a good predictor for ATT (<16 mm) with absolute and relative errors of <0.8 mm and <24%, respectively. The optical method compares favourably with calliper reading. The finding of a non-linear relationship of optical signal vs. ultrasound is explained by a theoretical two-layer model based on the diffusion approximation for the transport of photons. The crosstalk between the OLS and tissue hemoglobin concentration changes during an incremental cycling exercise was found to be small, indicating the robustness of OLS. Furthermore, the effect of ATT on spatially-resolved spectroscopy measurements is shown to decrease the calculated muscle hemoglobin concentration and to increase oxygen saturation.

Thermal interaction of short-pulsed laser focused beams with skin tissues

Time-dependent thermal interaction is developed in a skin tissue cylinder subjected to the irradiation of a train of short laser pulses. The skin embedded with a small tumor is stratified as three layers: epidermis, dermis and subcutaneous fat with different optical, thermal and physiological properties. The laser beam is focused to the tumor site by an objective lens for thermal therapy. The ultrafast radiation heat transfer of the focused beam is simulated by the transient discrete ordinates method. The transient Pennes bio-heat equation is solved numerically by the finite volume method with alternating direction implicit scheme. Emphasis is placed on the characterization of the focused beam propagation and absorption and the temperature rise in the focal spot. The effects of the focal spot size and location, the laser power, and the bio-heat equation are investigated. Comparisons with collimated irradiation are conducted. The focused beam can penetrate a greater depth and produce higher temperature rise at the target area, and thus reduce the possibility of thermal damage to the surrounding healthy tissue. It is ideal for killing cancerous cells and small tumors.

Crosstalk and error analysis of fat layer on continuous wave near-infrared spectroscopy measurements

Accurate estimation of concentration changes in muscles by continuous wave near-IR spectroscopy for muscle measurements suffers from underestimation and crosstalk problems due to the presence of superficial skin and fat layers. Underestimation error is basically caused by a homogeneous medium assumption in the calculations leading to the partial volume effect. The homogeneous medium assumption and wavelength dependence of mean partial path length in the muscle layer cause the crosstalk. We investigate underestimation errors and crosstalk by Monte Carlo simulations with a three layered (skin-fat-muscle) tissue model for a two-wavelength system where the choice of first wavelength is in the 675- to 775-nm range and the second wavelength is in the 825- to 900-nm range. Means of absolute underestimation errors and crosstalk over the considered wavelength pairs are found to be higher for greater fat thicknesses. Estimation errors of concentration changes for Hb and HbO(2) are calculated to be close for an ischemia type protocol where both Hb and HbO(2) are assumed to have equal magnitude but opposite concentration changes. The minimum estimation errors are found for the 700825- and 725825-nm pairs for this protocol.

Near-infrared spectroscopy/imaging for monitoring muscle oxygenation and oxidative metabolism in healthy and diseased humans

Near-infrared spectroscopy (NIRS) was initiated in 1977 by Jobsis as a simple, noninvasive method for measuring the presence of oxygen in muscle and other tissues in vivo. This review honoring Jobsis highlights the progress that has been made in developing and adapting NIRS and NIR imaging (NIRI) technologies for evaluating skeletal muscle O(2) dynamics and oxidative energy metabolism. Development of NIRS/NIRI technologies has included novel approaches to quantification of the signal, as well as the addition of multiple source detector pairs for imaging. Adaptation of NIRS technology has focused on the validity and reliability of NIRS measurements. NIRS measurements have been extended to resting, ischemic, localized exercise, and whole body exercise conditions. In addition, NIRS technology has been applied to the study of a number of chronic health conditions, including patients with chronic heart failure, peripheral vascular disease, chronic obstructive pulmonary disease, varying muscle diseases, spinal cord injury, and renal failure. As NIRS technology continues to evolve, the study of skeletal muscle function with NIRS first illuminated by Jobsis continues to be bright.

Angular distribution of diffuse reflectance in biological tissue

We measured angular-resolved diffuse reflectance in tissue samples of different anisotropic characteristics. Experimental measurements were compared with theoretical results based on the diffusion approximation. The results indicated that the angular distribution in isotropic tissue was the same as in isotropic phantoms. Under normal incidence, the measured angular profiles of diffuse reflectance approached the Lambertian distribution when the evaluation location was far away from the incident point. The skewed angular profiles observed under oblique incidence could be explained using the diffuse model. The anisotropic tissue structures in muscle showed clear effects on the measurements especially at locations close to the light incidence. However, when measuring across the muscle fiber orientations, the results were in good agreement with those obtained in isotropic samples.

Anisotropic light diffusion: an oxymoron?

Light propagation in anisotropic random media is studied in the steady-state and time domains. Solutions of the anisotropic diffusion equation are compared to results obtained by the Monte Carlo method. Contrary to what has been reported so far, we find that even in the "diffusive regime" the anisotropic diffusion equation does not describe correctly the light propagation in anisotropic random media.

Fully automated time domain spectrometer for the absorption and scattering characterization of diffusive media

We describe a system for absorption and scattering spectroscopy of diffusive media based on time-resolved reflectance and transmittance measurements. The system is operated with mode-locked lasers tunable in the 550-1050 nm spectral range and on a detection chain based on time-correlated single-photon counting. All measurement procedures such as laser tuning and optimization, signal conditioning, data acquisition, and analysis are completely automated, permitting spectral measurements over the whole range in a few minutes. The criticalities of the system are discussed together with the strategies to compensate them. The Medphot protocol devised for the characterization of photon migration instruments was applied to assess the system performances in terms of accuracy, linearity, noise, stability, and reproducibility. Finally, an example of application of the instrument to the spectroscopy of powders is presented.

Imaging 2D optical diffuse reflectance in skeletal muscle

We discovered a unique pattern of optical reflectance from fresh prerigor skeletal muscles, which can not be described using existing theories. A numerical fitting function was developed to quantify the equiintensity contours of acquired reflectance images. Using this model, we studied the changes of reflectance profile during stretching and rigor process. We found that the prominent anisotropic features diminished after rigor completion. These results suggested that muscle sarcomere structures played important roles in modulating light propagation in whole muscle. When incorporating the sarcomere diffraction in a Monte Carlo model, we showed that the resulting reflectance profiles quantitatively resembled the experimental observation.

Determination of the optical properties of anisotropic biological media using an isotropic diffusion model

We investigate anisotropic light propagation in biological tissue in steady-state and time domains. Monte Carlo simulations performed for tissue that consists of aligned cylindrical and spherical scatterers show that steady-state and time-resolved reflectance depends strongly on the measurement direction relative to the alignment of the cylinder axis. We examine the determination of optical properties using an isotropic diffusion model and find that in the time domain, in contrast to steady-state spatially resolved reflectance measurements, the obtained absorption coefficient does not depend on the measurement direction and is close to the true value. Contrarily, the derived reduced scattering coefficient depends strongly on the measurement direction in both domains. Measurements of the steady-state and time-resolved reflectance from bovine tendon confirm the theoretical findings.

Mean time-of-flight of photons in transillumination measurements of optically anisotropic tissue with an inclusion

We study the effect of optical anisotropy on the mean time-of-flight of photons in a slab of turbid medium containing an inclusion whose optical properties differ from those of the bulk. For this analysis the difference in the mean time for a photon introduced into the slab to reach a specified target point with and without the inclusion is calculated. This difference is defined to be a measure of the contrast. The theoretical model is based on a continuous-time random walk on a lattice, which can be solved exactly and furnishes an exact expression for the contrast. Qualitative and quantitative characteristics of the contrast are analysed as functions of the geometric configuration of the system components (locations of the source, the inclusion and the detector), parameters that specify the optical anisotropy of the medium, and either the scattering properties of the inclusion or the lifetime of the small fluorophore in the case of the time-resolved fluorescence experimental configuration.