— Functional imaging procedures for the non-invasive assessment of tissue microcirculation are highly requested, but require a mathematical approach describing the trans- and intercapillary passage of tracer particles. Up to now, two theoretical, for the moment different concepts have been established for tracer kinetic modeling of contrast agent transport in tissues: pharmacokinetic compartment models, which are usually written as coupled differential equations, and the indicator dilution theory, which can be generalized in accordance with the theory of linear-time-invariant (LTI) systems by using a convolution approach. Based on mathematical considerations, it can be shown that also in the case of an open two-compartment model well-known from functional imaging, the concentration-time course in tissue is given by a convolution, which allows a separation of the arterial input function from a system function being the impulse response function, summarizing the available information on tissue microcirculation. Due to this reason, it is possible to integrate the open two-compartment model into the system-theoretic concept of indicator dilution theory (IDT) and thus results known from IDT remain valid for the compartment approach. According to the long number of applications of compartmental analysis, even for a more general context similar solutions of the so-called forward problem can already be found in the extensively available appropriate literature of the seventies and early eighties. Nevertheless, to this day, within the field of biomedical imaging – not from the mathematical point of view – there seems to be a trench between both approaches, which the author would like to get over by exemplary analysis of the well-known model.

In view of an increasing use of breast MRI supplementing X-ray mammography, the purpose of this study was the development of a method for fast and efficient analysis of dynamic MR image series of the female breast. The image data sets were acquired with a saturation-recovery-turbo-FLASH sequence facilitating the detection of the kinetics of the contrast agent concentration in the whole breast with a high temporal and spatial resolution. In addition, a morphological 3D-FLASH data set was acquired. The dynamic image data sets were analyzed by tracer kinetic modeling in order to describe the physiological processes underlying the contrast enhancement in mathematical terms and thus enable the estimation of functional tissue specific parameters, reflecting the status of microcirculation. To display morphological and functional tissue information simultaneously, a multidimensional real-time visualization system (using 3D-texture mapping) was developed, which enables a practical and intuitive human-computer interface in virtual reality. The spatially differentiated representation of the computed functional tissue parameters superimposed on the anatomical information offers several possibilities: improved discernibility of contrast enhancement, inspection of the data volume in 3D-space and localization of lesions in space and thus fast and more natural recognition of topological coherencies. In a feasibility study, it could be demonstrated that multidimensional visualization of contrast enhancement in virtual reality is practical. Especially, detection and localization of multiple breast lesions may be an important application

In order to assess thermal response to RF exposure during MR procedures at the tissue level, simple analytical solutions to the non-stationary Pennes’ bio-heat equation were obtained using the Green’s function approach. Two thermal models appropriate for partial-body exposure were analyzed: In the first model, the temperature field at the periphery of an idealized volume RF resonator was modeled. The analytical solution reveals that tissue response to RF heating is characterized by an equilibration time and length. Both parameters are inversely related to tissue perfusion and vary for the soft-tissues considered between 0.27–25 min and 1.5–12 mm, respectively. None of the tissues investigated increase in temperature more than 0.5°C for each W/kg of power dissipated. Secondly, a homogeneous tissue solution was derived that predicts the temperature-time course to an MR examination with time-varying specific absorption rates (SAR). Since SAR limits indicated in current MR safety standards relate to running SAR averages computed over an appropriate period of time, an expression was formulated that gives an upper limit for the temperature rise averaged over the same period of time, as a function of both the upper limit of running SAR averages and the duration of the MR examination. The analysis revealed that the partial-body SAR limits indicated in the IEC standard may not guarantee under all circumstances compliance with the basic restrictions concerning temperature rise.