Tissue-like Media Research Articles

TH-AB-209-04: 3D Light Sheet Luminescence Imaging with Cherenkov Radiation

Purpose: To recover a three-dimensional density distribution of luminescent molecular probes located several centimeters deep within a highly scattering tissue. Methods: We developed a novel sheet beam Cherenkov-excited luminescence scanned imaging (CELSI) methodology. The sample was irradiated by a horizontally oriented, vertically scanned 6 MV X-ray sheet beam (200mm × 5mm, 0.2mm vertical step) from a radiotherapy linear accelerator. The resulting Cherenkov light emission – and thus luminescent probe excitation – occurred exclusively along the irradiation plane due to a short diffusion path of secondary particles and Cherenkov photons. Cherenkov-excited luminescence was detected orthogonally to the sheet beam by gated, intensified charge coupled device camera. Analogously to light sheet microscopy, a series of luminescence images was taken for varied axial positions (depths) of the Cherenkov light sheet in sample. Knowledge of the excitation plane position allowed a 3D image stack deconvolution and depth-variant attenuation correction. The 3D image post-processing yielded a true spatial density distribution of luminescent molecules in highly scattering tissue. Results: We recovered a three-dimensional shape and position of 400 µL lesion-mimicking phantom tubes containing 25 µM solution of PtG4 molecular probe from 3 centimeter deep tissue-like media. The high sensitivity of CELSI also allowed resolving 100 micron capillaries of test solution. Functional information of partial oxygen pressure at the site of PtG4 molecular probe was recovered from luminescence lifetime CELSI. Finally, in-vivo sheet beam CELSI localized milimeter-sized PtG4-labelled tumor phantoms in multiple biological objects (hairless mice) from single scan. Conclusion: Presented sheet beam CELSI technique greatly extended the useful depth range of luminescence molecular imaging. More importantly, the light sheet microscopy approach was successfully adapted to CELSI, providing means to recover a completely attenuation-corrected 3D image of luminescent probe distribution. Gated CELSI acquisition yielded functional information of a spatially resolved oxygen concentration map of deep lying targets. This work was supported by NIH research grant R01CA109558 and R21EB017559, as well as by Pilot Grant Funds from the Norris Cotton Cancer Center.

An efficient technique for estimating the two-dimensional temperature distributions around multiple cryo-surgical probes based on combining contributions of unit circles

This study presents an efficient, fast and accurate method for estimating the two-dimensional temperature distributions around multiple cryo-surgical probes. The identical probes are inserted into the same depth and are operated simultaneously and uniformly. The first step in this method involves numerical derivation of the temporal performance data of a single probe, embedded in a semi-infinite, tissue-like medium. The results of this derivation are approximated by algebraic expressions that form the basis for computing the temperature distributions of multiple embedded probes by combining the data of a single probe. Comparison of isothermal contours derived by this method to those computed numerically for a variety of geometrical cases, up to 15 inserted probes and 2–10 min times of operation, yielded excellent results. Since this technique obviates the solution of the differential equations of multiple probes, the computational time required for a particular case is several orders of magnitude shorter than that needed for obtaining the full numerical solution. Blood perfusion and metabolic heat generation rates are demonstrated to inhibit the advancement of isothermal fronts. Application of this method will significantly shorten computational times without compromising the accuracy of the results. It may also facilitate expeditious consideration of the advantages of different modes of operation and the number of inserted probes at the early design stage.

Evaluation of neutron radiation field in carbon ion therapy

Carbon ions have significant advantages in tumor therapy because of their physical and biological properties. In view of the radiation protection, the safety of patients is the most important issue in therapy processes. Therefore, the effects of the secondary particles produced by the carbon ions in the tumor therapy should be carefully considered, especially for the neutrons. In the present work, the neutron radiation field induced by carbon ions was evaluated by using the FLUKA code. The simulated results of neutron energy spectra and neutron dose was found to be in good agreement with the experiment data. In addition, energy deposition of carbon ions and neutrons in tissue-like media was studied, it is found that the secondary neutron energy deposition is not expected to exceed 1% of the carbon ion energy deposition in a typical treatment.

Nonlinear radial oscillations of micro-bubbles in a compressible UCM medium

ABSTRACTThe nonlinear oscillations of acoustically forced spherical gas bubbles in an upper-convected Maxwell (UCM) compressible fluid are investigated. The nonlinear viscoelastic model used is suitable for large-amplitude excitation of bubbles that cannot be captured by linear models. The effects of acoustic excitation are studied for compressible nonlinear viscoelastic media, which increases the complexity and nonlinearity of the behavior. The Keller–Miksis equation is used to model the dynamics of a single bubble. The constitutive equations of compressible UCM are used for viscoelastic media. These governing equations are non-dimensionalized and coupled to determine the bubble dynamic behavior. The set of derived non-dimensionalized integro-differential equations developed are numerically solved simultaneously using the fourth-order Runge–Kutta method featured by the automatic variable time step-size module. The combined effects of compressibility and viscoelasticity of the fluid on bubble radius are investigated. The results show that the combination of compressibility and nonlinear viscoelasticity for bubble radial oscillations makes forced bubble dynamics more applicable for human needs, especially for large deformations in highly non-Newtonian fluids like industrial polymers or even tissue-like media. It can be seen that compressibility controls the oscillations at higher forcing amplitudes. The relevance and importance of these bubble dynamics to biomedical ultrasound applications and light emissions by sonoluminescence and other industries are evident.

Transport of secondary electrons and reactive species in ion tracks

The transport of reactive species brought about by ions traversing tissue-like medium is analysed analytically. Secondary electrons ejected by ions are capable of ionizing other molecules; the transport of these generations of electrons is studied using the random walk approximation until these electrons remain ballistic. Then, the distribution of solvated electrons produced as a result of interaction of low-energy electrons with water molecules is obtained. The radial distribution of energy loss by ions and secondary electrons to the medium yields the initial radial dose distribution, which can be used as initial conditions for the predicted shock waves. The formation, diffusion, and chemical evolution of hydroxyl radicals in liquid water are studied as well.

Stress and strain fields produced by violent bubble collapse

Cavitation finds a key application in therapeutic ultrasound. For example, histotripsy relies on the rapid expansion of cavitation bubbles to fractionate soft tissue. To fully understand the mechanisms responsible for tissue fractionation, we numerically model cavitation in a tissuelike medium, focusing on the effect of its viscoelastic properties (viscosity, elasticity, and relaxation). It is hypothesized that ablation is caused by high strain rates and stresses exerted on the surrounding tissue as bubbles rapidly expand from nanometer to micron scales. The present study uses robust numerical techniques to compute the stress fields in the surrounding medium produced by single-bubble expansion. Bubble expansion is driven by a waveform that approximates a histotripsy pulse with relevant parameters, and soft tissue surrounding the bubble is modeled as a viscoelastic medium with Neo-Hookean elasticity. We will examine the stress, strain, and temperature fields produced during this process to explain potential damage mechanisms.

On measurement of the acoustic nonlinearity parameter using the finite amplitude insertion substitution (FAIS) technique

The acoustic nonlinearity parameter, B/A, is an important parameter which defines the way a propagating finite amplitude acoustic wave progressively distorts when travelling through any medium. One measurement technique used to determine its value is the finite amplitude insertion substitution (FAIS) method which has been applied to a range of liquid, tissue and tissue-like media. Importantly, in terms of the achievable measurement uncertainties, it is a relative technique. This paper presents a detailed study of the method, employing a number of novel features. The first of these is the use of a large area membrane hydrophone (30 mm aperture) which is used to record the plane-wave component of the acoustic field. This reduces the influence of diffraction on measurements, enabling studies to be carried out within the transducer near-field, with the interrogating transducer, test cell and detector positioned close to one another, an attribute which assists in controlling errors arising from nonlinear distortion in any intervening water path. The second feature is the development of a model which estimates the influence of finite-amplitude distortion as the acoustic wave travels from the rear surface of the test cell to the detector. It is demonstrated that this can lead to a significant systematic error in B/A measurement whose magnitude and direction depends on the acoustic property contrast between the test material and the water-filled equivalent cell. Good qualitative agreement between the model and experiment is reported. B/A measurements are reported undertaken at (20 ± 0.5) °C for two fluids commonly employed as reference materials within the technical literature: Corn Oil and Ethylene Glycol. Samples of an IEC standardised agar-based tissue-mimicking material were also measured. A systematic assessment of measurement uncertainties is presented giving expanded uncertainties in the range ±7% to ±14%, expressed at a confidence level close to 95%, dependent on specimen details.

Cherenkov-excited luminescence scanned imaging.

Ionizing radiation is commonly delivered by medical linear accelerators (LINAC) in the form of shaped beams, and it is able to induce Cherenkov emission in tissue. In fluorescence-based microscopy excitation from scanned spots, lines, or sheets can be used for fast high-resolution imaging. Here we introduce Cherenkov-excited luminescence scanned imaging (CELSI) as a new imaging methodology utilizing 2-dimensional (∼5-mm-thick) sheets of LINAC radiation to produce Cherenkov photons, which in turn excite luminescence of probes distributed in biological tissues. Imaging experiments were performed by scanning these excitation sheets in three orthogonal directions while recording Cherenkov-excited luminescence. Tissue phantom studies have shown that single luminescent inclusions ∼1 mm in diameter can be imaged within 20-mm-thick tissue-like media with minimal loss of spatial resolution. Using a phosphorescent probe for oxygen, PtG4 with the CELSI methodology, an image of partial pressure of oxygen (pO₂) was imaged in a rat lymph node, quantitatively restoring pO₂ values in differently oxygenated tissues.

Localizing fluorophore (centroid) inside a scattering medium by depth perturbation.

Fluorescence molecular tomography (FMT) imaging can be used to determine the location, size, and biodistribution of fluorophore biomarkers inside tissues. Yet when using FMT in the reflectance geometry it is challenging to accurately localize fluorophores. A depth perturbation method is proposed to determine the centroid of fluorophore inside a tissue-like medium. Through superposition of a known thin optical phantom onto the medium surface, the fluorophore depth is deliberately perturbed and signal localization is improved in a stable way. We hypothesize that the fluorophore centroid can be better localized through use of this fluorescent intensity variation resulting from the depth perturbation. This hypothesis was tested in tissue-like phantoms. The results show that a small-size fluorophore inclusion (1.2 mm(3)volume, depth up to 4.8 mm) can be localized by the method with an error of 0.2 to 0.3 mm. The method is also proven to be capable of handling multiple fluorescent inclusion conditions with the assistance of other strategies. Additionally, our further studies showed that the method's performance in the presence of background fluorophores indicated that the small inclusion could be located at a 1.8 (3.8) mm depth with accurate localization only when its concentration was not <10 (100) times the background level.

Counterpropagation of waves with shock fronts in a nonlinear tissue-like medium

A numerical model for describing the counterpropagation of one-dimensional waves in a nonlinear medium with an arbitrary power law absorption and corresponding dispersion is developed. The model is based on general one-dimensional Navier-Stokes equations with absorption in the form of a time-domain convolution operator in the equation of state. The developed algorithm makes it possible to describe wave interactions in the presence of shock fronts in media like biological tissue. Numerical modeling is conducted by the finite difference method on a staggered grid; absorption and sound speed dispersion are taken into account using the causal memory function. The developed model is used for numerical calculations, which demonstrate the absorption and dispersion effects on nonlinear propagation of differently shaped pulses, as well as their reflection from impedance acoustic boundaries.

CHARACTERISTIC FEATURES OF MUELLER MATRIX PATTERNS FOR POLARIZATION SCATTERING MODEL OF BIOLOGICAL TISSUES

We developed a model to describe polarized photon scattering in biological tissues. In this model, tissues are simplified to a mixture of scatterers and surrounding medium. There are two types of scatterers in the model: solid spheres and infinitely long solid cylinders. Variables related to the scatterers include: the densities and sizes of the spheres and cylinders, the orientation and angular distribution of cylinders. Variables related to the surrounding medium include: the refractive index, absorption coefficient and birefringence. In this paper, as a development we introduce an optical activity effect to the model. By comparing experiments and Monte Carlo simulations, we analyze the backscattering Mueller matrix patterns of several tissue-like media, and summarize the different effects coming from anisotropic scattering and optical properties. In addition, we propose a possible method to extract the optical activity values for tissues. Both the experimental and simulated results show that, by analyzing the Mueller matrix patterns, the microstructure and optical properties of the medium can be obtained. The characteristic features of Mueller matrix patterns are potentially powerful tools for studying the contrast mechanisms of polarization imaging for medical diagnosis.

Quantitative comparison of analysis methods for spectroscopic optical coherence tomography

Spectroscopic optical coherence tomography (sOCT) enables the mapping of chromophore concentrations and image contrast enhancement in tissue. Acquisition of depth resolved spectra by sOCT requires analysis methods with optimal spectral/spatial resolution and spectral recovery. In this article, we quantitatively compare the available methods, i.e. the short time Fourier transform (STFT), wavelet transforms, the Wigner-Ville distribution and the dual window method through simulations in tissue-like media. We conclude that all methods suffer from the trade-off in spectral/spatial resolution, and that the STFT is the optimal method for the specific application of the localized quantification of hemoglobin concentration and oxygen saturation.

Monte Carlo calculations of the energy deposited in biological samples and shielding materials

The energy deposited by gamma radiation from the Cs-137 isotope into body tissues (bone and muscle), tissue-like medium (water), and radiation shielding materials (concrete, lead, and water), which is of interest for radiation dosimetry, was obtained using a simple Monte Carlo algorithm. The algorithm also provides a realistic picture of the distribution of backscattered photons from the target and the distribution of photons scattered forward after several scatterings in the scatterer, which is useful in studying radiation shielding. The presented method in this work constitutes an attempt to evaluate the amount of energy absorbed by body tissues and shielding materials.

Nonlinear oscillations following the Rayleigh collapse of a gas bubble in a linear viscoelastic (tissue-like) medium

In a variety of biomedical engineering applications, cavitation occurs in soft tissue, a viscoelastic medium. The present objective is to understand the basic physics of bubble dynamics in soft tissue. To gain insights into this problem, theoretical and numerical models are developed to study the Rayleigh collapse and subsequent oscillations of a gas bubble in a viscoelastic material. To account for liquid compressibility and thus accurately model large-amplitude oscillations, the Keller-Miksis equation for spherical bubble dynamics is used. The most basic linear viscoelastic model that includes stress relaxation, viscosity, and elasticity (Zener, or standard linear solid) is considered for soft tissue, thereby adding two ordinary differential equations for the stresses. The present study seeks to advance past studies on cavitation in tissue by determining the basic effects of relaxation and elasticity on the bubble dynamics for situations in which compressibility is important. Numerical solutions show a clear dependence of the oscillations on the viscoelastic properties and compressibility. The perturbation analysis (method of multiple scales) accurately predicts the bubble response given the relevant constraints and can thus be used to investigate the underlying physics. A third-order expansion of the radius is necessary to accurately represent the dynamics. Key quantities of interest such as the oscillation frequency and damping, minimum radius, and collapse time can be predicted theoretically. The damping does not always monotonically decrease with decreasing elasticity: there exists a finite non-zero elasticity for which the damping is minimum; this value falls within the range of reported tissue elasticities. Also, the oscillation period generally changes with time over the first few cycles due to the nonlinearity of the system, before reaching an equilibrium value. The analytical expressions for the key bubble dynamics quantities and insights gained from the analysis may prove valuable in the development and optimization of certain biomedical applications.

Implementation of a multisource model for gold nanoparticle‐mediated plasmonic heating with near‐infrared laser by the finite element method

The use of optically tunable gold nanoparticles (GNPs) in conjunction with near-infrared (NIR) laser has emerged as an attractive option for laser-induced thermal therapy (LITT), as it capitalizes on plasmonic heating of GNPs tuned to absorb light strongly in the NIR region. Previously, the authors developed a multisource model to predict the temperature change in a GNP-laden tissue-like medium illuminated by NIR laser and implemented it by a linear superposition (LS) method combining analytic and finite element method (FEM) solutions. While it is intuitive and straightforward, the LS approach might be somewhat cumbersome to implement for realistic LITT cases because it requires separate calculations of the temperature change due to individual GNP heat sources and the laser heat source. Therefore, the current investigation aimed to develop a simpler yet mathematically more elegant and computationally more efficient method solely based on FEM to implement the authors' multisource model. A multisource FEM model was developed to calculate the full spatiotemporal temperature distribution due to all heat sources (i.e., individual GNPs and the laser heat source) by solving the heat diffusion equation with multiple heat sources using FEM. This model was tested for its validity using two computational phantoms, a two-layer GNP-laden cylindrical phantom and a breast phantom with a GNP-laden microcavity. For comparison, the results for the two phantom cases were also obtained from the LS method. For the two-layer phantom case, the FEM approach resulted in a maximum temperature increase of 16.4 °C at a depth of 1.35 cm, 2.5 mm below the interface between the two layers, while the LS method produced a maximum temperature increase of 16.7 °C at a depth of 1.3 cm, 2 mm below the interface between the two layers. A comparison of the depth versus temperature changes obtained from the two approaches showed reasonably good agreement within 6%. In the breast phantom case, the LS results show a maximum temperature increase of 16.35 °C at a depth of 2.17 cm, 0.3 mm away from the center of the cavity in the direction closer to the laser. The FEM results show the same characteristics as those obtained via the LS method with a maximum temperature increase of 16.2 °C at a depth of 2.16 cm, 0.4 mm away from the center of the cavity in the direction closer to the laser. The two methods produced good agreement within 2% for the depth versus temperature distributions. The current multisource FEM model not only reproduced the results from the previous LS model, but also dramatically reduced computation time by 2 orders of magnitude, despite a generally more stringent requirement for computer memory. With further experimental validation, the FEM model can be used to predict the distinct plasmonic heating characteristics expected from NIR laser illumination of tissue-like media filled with GNPs, while offering the capability of handling heterogeneous spatial distribution of GNPs for realistic clinical cases.

Focused, radially polarized shear wave beams in tissue-like media

In the past decade there has been a surge in the optics literature regarding the unique characteristics of focused, radially-polarized light beams. Of particular interest is the existence of a longitudinal component to the electric field in the focal region of the beam, of comparable amplitude to the radial component and yet with a smaller beamwidth [cf. Q. Zhan, Adv. Opt. Photon. 1, 1-57 (2009)]. In the linear approximation there exists a direct analogy between these light beams and radially-polarized shear wave beams in incompressible elastic media, and hence we may interpret the results found in the optics literature as applying to low-frequency shear waves propagating through tissue-like media. When considering nonlinear effects, however, the fact that the gradient of the field experiences a larger gain due to focusing than the field itself implies that the shear wave case is more susceptible to nonlinear behavior than its optical analog. Second-harmonic generation in the focal region of a focused, radially-polarized shear wave beam in a soft solid is investigated. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and by NIH DK070618.]

Simulation of depth–dose distributions for various ions in polyethylene medium

Study of depth–dose distributions for intermediate energy ion beams in tissue-like media such as polyethylene (CH2)n provides a good platform for further improvements in the fields of hadrontherapy and space radiation shielding. The depth–dose distributions for 12C ions at various energies and for light and intermediate ion beams (3He, 16O, 20Ne and 28Si) as well as for heavy ions 56Fe in polyethylene were estimated by using simulation toolkit: Geant4. Calculations were performed mainly by considering two different combinations of standard electromagnetic (EM), binary cascade (BIC), statistical multifragmentation (SMF) and Fermi breakup (FB) models. The energies of the ion beams were selected to achieve the Bragg peaks at predefined position (∼60mm) and as per their availability. Variations of peak-to-entrance ratio (from 7.44±0.05 to 8.87±0.05), entrance dose (from 2.89±0.01 to 203.71±0.63MeV/mm) and entrance stopping power (from 3.608 to 208.858MeV/mm, calculated by SRIM) with atomic number (Z) were presented in a systematic manner. The better peak-to-entrance ratio and less entrance dose in the region Z=2 to 8 (i.e. 3He to 16O) may provide the suitability of the ion beams for hadrontherapy.

Non-contact time-resolved diffuse reflectance imaging at null source-detector separation

We report results of the proof-of-principle tests of a novel non-contact tissue imaging system. The system utilizes a quasi-null source-detector separation approach for time-domain near-infrared spectroscopy, taking advantage of an innovative state-of-the-art fast-gated single photon counting detector. Measurements on phantoms demonstrate the feasibility of the non-contact approach for the detection of optically absorbing perturbations buried up to a few centimeters beneath the surface of a tissue-like turbid medium. The measured depth sensitivity and spatial resolution of the new system are close to the values predicted by Monte Carlo simulations for the inhomogeneous medium and an ideal fast-gated detector, thus proving the feasibility of the non-contact approach for high density diffuse reflectance measurements on tissue. Potential applications of the system are also discussed.

Analyse théorique et expérimentale de la diffusion de la lumière générée par une diode électroluminescente dans des répliques tissulaires

The knowledge of the spatial distribution of light within a biological tissue exited by a light source (LASER or LED) is fundamental to achieve optimal photodynamic treatment. In this paper, we develop an analytical model relative to the diffuse fluence rate within a tissue-like medium irradiated by a continuous-wave light emitting diode (LED). The model is based on the two dimensional Fourier transform and applied to a homogeneous tissue slab. The total fluence rate along the axis of the medium was computed by adding the collimated and the diffuse components. The analytical solution was also used to study the depth evolution of the photon fluence rate as functions of the finite source beam size and the tissue optical parameters. Measurement results were performed using a tank filled with a liquid-simulating turbid medium (milk) illuminated with a LED beam. The experimental behaviour results agree with the theoretical predictions.

Modeling of shear waves generated in a soft solid by a piston

This work is motivated by the transient elastography experiments described by Catheline etal. [J. Am. Stat. Assoc. 105, 2941–2950 (1999)], the purpose of which was to measure the phase speed of shear waves propagating through tissue phantoms. In that work, a small circular piston was used to generate the shear waves, the motion of which was perpendicular to the bounding surface of the sample. The current work is a theoretical investigation of this type of source condition based on the assumption of a linear elastic medium and using an angular spectrum approach to solve for the entire elastic field, both compressional and shear waves, that results from a given velocity distribution at the source plane. Special attention is paid to the velocity field near the source, in particular how the near incompressibility of the tissue-like medium is conducive to the generation of shear waves from such a compressive piston source. For high-frequency excitation, in which the resulting shear wave disturbances are beam-like, the validity of using a parabolic approximation to describe diffraction of the transverse motion of the field in the paraxial region is investigated. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]