John B. Weaver

An overlapping subzone technique for MR-based elastic property reconstruction.

A finite element–based nonlinear inversion scheme for magnetic resonance (MR) elastography is detailed. The algorithm operates on small overlapping subzones of the total region of interest, processed in a hierarchical order as determined by progressive error minimization. This zoned approach allows for a high degree of spatial discretization, taking advantage of the data‐rich environment afforded by the MR. The inversion technique is tested in simulation under high‐noise conditions (15% random noise applied to the displacement data) with both complicated user‐defined stiffness distributions and realistic tissue geometries obtained by thresholding MR image slices. In both cases the process has proved successful and has been capable of discerning small inclusions near 4 mm in diameter. Magn Reson Med 42:779–786, 1999.

Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure

An imaging system that simultaneously performs near infrared (NIR) tomography and magnetic resonance imaging (MRI) is used to study breast tissue phantoms and a healthy woman in vivo. An NIR image reconstruction that exploits the combined data set is presented that implements the MR structure as a soft-constraint in the NIR property estimation. The algorithm incorporates the MR spatially segmented regions into a regularization matrix that links locations with similar MR properties, and applies a Laplacian-type filter to minimize variation within each region. When prior knowledge of the structure of phantoms is used to guide NIR property estimation, root mean square (rms) image error decreases from 26 to 58%. For a representative in vivo case, images of hemoglobin concentration, oxygen saturation, water fraction, scattering power, and scattering amplitude are derived and the properties of adipose and fibroglandular breast tissue types, identified from MRI, are quantified. Fibroglandular tissue is observed to have more than four times as much water content as adipose tissue, almost twice as much blood volume, and slightly reduced oxygen saturation. This approach is expected to improve recovery of abnormalities within the breast, as the inclusion of structural information increases the accuracy of recovery of embedded heterogeneities, at least in phantom studies.

Three‐dimensional subzone‐based reconstruction algorithm for MR elastography

Accurate characterization of harmonic tissue motion for realistic tissue geometries and property distributions requires knowledge of the full three‐dimensional displacement field because of the asymmetric nature of both the boundaries of the tissue domain and the location of internal mechanical heterogeneities. The implications of this for magnetic resonance elastography (MRE) are twofold. First, for MRE methods which require the measurement of a harmonic displacement field within the tissue region of interest, the presence of 3D motion effects reduces or eliminates the possibility that simpler, lower‐dimensional motion field images will capture the true dynamics of the entire stimulated tissue. Second, MRE techniques that exploit model‐based elastic property reconstruction methods will not be able to accurately match the observed displacements unless they are capable of accounting for 3D motion effects. These two factors are of key importance for MRE techniques based on linear elasticity models to reconstruct mechanical tissue property distributions in biological samples. This article demonstrates that 3D motion effects are present even in regular, symmetric phantom geometries and presents the development of a 3D reconstruction algorithm capable of discerning elastic property distributions in the presence of such effects. The algorithm allows for the accurate determination of tissue mechanical properties at resolutions equal to that of the MR displacement image in complex, asymmetric biological tissue geometries. Simulation studies in a realistic 3D breast geometry indicate that the process can accurately detect 1‐cm diameter hard inclusions with 2.5× elasticity contrast to the surrounding tissue. Magn Reson Med 45:827–837, 2001.

Magnetic nanoparticle temperature estimation.

The authors present a method of measuring the temperature of magnetic nanoparticles that can be adapted to provide in vivo temperature maps. Many of the minimally invasive therapies that promise to reduce health care costs and improve patient outcomes heat tissue to very specific temperatures to be effective. Measurements are required because physiological cooling, primarily blood flow, makes the temperature difficult to predict a priori. The ratio of the fifth and third harmonics of the magnetization generated by magnetic nanoparticles in a sinusoidal field is used to generate a calibration curve and to subsequently estimate the temperature. The calibration curve is obtained by varying the amplitude of the sinusoidal field. The temperature can then be estimated from any subsequent measurement of the ratio. The accuracy was 0.3 degree K between 20 and 50 degrees C using the current apparatus and half-second measurements. The method is independent of nanoparticle concentration and nanoparticle size distribution.

Frequency distribution of the nanoparticle magnetization in the presence of a static as well as a harmonic magnetic field.

We explore the properties of the signal from magnetic nanoparticles. The nanoparticle signal has been used to generate images in magnetic particle imaging (MPI). MPI promises to be one of the most sensitive methods of imaging small numbers magnetic nanoparticles and therefore shows promise for molecular imaging. The nanoparticle signal is generated with a pure sinusoidal magnetic field that repeatedly saturates the nanoparticles creating harmonics in the induced magnetization that are easily isolated from the driving field. Signal from a selected position is isolated using a static magnetic field to completely saturate all of the particles outside a voxel enabling an image to be formed voxel by voxel. The signal produced by the magnetization of the nanoparticles contains only odd harmonics. However, it is demonstrated experimentally that with the addition of a static magnetic field bias even harmonics are introduced which increase the total signal significantly. Further, the distribution of signal among the harmonics depends on the static bias field so that information might be used to localize the nanoparticle distribution. Finally, the field required to completely saturate nanoparticles can be quite large and theory predicts that the field required is determined by the smallest nanoparticles in the sample.

Elasticity reconstruction from experimental MR displacement data: initial experience with an overlapping subzone finite element inversion process

The determination of the elastic property distribution in heterogeneous gel samples with a finite element based reconstruction scheme is considered. The algorithm operates on small overlapping subzones of the total field to allow for a high degree of spatial discretization while maintaining computational tractability. By including a Maxwellian-type viscoelastic property in the model physics and optimizing the spatial distribution of this property in the same manner as elasticity, a Youngs modulus image is obtained which reasonably reflects the true distribution within the gel. However, the image lacks the clarity and accuracy expected based on simulation experience. Preliminary investigations suggest that transient effects in the data are the cause of a significant mismatch between the inversion model, which assumes steady-state conditions, and the actual displacements as measured by a phase contrast MR technique.

Spectral priors improve near-infrared diffuse tomography more than spatial priors

We compare the benefits of spatial and spectral priors in near-infrared diffuse tomography image reconstruction. Although previous studies that incorporated anatomical spatial priors have shown improvement in algorithm convergence and resolution, our results indicate that functional parameter quantification by this approach can be suboptimal. The incorporation of a priori spectral information significantly improves the accuracy observed in recovered images. Specifically, phantom results show that the maximum total hemoglobin concentration ([Hb(T)]) in a region of heterogeneity reached 91% of the true value compared to 63% using spatial priors. The combination of both priors produced results accurate to 98% of the true [Hb(T)]. When both spatial and spectral priors were applied in a healthy volunteer, glandular tissue showed a higher [Hb(T)], water fraction, and scattering power compared to adipose tissue.

Subzone based magnetic resonance elastography using a Rayleigh damped material model.

PURPOSE Recently, the attenuating behavior of soft tissue has been addressed in magnetic resonance elastography by the inclusion of a damping mechanism in the methods used to reconstruct the resulting mechanical property image. To date, this mechanism has been based on a viscoelastic model for material behavior. Rayleigh, or proportional, damping provides a more generalized model for elastic energy attenuation that uses two parameters to characterize contributions proportional to elastic and inertial forces. In the case of time-harmonic vibration, these two parameters lead to both the elastic modulus and the density being complex valued (as opposed to the case of pure viscoelasticity, where only the elastic modulus is complex valued). METHODS This article presents a description of Rayleigh damping in the time-harmonic case, discussing the differences between this model and the viscoelastic damping models. In addition, the results from a subzone based Rayleigh damped elastography study of gelatin and tofu phantoms are discussed, along with preliminary results from in vivo breast data. RESULTS Both the phantom and the tissue studies presented here indicate a change in the Rayleigh damping structure, described as Rayleigh composition, between different material types, with tofu and healthy tissue showing lower Rayleigh composition values than gelatin or cancerous tissue. CONCLUSIONS It is possible that Rayleigh damping elastography and the concomitant Rayleigh composition images provide a mechanism for differentiating tissue structure in addition to measuring elastic stiffness and attenuation. Such information could be valuable in the use of Rayleigh damped magnetic resonance elastography as a diagnostic imaging tool.

Measurement of magnetic nanoparticle relaxation time.

PURPOSE Nanoparticle relaxation time measurements have many applications including characterizing molecular binding, viscosity, heating, and local matrix stiffness. The methods capable of in vivo application are extremely limited. The hypothesis investigated by the authors was that the relaxation time could be measured quantitatively using magnetic spectroscopy of nanoparticle Brownian motion (MSB). METHODS The MSB signal (1) reflects the nanoparticle rotational Brownian motion, (2) can be measured from very low nanoparticle concentrations, and (3) is a function of the product of the drive frequency and the relaxation time characterizing Brownian motion. To estimate the relaxation time, the MSB signal was measured at several frequencies. The MSB signal for nanoparticles with altered relaxation time is a scaled version of that for reference nanoparticles with a known relaxation time. The scaling factor linking the altered and reference MSB measurements is the same factor linking the altered and reference relaxation times. The method was tested using glycerol solutions of varying viscosities to obtain continuously variable relaxation times. RESULTS The measured relaxation time increased with increasing viscosity of the solution in which the nanoparticles resided. The MSB estimated relaxation time matched the calculated relaxation times based on viscosity with 2% average error. CONCLUSIONS MSB can be used to monitor the nanoparticle relaxation time quantitatively through a scale space correlation of the MSB signal as a function of frequency.

Contrast detection in fluid‐saturated media with magnetic resonance poroelastography

PURPOSE Recent interest in the poroelastic behavior of tissues has led to the development of magnetic resonance poroelastography (MRPE) as an alternative to single-phase MR elastographic image reconstruction. In addition to the elastic parameters (i.e., Lamés constants) commonly associated with magnetic resonance elastography (MRE), MRPE enables estimation of the time-harmonic pore-pressure field induced by external mechanical vibration. METHODS This study presents numerical simulations that demonstrate the sensitivity of the computed displacement and pore-pressure fields to a priori estimates of the experimentally derived model parameters. In addition, experimental data collected in three poroelastic phantoms are used to assess the quantitative accuracy of MR poroelastographic imaging through comparisons with both quasistatic and dynamic mechanical tests. RESULTS The results indicate hydraulic conductivity to be the dominant parameter influencing the deformation behavior of poroelastic media under conditions applied during MRE. MRPE estimation of the matrix shear modulus was bracketed by the values determined from independent quasistatic and dynamic mechanical measurements as expected, whereas the contrast ratios for embedded inclusions were quantitatively similar (10%-15% difference between the reconstructed images and the mechanical tests). CONCLUSIONS The findings suggest that the addition of hydraulic conductivity and a viscoelastic solid component as parameters in the reconstruction may be warranted.