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Translational Aspects of Pathodynamics

Signals are relatively easy to isolate and model in in vitro conditions, due mostly to the ability to control the environment and to the lack of exposure to the biological system network. If the biomarker cannot be characterized and modeled in the laboratory, the chance of getting meaningful information in vivo is slim to none. Once a laboratory model is established, an animal model can be chosen and the pathodynamics work starts all over again until the biomarker can be characterized and modeled in vivo. As all biologists know, just because it works in one species, it is not necessarily going to work in another species. Before going into humans, a pathodynamic model for the biomarker should be studied in several species. The similarities and differences in these interspecies results should provide guidance about the applicability in humans.

For translation across species, the pathodynamic models must have some characteristics that are invariant. Without this invariance, all the preclinical work will probably be a waste of time and money. Mathematical physics would not exist without laws of invariance such as conservation of mass and energy. The same will probably hold true in biology. In the context of this chapter, P (probability structure), Y (biomarkers), and D (disease or decision space) have to be invariant in some sense. Here having invariance in P is not as strong as it seems. The simplest distribution type is the same, but the parameters of the distribution model have species- specific variation. A more complicated type of invariance is that the topologies of the interspecies probability spaces are equivalent. This just means that any "physical" distortion of the response distribution does not create or remove any holes. To a greater extreme, a type of invariance would be present if there is a one-for-one matching of probability objects between species (i.e., when a particular probability object is present in one species with disease, or response, D, there is always a probability object, not necessarily similar, in another species that represents D). The bottom line for biologists is that this will probably require more mathematics than most can presently do.

This approach to translation is relatively worthless without laboratory standards. When biomarkers are developed and applied, either the exact assay methods and standards must be applied in every experiment or there needs to be a mathematical transformation that makes them equivalent. Currently in the clinic, these standards do not exist. Therefore, preclinical experiments using the same methods may work fine, but when the clinical trial is run, variation in methods and sample handling may distort or destroy the information.

### Future Needs in Method Development

Biologists need to get involved directly in pathodynamics to get an efficient merger of the biology and the mathematics. It is a rare mathematician or statistician that has biology training and intuition. Once the biologist gets involved in developing the models, progress will accelerate. Remember, the OU model is basically the simplest case for a pathodynamic model. As is illustrated in the examples above, simpler models will have information loss. Therefore, standard experimental design and analysis may not be sufficient.

The second issue is whether the OU model is correct. Preliminary research suggests that it is not [34] . but only minor modifications may be needed for modeling homeostasis (i.e., dynamic equilibrium). The models for disease or therapeutic effects are mostly unknown. Chronic effects may be directional diffusion or slow convection, while acute effects are likely to generate trajectories such as liver injury [31] . The mathematics of statistical physics [17] is likely to be needed.

It seems clear from the examples presented here that the current statistical estimation algorithms commonly used and available are not efficient in a Fisher information sense when autocorrelation is present. This has been handled in the economic applications for equally spaced measurement times, but biology is not quite so regular, especially clinical trials, even under the strictest protocols.

The communication/information theory and decision theory that is presented here was only an introduction. Optimal information and decision algorithms need to be developed in the context of pathodynamics. Such algorithms may be synergistic with Fisher information optimization or may have some conflict. How the information will be used should determine the optimization approach.

In this chapter biomarkers have been defined as functions of parameters, as vectors of tests, and as signals. These are just aspects of the same mathematical object called a probability distribution function P(Y).The parameters are an integral part of the probability model, the vector Y represents the measurements that get combined in the model, and change in these measurements with time is the signal.

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