Monday, March 25, 2013

Other Models for Cancer Propagation

As we have described before in our diffusion model and in our Markov chain enhancement, cancer can be modeled as a complex process of; (i) diffusion, (ii) propagation, (iii) proliferation, and (iv) mutation. In each of the above we have defined and measurable processes that result from external and internal physiological and genetic known paths. For example we know that cancer cells when propagated to say the liver will use the liver cells to increase propagation, and in addition will also use liver extracellular factors to potentially suppress gene expression, a factor that appears as a loss of a gene in a pathway.

In a recent paper by Newton et al the authors have developed an alternative ad hoc model, independent of pathways. They state:

The classic view of metastatic cancer progression is that it is a unidirectional process initiated at the primary tumor site, progressing to variably distant metastatic sites in a fairly predictable, though not perfectly understood, fashion. 

A Markov chain Monte Carlo mathematical approach can determine a pathway diagram that classifies metastatic tumors as 'spreaders' or 'sponges' and orders the timescales of progression from site to site. In light of recent experimental evidence highlighting the potential significance of self-seeding of primary tumors, we use a Markov chain Monte Carlo (MCMC) approach, based on large autopsy data sets, to quantify the stochastic, systemic, and often multi-directional aspects of cancer progression. 

We quantify three types of multi-directional mechanisms of progression: (i) self-seeding of the primary tumor; (ii) re-seeding of the primary tumor from a metastatic site (primary re-seeding); and (iii) re-seeding of metastatic tumors (metastasis re-seeding). The model shows that the combined characteristics of the primary and the first metastatic site to which it spreads largely determine the future pathways and timescales of systemic disease. 

For lung cancer, the main `spreaders' of systemic disease are the adrenal gland and kidney, whereas the main `sponges' are regional lymph nodes, liver, and bone. Lung is a significant self-seeder, although it is a `sponge' site with respect to progression characteristics. 

Now we believe that this is an ad hoc model because it fails to allow for the inclusion of the cellular pathway dynamics expressly.  We believe that it is essential to have the underlying "system model" based on reality as an integral part of the essential model and not just posit an ad hoc model. Our approach has that at its core.

The advantages of including such a model are as follows:

(1) The inclusion allows for the validation based on reality.

(2) The model allows for the inclusion of a model useful for controllability and observability factors. Namely it facilitates the ability to predict usefulness of therapeutics.

(3) A model where the coefficients can be estimated from data and where the estimation is based upon a known physical reality. Thus diffusion is key when say in melanoma we lose E cadherin and thus a melanocyte starts to drift, and where in melanoma we lose RAF control and proliferation begins to occur, or in prostate cancer where in the bone marrow we have excess growth factors and enhanced receptors allowing the malignant prostate cell to proliferate. The nexus with the details of reality are a key and essential factor, a sine qua non, for any such model.

Thus although models of this type may mimic reality I feel that they lack the true essence of reality. One of the essential elements of control theory is the ability to have models of reality which are predicated on essential underlying physical truth.