This seminar is intended to provide a broad overview of tracer kinetic modeling. While the basic underlying concepts are quite simple, there are innumerable details which bear close consideration when electing to utilize these methods to characterize the physiologic properties of various tissues in vivo. Multiple steps are involved in optimization of data acquisition and modeling, all of which must be appropriately adapted to the underlying unknowns. Participants should come away from this seminar with an understanding of these steps and a grasp of what considerations arise in planning and executing tracer kinetic studies.
Topics to be covered include the central volume principle, the Fick principle, the Stewart-Hamilton equation, the Renkin-Crone equation, the Kety-Schmidt method, and impulse response modeling and arterial input functions. The derivation and interpretation of different physiologically-significant parameters that can be derived via tracer kinetic methods will be discussed. Various approaches extending basic compartmental modeling will also be briefly considered.
Tracer kinetic analysis is a method of characterizing tissue physiology via the introduction of a detectable agent into the body and using its distribution to determine various quantities of interest. The fundamental physical principles underlying tracer kinetic methods are conservation of matter, compartmentation, and linear first order intercompartmental kinetics. Conservation of matter simply requires that all molecules of tracer that are introduced are accounted for. Compartmentation implies that distinct volumes exist within the tissue(s) of interest where the tracer is rapidly and uniformly distributed, so that there are no concentration gradients within the compartments. Linear kinetics dictate that the rate at which tracer is exchanged between connected compartments is linearly related to the concentration difference between them. These simple assumptions, which themselves are not guaranteed to be valid in all situations, hide a myriad of details regarding the spatial and temporal scales at which tracer distribution are characterized, the tissues within which the tracer is distributed, how the tracer interacts with physicochemical processes within the tissues, and how the tracer distribution is measured, to name a few. As a result, it is crucial to adapt the chosen tracer, data acquisition, and modeling methodology to the specific tissue and physiology of interest.
Once an appropriate modeling framework has been chosen that is matched to the tissue and process of interest, details of the measurement methodology must be worked out. These include determining what tracer and how much should be administered to provide an adequate signal, and what spatial and temporal resolution are needed to identify the expected effect. For example, measurement of small changes in the permeability of the blood-brain barrier will place different requirements on the experimental methods than measurement of myocardial perfusion. If measurements are not appropriately adapted, it is possible to obtain misleading and/or meaningless results.
After measurements have been acquired, various modeling approaches may be applied to generate quantitative or semi-quantitative physiological parameter estimates. Here, regardless of the specifics of the modeling method, a detailed understanding of the relationship between measured data and the underlying model parameters is critical. In general, one cannot assume linearity of the relationship between tracer concentration and the MRI signal measurements. In addition, the modeling method itself must be chosen such that it is able to adequately describe measured data without “overfitting”. Attempts apply a model with more parameters than are supported by the data will lead to inaccurate parameter estimates, while using an inadequately sophisticated model to fit data may result in poor model fits and similarly inaccurate parameter estimates.
Finally, it is important to carefully consider measurement uncertainties and their effect on parameter estimates. At a minimum, simple estimates may be based on model covariance matrices, but more accurate methods such as Monte Carlo simulations may be necessary to accurately represent parametric uncertainties over a broad range of physiologic states. When comparing heterogenous data, biases in parameter estimates become particularly important. Common sources of these are discussed.
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