Diffuse-diffuse photon coupling via nonscattering void in the presence of refractive index mismatch on the void boundary

It is well established that the diffusion approximation (DA) is valid for light propagation in highly scattering media, but it breaks down in nonscattering void regions. The methods that handle the void with refractive index matched boundary were previously developed. For the void with refractive index mismatched boundary, no theory is yet available. We derived the finite element method that can handle the void problem with refractive index mismatch on its boundary. The method uses the ray tracing to account for the multiple reflections of rays within the void due to refractive index mismatch on the void boundary. We applied the method to the four-layer adult head model and the good agreements with Monte Carlo simulation results were found in the mean time of flight data.     

Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography

We investigate fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography for applications in small animal imaging. Our forward model uses a diffusion approximation for optically inhomogeneous tissue, which we solve using a finite element method (FEM). We examine two approaches to incorporating the forward model into the solution of the inverse problem. In a conventional direct calculation approach one computes the full forward model by repeated solution of the FEM problem, once for each potential source location. We describe an alternative on-the-fly approach where one does not explicitly solve for the full forward model. Instead, the solution to the forward problem is included implicitly in the formulation of the inverse problem, and the FEM problem is solved at each iteration for the current image estimate. We evaluate the convergence speeds of several representative iterative algorithms. We compare the computation cost of those two approaches, concluding that the on-the-fly approach can lead to substantial reductions in total cost when combined with a rapidly converging iterative algorithm.     

Spectroscopic sensitive polarimeter for biomedical applications

We present the design and calibration of a spectroscopic sensitive polarimeter. The polarimeter can measure the full Stokes vector in the wavelength range 550 to 750 nm with 1-nm resolution and consists of a fiber-based spectrophotometer, a white light emitting diode light source, two liquid crystal retarders, and one polarizer. Calibration of the system is achieved with a scheme that does not require knowledge of the polarizing elements' orientation or retardation. Six intensity spectra are required to calculate the full spectrum Stokes vector. Error in the polarimeter is less than 5%. We report the Stokes vectors for light transmitted through nonscattering polarizing elements as well as a measurement of the depolarizing properties of chicken muscle at several wavelengths.     

Finite Element Modeling of Diffusion and Partitioning in Biological Systems: The Infinite Composite Medium Problem

Four methods are proposed for modeling diffusion in heterogeneous media where diffusion and partition coefficients take on differing values in each subregion. The exercise was conducted to validate finite element modeling (FEM) procedures in anticipation of modeling drug diffusion with regional partitioning into ocular tissue, though the approach can be useful for other organs, or for modeling diffusion in laminate devices. Partitioning creates a discontinuous value in the dependent variable (concentration) at an intertissue boundary that is not easily handled by available general-purpose FEM codes, which allow for only one value at each node. The discontinuity is handled using a transformation on the dependent variable based upon the region-specific partition coefficient. Methods were evaluated by their ability to reproduce a known exact result, for the problem of the infinite composite medium (Crank, J. The Mathematics of Diffusion, 2nd ed. New York: Oxford University Press, 1975, pp. 38–39.). The most physically intuitive method is based upon the concept of chemical potential, which is continuous across an interphase boundary (method III). This method makes the equation of the dependent variable highly nonlinear. This can be linearized easily by a change of variables (method IV). Results are also given for a one-dimensional problem simulating bolus injection into the vitreous, predicting time disposition of drug in vitreous and retina. © 2000 Biomedical Engineering Society. PAC00: 8710+e, 0270Dh, 4266Ew     

The quasi-static response of compliant prosthetic sockets for transtibial amputees using finite element methods

The finite element method (FEM) is a very powerful tool for analyzing the behavior of structures, especially when the geometry and mechanics are too complex to be modeled with analytical methods. This study focuses on the analysis of patellar tendon bearing prosthetic sockets with integrated compliant features designed to relieve contact pressure between the residual limb and socket. We developed a FEM model composed of a socket, liner and residual limb and analyzed it under quasi-static loading conditions derived from experimentally measured ground reaction forces. The geometry of the residual limb, liner and socket were acquired from computed tomography (CT) data of a transtibial amputee. Three different compliant designs were analyzed using FEM to assess the structural integrity of the sockets and their ability to relieve local pressure at the fibula head during normal walking. The compliant features consisted of thin-wall sections and two variations of spiral slots integrated within the socket wall. One version of the spiral slots produced the largest pressure relief, with an average reduction in local interface pressure during single-leg stance (20-80% of the stance phase) from 172 to 66.4 kPa or 65.8% compared to a baseline socket with no compliant features. These results suggest that the integration of local compliant features is an effective method to reduce local contact pressure and improve the functional performance of prosthetic sockets.     

Implementation of a practical model for light and heat distribution using laser-induced thermotherapy near to a large vessel

This paper introduces a simulation model for light and heat transport in tissues including perfusion effects. The model enables an efficient simulation of the damaged zone induced with an optical fibre for laser interstitial thermotherapy (LITT). It is designed specially for, but not limited to, tissue ablation in the neck region near to vessels. We describe in detail the effects of the rise in temperature caused by the absorption of light in tissue, using the heat equation and including the cooling effects of flow in vessels and of microperfusion in tissue in order to determine the extent of thermal damage. The extent of the necrosis zone is calculated with a damage function at each point of a finite element method (FEM) mesh. The FEM mesh is implemented with FEMLAB 2.3 as an add-on for finite element modelling for Matlab 6.5. LITT for tumour ablation in liver and some other anatomical regions is a well-known and established method (Bundes?rztekammer und Kassen?rztliche Bundesvereinigung 2002 Assessment der Bundes?rztekammer und der Kassen?rztlichen Bundesvereinigung, K?ln). Investigations of treatments using LITT in the neck region are still in progress. We propose a refined model to validate the LITT method in the future in another anatomic region, e.g., in the highly sensitive region of the neck. Our calculations show that in order to induce a lesion with a maximum diameter of about 1 cm near to a large vessel, an application time between 3 and 4 min is needed using a laser power of about 10 W with a Nd:YAG 1064 nm radiation wavelength.     

A modelling error approach for the estimation of optical absorption in the presence of anisotropies

Optical tomography is an emerging method for non-invasive imaging of human tissues using near-infrared light. Generally, the tissue is assumed isotropic, but this may not always be true. In this paper, we present a method for the estimation of optical absorption coefficient allowing the background to be anisotropic. To solve the forward problem, we model the light propagation in tissue using an anisotropic diffusion equation. The inverse problem consists of the estimation of the absorption coefficient based on boundary measurements. Generally, the background anisotropy cannot be assumed to be known. We treat the uncertainties in the background anisotropy parameter values as modelling error, and include this in our model and reconstruction. We present numerical examples based on simulated data. For reference, examples using an isotropic inversion scheme are also included. The estimates are qualitatively different for the two methods.     

A second-order finite element algorithm for solving the three-dimensional EEG forward problem

A finite element algorithm has been developed to solve the electroencephalogram (EEG) forward problem. A new computationally efficient approach to calculate the stiffness matrix of second-order tetrahedral elements has been developed for second-order tetrahedral finite element models. The present algorithm has been evaluated by means of computer simulations, by comparing with analytic solutions in a multi-spheres concentric head model. The developed finite element method (FEM) algorithm has also been applied to address questions of interest in the EEG forward problem. The present simulation study indicates that the second-order FEM provides substantially enhanced numerical accuracy and computational efficiency, as compared with the first-order FEM for comparable numbers of tetrahedral elements. The anisotropic conductivity distribution of the head tissue can be taken into account in the present FEM algorithm. The effects of dipole eccentricity, size of finite elements and local mesh refinement on solution accuracy are also addressed in the present simulation study.     

Effects of Stent Structure on Stent Flexibility Measurements

Adequate delivery and placement of intracoronary artery stents is dependent on various properties of the stent itself, including flexibility and high-radial strength. Although these properties can be assessed via determination of the bending stiffness and radial stiffness of a stent, the mesh structure of the stent does not lend easily to such measurements. The goal of the present study was to determine an optimal method for determining stent bending stiffness. The four-points bending test was used to evaluate stent flexibility, and the finite element method (FEM) was employed to assess the effect of stent structure on flexibility in stents with differing link structures. The four-points bending test yielded the following bending stiffness values: 85.28 N mm² for the stent with an S-shaped link; 41.67 N mm² for the stent with an N-shaped link; 78.79 N mm² for the stent with a modified W-shaped link; and 188.67 N mm² for the stent with a W-shaped link. The stent with the point symmetric link configuration (S-, N- and modified W-shaped link) had high flexibility. FEM analysis revealed that low flexibility resulted from interference between the struts at the compressive side. Further, the flexibility predicted from FEM analysis correlated with bending stiffness of the stents. We conclude that use of the four-points bending test yields information that is critical for the design of flexible stents.     

A simplified method for testing Bordetella pertussis for resistance to erythromycin and other antimicrobial agents

Present methods of antimicrobial susceptibility testing of Bordetella pertussis are time consuming and require specialized media that are not commercially available. We tested 52 isolates of B. pertussis for resistance to erythromycin, trimethoprim-sulfamethoxazole, chloramphenicol, and rifampin by agar dilution with Bordet-Gengou agar (BGA) containing 20% horse blood (reference method), Etest using BGA and Regan-Lowe agar without cephalexin (RL-C), and disk diffusion using BGA and RL-C. The organisms tested included four erythromycin-resistant isolates of B. pertussis from a single patient, a second erythromycin-resistant strain of B. pertussis from an unrelated patient in another state, and 47 nasopharyngeal surveillance isolates of B. pertussis from children in the western United States. The results of agar dilution testing using direct inoculation of the organisms suspended in Mueller-Hinton broth were within +/-1 dilution of those obtained after overnight passage of the inoculum in Stainer-Scholte medium, which is the traditional method of testing B. pertussis. The Etest method produced MICs similar to those of the agar dilution reference method for three of the four antimicrobial agents tested; the trimethoprim-sulfamethoxazole results were lower with Etest, particularly when the direct suspension method was used. Most of the Etest MICs, except for that of erythromycin, were on scale. Disk diffusion testing using RL-C medium was helpful in identifying the erythromycin-resistant strains, which produced no zone of inhibition around the disk; susceptible isolates produced zones of at least 42 mm. Thus, the antimicrobial susceptibility testing of B. pertussis can be simplified by using the Etest or disk diffusion on RL-C to screen for erythromycin-resistant isolates of B. pertussis.     

A born-type approximation method for bioluminescence tomography

In this paper, we present a Born-type approximation method for bioluminescence tomography (BLT), which is to reconstruct an internal bioluminescent source from the measured bioluminescent signal on the external surface of a small animal. Based on the diffusion approximation for the photon propagation in biological tissue, this BLT method utilizes the Green function to establish a linear relationship between the measured bioluminescent signal and the internal bioluminescent source distribution. The Green function can be modified to describe a heterogeneous medium with an arbitrary boundary using the Born approximation. The BLT reconstruction is formulated in a linear least-squares optimization framework with simple bounds constraint. The performance of this method is evaluated in numerical simulation and phantom experiments.     

A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media

In this work, development and evaluation of a three-dimensional (3D) finite element model (FEM) based on the diffusion approximation of time-domain (TD) near-infrared fluorescence light transport in biological tissue is presented. This model allows both excitation and fluorescence temporal point-spread function (TPSF) data to be generated for heterogeneous scattering and absorbing media of arbitrary geometry. The TD FEM is evaluated via comparisons with analytical and Monte Carlo (MC) calculations and is shown to provide a quantitative accuracy which has less than 0.72% error in intensity and less than 37 ps error for mean time. The use of the Born-Ratio normalized data is demonstrated to reduce data mismatch between MC and FEM to less than 0.22% for intensity and less than 22 ps in mean time. An image reconstruction framework, based on a 3D FEM formulation, is outlined and simulation results based on a heterogeneous mouse model with a source of fluorescence in the pancreas is presented. It is shown that using early photons (i.e. the photons detected within the first 200 ps of the TPSF) improves the spatial resolution compared to using continuous-wave signals. It is also demonstrated, as expected, that the utilization of two time gates (early and latest photons) can improve the accuracy both in terms of spatial resolution and recovered contrast.     

Dipole estimation errors due to differences in modeling anisotropic conductivities in realistic head models for EEG source analysis

To improve the EEG source localization in the brain, the conductivities used in the head model play a very important role. In this study, we focus on the modeling of the anisotropic conductivity of the white matter. The anisotropic conductivity profile can be derived from diffusion weighted magnetic resonance images (DW-MRI). However, deriving these anisotropic conductivities from diffusion weighted MR images of the white matter is not straightforward. In the literature, two methods can be found for calculating the conductivity from the diffusion weighted images. One method uses a fixed value for the ratio of the conductivity in different directions, while the other method uses a conductivity profile obtained from a linear scaling of the diffusion ellipsoid. We propose a model which can be used to derive the conductivity profile from the diffusion tensor images. This model is based on the variable anisotropic ratio throughout the white matter and is a combination of the linear relationship as stated in the literature, with a constraint on the magnitude of the conductivity tensor (also known as the volume constraint). This approach is stated in the paper as approach A. In our study we want to investigate dipole estimation differences due to using a more simplified model for white matter anisotropy (approach B), while the electrode potentials are derived using a head model with a more realistic approach for the white matter anisotropy (approach A). We used a realistic head model, in which the forward problem was solved using a finite difference method that can incorporate anisotropic conductivities. As error measures we considered the dipole location error and the dipole orientation error. The results show that the dipole location errors are all below 10 mm and have an average of 4 mm in gray matter regions. The dipole orientation errors ranged up to 66.4 degrees, and had a mean of, on average, 11.6 degrees in gray matter regions. In a qualitative manner, the results show that the orientation and location error is dependent on the orientation of the test dipole. The location error is larger when the orientation of the test dipole is similar to the orientation of the anisotropy, while the orientation error is larger when the orientation of the test dipole deviates from the orientation of the anisotropy. From these results, we can conclude that the modeling of white matter anisotropy plays an important role in EEG source localization. More specifically, accurate source localization will require an accurate modeling of the white matter conductivity profile in each voxel.     

Computerized method for nonrigid MR-to-PET breast-image registration

We have developed and tested a new simple computerized finite element method (FEM) approach to MR-to-PET nonrigid breast-image registration. The method requires five-nine fiducial skin markers (FSMs) visible in MRI and PET that need to be located in the same spots on the breast and two on the flanks during both scans. Patients need to be similarly positioned prone during MRI and PET scans. This is accomplished by means of a low gamma-ray attenuation breast coil replica used as the breast support during the PET scan. We demonstrate that, under such conditions, the observed FSM displacement vectors between MR and PET images, distributed piecewise linearly over the breast volume, produce a deformed FEM mesh that reasonably approximates nonrigid deformation of the breast tissue between the MRI and PET scans. This method, which does not require a biomechanical breast tissue model, is robust and fast. Contrary to other approaches utilizing voxel intensity-based similarity measures or surface matching, our method works for matching MR with pure molecular images (i.e. PET or SPECT only). Our method does not require a good initialization and would not be trapped by local minima during registration process. All processing including FSMs detection and matching, and mesh generation can be fully automated. We tested our method on MR and PET breast images acquired for 15 subjects. The procedure yielded good quality images with an average target registration error below 4 mm (i.e. well below PET spatial resolution of 6-7 mm). Based on the results obtained for 15 subjects studied to date, we conclude that this is a very fast and a well-performing method for MR-to-PET breast-image nonrigid registration. Therefore, it is a promising approach in clinical practice. This method can be easily applied to nonrigid registration of MRI or CT of any type of soft-tissue images to their molecular counterparts such as obtained using PET and SPECT.     

Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms

Frequency-domain tissue spectroscopy is a method to measure the absolute absorption coefficient of bulk tissues, assuming that a representative model can be found to recover the optical properties from measurements. While reliable methods exist to calculate absorption coefficients from source-detector measurements less than a few centimeters apart along a flat tissue volume, it is less obvious what methods can be used for transmittance through the larger tissue volumes typically associated with neonatal cerebral monitoring. In this study we compare the use of multiple distance frequency-domain measurements processed with (i) a modified Beer-Lambert law method, (ii) an analytic infinite-medium diffusion theory expression, and (iii) a numerical finite element solution of the diffusion equation, with the goal of recovering the absolute absorption coefficient of the medium. Based upon our observations, the modified Beer-Lambert method provides accurate absolute changes in the absorption coefficient, while analytic infinite-medium diffusion theory solutions or finite element-based numerical solutions can be used to calculate the absolute absorption coefficient, assuming that the data can be measured at multiple source-detector distances. We recommend that the infinite-medium multi-distance method or the finite element method be used across large tissue regions for calculation of the absolute absorption coefficient using frequency-domain near-infrared measurements at multiple positions along the head.     

An anisotropic diffusion method for denoising dynamic susceptibility contrast-enhanced magnetic resonance images.

The purpose of this study was to present an application of a novel denoising technique for improving the accuracy of cerebral blood flow (CBF) images generated from dynamic susceptibility contrast-enhanced magnetic resonance imaging (DSC-MRI). The method presented in this study was based on anisotropic diffusion (AD). The usefulness of this method was firstly investigated using computer simulations. We applied this method to patient data acquired using a 1.5 T MR system. After a bolus injection of Gd-DTPA, we obtained 40-50 dynamic images with a 1.32-2.08 s time resolution in 4-6 slices. The dynamic images were processed using the AD method, and then the CBF images were generated using pixel-by-pixel deconvolution analysis. For comparison, the CBF images were also generated with or without processing the dynamic images using a median or Gaussian filter. In simulation studies, the standard deviation of the CBF values obtained after processing by the AD method was smaller than that of the CBF values obtained without any processing, while the mean value agreed well with the true CBF value. Although the median and Gaussian filters also reduced image noise, the mean CBF values were considerably underestimated compared with the true values. Clinical studies also suggested that the AD method was capable of reducing the image noise while preserving the quantitative accuracy of CBF images. In conclusion, the AD method appears useful for denoising DSC-MRI, which will make the CBF images generated from DSC-MRI more reliable.     

Coupling between elastic strain and interstitial fluid flow: ramifications for poroelastic imaging

We study the effects of interstitial fluid flow and interstitial fluid drainage on the spatio-temporal response of soft tissue strain. The motivation stems from the ability to measure in vivo strain distributions in soft tissue via elastography, and the desire to explore the possibility of using such techniques to investigate soft tissue fluid flow. Our study is based upon a mathematical model for soft tissue mechanics from the literature. It is a simple generalization of biphasic theory that includes coupling between the fluid and solid phases of the soft tissue, and crucially, fluid exchange between the interstitium and the local microvasculature. We solve the mathematical equations in two dimensions by the finite element method (FEM). The finite element implementation is validated against an exact analytical solution that is derived in the appendix. Realistic input tissue properties from the literature are used in conjunction with FEM modelling to conduct several computational experiments. The results of these lead to the following conclusions: (i) different hypothetical flow mechanisms lead to different patterns of strain relaxation with time; (ii) representative tissue properties show fluid drainage into the local microvasculature to be the dominant flow-related stress/strain relaxation mechanism; (iii) the relaxation time of strain in solid tumours due to drainage into the microvasculature is on the order of 5-10 s; (iv) under realistic applied pressure magnitudes, the magnitude of the strain relaxation can be as high as approximately 0.4% strain (4000 microstrains), which is well within the range of strains measurable by elastography.     

Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization

Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (?(2)B(z)) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ?(2)B(z)-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.