A review of basic principles of fractals and their application to pharmacokinetics.

Pharmacokinetic models play a crucial role in analyzing and assessing the results of in vitro and in vivo studies. In this review, comparative analysis of pharmacokinetic models under homogeneous and heterogeneous conditions is performed, placing special focus on the role of fractal theory. The concept of fractals provides a new perspective from which processes occurring in heterogeneous, confined, or poorly mixed environments can be modeled. Following a brief theoretical overview, the applicability of fractals in characterizing anatomical structures and physiological processes as well as the transport and reaction of drugs within the body is discussed. There is significant evidence that drug absorption, distribution, metabolism, and excretion are often anomalous, that is to say their behavior deviates from classical theory, and possible reasons and appropriate models are considered.

Monte Carlo investigation of single cell beta dosimetry for intraperitoneal radionuclide therapy.

Single event spectra for five beta-emitting radionuclides (Lu-177, Cu-67, Re-186, Re-188, Y-90) were calculated for single cells from two source geometries. The first was a surface-bound isotropically emitting point source and the second was a bath of free radioactivity in which the cell was submerged. Together these represent a targeted intraperitoneal radionuclide therapy. Monoenergetic single event spectra were calculated over an energy range of 11 keV to 2500 keV using the EGSnrc Monte Carlo system. Radionuclide single event spectra were constructed by weighting monoenergetic single event spectra according to radionuclide spectra appropriate for each source geometry. In the case of surface-bound radioactivity, these were radionuclide beta decay spectra. For the free radioactivity, a continuous slowing down approximation spectrum was used that was calculated based on the radionuclide decay spectra. The frequency mean specific energy per event increased as the energy of the beta emitter decreased. This is because, at these energies, the stopping power of the electrons decreases with increasing energy. The free radioactivity produced a higher frequency mean specific energy per event than the corresponding surface-bound value. This was primarily due to the longer mean path length through the target for this geometry. This information differentiates the radionuclides in terms of the physical process of energy deposition and could be of use in the radionuclide selection procedure for this type of therapy.

A numerical approach to non-circular birdcage RF coil optimization: verification with a fourth-order coil.

It is demonstrated that birdcage resonators, satisfying conditions of quadrature operation and radiofrequency field homogeneity, can be realized in practice on formers of non-circular cross section described by an equation of the form (x/a)n + (y/b)n = 1 where a and b are constants and n > or = 2 is an integer. Using a ladder network analogous to that of a conventional circular birdcage, optimization algorithms were employed to determine the elemental current distribution on the non-circular cylindrical surfaces. A comparison of circular, elliptical, symmetric and asymmetric fourth-order (n = 4) section birdcage current distributions is presented. A short, asymmetric fourth-order cage was constructed and tested experimentally at 3 T and compared with a conventional circular-section head coil.

Approximate 3D iterative reconstruction for SPECT.

Compared with slice-by-slice approaches for SPECT reconstruction, three-dimensional iterative methods provide a more accurate physical model and an improved SPECT image. Clinical application of these methods, however, is limited primarily to their computational demands. This paper investigates the methods for approximate 3D iterative reconstruction that greatly reduce this demand by excluding from the reconstruction the smaller magnitude elements of the system matrix. A new method is described which is designed to control the resulting bias in the SPECT image for a given reduction in computation. The approximate methods were compared to fully 3D iterative reconstruction in terms of SPECT image bias and visual quality. All methods were incorporated into the ML-EM algorithm and applied to data from 3D mathematical and experimental brain phantoms. The SPECT images reconstructed by the approximate methods exhibited a positive bias throughout the image that was in general smaller with the new method (in the rage of 2%-6%). The bias was smallest in locally hot regions and largest in locally cold regions. The high quality brain phantom images demonstrated the capability of the new method in realistic imaging contexts. The time per iteration for an entire 3D brain phantom on a modern workstation using the approximate 3D method was 7.0 s.

Experimental and numerical investigation of the 3D SPECT photon detection kernel for non-uniform attenuating media.

Experimental tests for non-uniform attenuating media are performed to validate theoretical expressions for the photon detection kernel, obtained from a recently proposed analytical theory of photon propagation and detection for SPECT. The theoretical multi-dimensional integral expressions for the photon detection kernel, which are computed numerically, describe the probability that a photon emitted from a given source voxel will trigger detection of a photon at a particular projection pixel. The experiments were performed using a cylindrical water-filled phantom with large cylindrical air-filled inserts to simulate inhomogeneity of the medium. A point-like, a short thin cylindrical and a large cylindrical radiation source of 99Tcm were placed at various positions within the phantom. The values numerically calculated from the theoretical kernel expression are in very good agreement with the experimentally measured data. The significance of Compton-scattered photons in planar image formation is discussed and highlighted by these results. Using both experimental measurements and the calculated values obtained from the theory, the kernel's size is investigated. This is done by determining the square N x N pixel neighbourhood of the gamma camera that must be connected to a particular radiation source voxel to account for a specific fraction of all counts recorded at all camera pixels. It is shown that the kernel's size is primarily dependent upon the source position and the properties of the attenuating medium through Compton scattering events, with 3D depth-dependent collimator resolution playing an important but secondary role, at least for imaging situations involving parallel hole collimation. By considering small point-like sources within a non-uniform elliptical phantom, approximating the human thorax, it is demonstrated that on average a 12 cm x 12 cm area of the camera plane is required to collect 85% of the total count recorded. This is a significantly larger connectivity than the 3 cm x 3 cm area required if scattering contributions are ignored and only the 3D depth-dependent collimator resolution is considered.

Photon propagation and detection in single-photon emission computed tomography--an analytical approach.

An analytical theory of photon propagation and detection in single-photon emission computed tomography (SPECT) for collimated detectors is developed from first principles. The total photon detection kernel is expressed as a sum of terms due to the primary and the Compton scattered photons. The primary as well as contributions due to every order of Compton scattering are calculated separately. The model accounts for the three-dimensional depth dependence of the collimator holes as well as for nonhomogeneous attenuation. No specific assumptions about the boundary or the homogeneity of the attenuating medium are made. The energy response of the detector is also modeled by the theory. Analytical expressions are obtained for various contributions to the photon detection kernel, and the multidimensional integrals involved are calculated using standard numerical integration methods. Theoretically calculated projections and scatter fractions for the primary and the first through second scattering orders are compared with our own experimental results for a small cylindrical primary radiation source immersed at various positions in a uniform cylindrical phantom. Also, theoretically calculated scatter fractions for a small spherical (pointlike) source in a uniform elliptic phantom are compared with experimental and Monte Carlo simulation results taken from the recent literature. The results from the analytical method are essentially exact and are free from the inaccuracies inherent in the numerical simulation methods used to deal with the photon propagation and detection problem in SPECT so far. The method developed here is unique in the sense that it provides accurate theoretical predictions of results averaged over an infinite number of simulations or experiments. We believe that our theory enhances an intuitive understanding of the complex image formation process in SPECT and is an important step toward solving the inverse problem, that of reconstructing the primary radiation source distribution from the measured gamma camera projections.