Behind the Study: Advance Cancer Therapy Using Functional Information

Dr. R. Craig Herndon from the Department of Radiation Oncology at the Shannon Medical Center in San Angelo, TX, shares a presentation on a recent editorial he authored that was published by Oncoscience in Volume 11, entitled, “Functional information offers individualized adaptive cancer therapies.”

Behind the Study is a series of transcribed videos from researchers elaborating on their recent studies published by Oncoscience. Visit the Oncoscience YouTube channel for more insights from outstanding authors.

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Welcome. This overview presents functional information as a mechanism for adaptive cancer therapies. A simple example is presented to demonstrate the utility of the functional information methodology. Then a complex example, which is insoluble using traditional methods, is solved using this functional information method. Simple problems are defined as solvable problems. The simple problem presented here focuses on the ideal inelastic collision of two objects resulting in a fusion of mass, M1 and mass M2. First, the solution is found using traditional methods. Then a solution is found using functional information. The purpose of the simple example is to demonstrate the viability of functional information.

The inelastic collision is modeled using the conservation of momentum and conservation of energy laws. The momentum and kinetic energy models are describing the same event. Therefore, they are mathematically connected. Information flows through this mathematical conduit. Here’s the problem. You are given the kinetic energy response data to the inelastic collision, as shown in the orange curve plotted in the kinetic energy graph. The goal is to increase the orange kinetic energy response curve to the response curve shown in blue, and determine the effect of this change on the momentum model. The value of M2 prime equals 3.74 kilograms is determined using the mass and curve fit data shown here. The resulting impact on momentum is shown here.

Next, we’ll use the functional information method to solve this problem. Here are graphs of the momentum and kinetic energy model data of the collision event used in this problem. There is a mathematical connection between the momentum and energy conservation laws. Functional information is exchanged on this mathematical conduit because the models describe the same event. Next, the relationship between functional information and Shannon information entropy is presented, followed by the functional information methodology used to solve this problem. Shannon information entropy, H, can be decomposed into constituent components, namely functional information, I sub F, and transitional information, I sub T. This equation is used to calculate a functional information value for the normalized mathematical model F of X sub N, cross a range of interest quantified by the index term N.

Here’s an overview of the methodology used in this application. Here, models A and B provide mathematical descriptions of the same effect. Therefore, functional information is exchanged between them. If a parametric change is made to model B resulting in model B prime, the functional information relationship between models B and B prime will be proportional. The functional information relationship between model A prime and model B prime corresponds to the functional information exchange between models A and B. Conservation of information dictates that the functional information changes between the initial and modified models are the same. Therefore, the ratios of the modified models to the initial models are equal. This is the equation used for this application of functional information.

Now, we will apply the functional information methodology to the collision example. Here we have the graphical descriptions of the initial and modified momentum and kinetic energy models from the previous solution. As noted, functional information for the momentum model is exchanged through the mathematical conduit with the kinetic energy model. In this example, we are analyzing process change. Specifically what change in mass is required to change the initial orange curve to the modified blue curve in the kinetic energy graph. A change in the mass results in a change to the kinetic energy model indicated by KE prime. Correspondingly, the KE prime model exchanges functional information with the P prime model. Information change is conserved and used to create the functional information relationship between momentum and kinetic energy. Next, we’ll use this equation to solve the problem.

The functional information methodology will now be used to produce the answer derived from the traditional method. Here is another view of the momentum model connection through a mathematical chain of functions to the kinetic energy model. Both momentum and kinetic energy models communicate in the units of information. Calculated here in decimal digits referred to as dits. Next, functional information is calculated for the KE prime curve, which corresponds to the change in mass M2 prime. Note that the functional information for the KE prime data is the same as the initial KE data and the functional information for the P prime data is also unchanged. This occurs because both models are functions of velocity, where the mass parameters provide scale to the outputs. Since scaling factors do not carry any functional information, the method equation produces ratios of one-

To transfer the mass parameters via functional information, it is necessary to augment the mathematical chain connecting the momentum and kinetic energy models with models A and B. It is convenient to choose an exponential function where the constant is 10 because the definition of functional information is in terms of base 10. The functional information flowing from model A to B now carries the desired mass scaling information. Now, the change in the model curvatures due to the scaling factors is quantifiably different, as reflected in the method equation result of 1.93, yielding results equivalent to the traditional method for mass M2 prime and the momentum P prime graph.

Now following the methodology just outlined, we proceed from the simple mechanics example where both models were in the velocity domain to a complex biological example where both models are in different domains. The oncology example is drawn from radiation therapy where the effect being modeled is tumor sterilization, and the two models of this effect are a cell survival model in the dose domain and a tumor volume model in the time domain. Functional information allows you to use biological information to adapt radiation therapy dose. It is expected that functional information is exchanged between the cell survival biological response model and the tumor volume biological marker model.

If the biomarker data reveals the current radiotherapy dose is not producing the expected decrease in tumor volume, then the curvature of the model V is adjusted to the desired goal. V prime and functional information values are calculated. Analysis is performed in the functional information domain and the proportion of functional information change between the initial and adapted models is the same. I.e. delta I sub S equals delta I sub V. Using the functional information method equation, we can determine I sub S prime. And for I sub S prime, we can solve for the adaptive dose necessary to produce the tumor volume reduction goal specified by I sub V prime. This method is extensible to biomarker research and development efforts across oncology.

These references present the theoretical basis for functional information and provide detailed implementation instructions. Thank you for your time.

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