Progress Model

NICHOLAS H. G. HOLFORD, DIANE R. MOULD AND CARL C. PECK  

Disease progress refers to the evolution ot a disease over time. Specifically, it can be used to describe the time course ot a biomarker or clinical outcome, reflecting the status of a disease. The status is a reflection ot the state ot the disease at a point in time. The disease status may improve or worsen over time, or may be a cyclical phenomenon (e.g., malarial quartan fever or seasonal affective disorder). Therefore, a model ot disease progress is a mathematical expression that describes the expected changes in status over time. 

Drug action refers to all the pharmacokinetic and pharmacodynamic processes involved in producing a drug effect on the disease. The effect ot the drug is assumed to influence the disease status. Pharmacokinetic and pharmacodynamic drug properties are the major attributes determining drug action and its 

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The shell progressive model in Example 11.15, part (b) envisions a mass transfer limitation. Is the limitation more likely to be based on oxygen diffusing in or on the combustion products diffusing out ... 

These and other inconsistencies fueled the proposal of an alternative model known as the cisternal maturation/ progression model [40]. In the cisternal maturation... 

Water evaporation occurs when the vapor pressure of the water at the surface, which is temperature dependent, is greater than the water pressure in the subsurface, which is dependent on relative humidity and temperature. The isothermal evaporation process is described by Stumm and Morgan (1996) via a reaction progress model, in which the effects of the initial reaction path are based on the concept of partial equilibrium. Stumm and Morgan (1996) describe partial equilibrium as a state in which a system is in equilibrium with respect to one reaction but out of equilibrium with respect to others. As an example, Stumm and Morgan (1996) indicate (Fig. 7.1) that water with a negative residual alkalinity (i.e.. 

Kraemer WJ, Adams K, Cafarelli E, Dudley GA, Dooly C, Feigenbaum GA, Fleck SJ, Franklin B, Fry AC, Hoffman JR, Newton RU, Potteiger J, Stone MH, Ratamess NA, Triplett-McBride T. Progression models in resistance training for healthy adults. Med Sci Sports Exerc 2002 34 364-380. 

Trosko JE, Chang C-C, Madhukar BV, et al. 1995. Intercellular communication A paradigm for the interpretation of the initiation/promotion/progression model of carcinogenesis. In Chemical induction of cancer Modulation and combustion effects. 205-225. 

Morrison SJ, Metzler DR, Dwyer BP. Removal of As, Mn, Mo, Se, U, V and Zn from groundwater by zero-valent iron in a passive treatment cell reaction progress modeling. J Contam Hydrol 2002 56(1 2) 99—116. 

Post, T. M., Freijer, J. I., Dejongh, J., Dan-hof, M. Disease system analysis basic disease progression models in degenerative disease. Pharm Res 2005, 22 1038-1049. 

A disease progression model describing the change in underlying disease during the course of the trial without treatment. 

Disease progression can be defined as the change in disease status over time. For the simulation of long-term administration of drugs intended to treat degenerative diseases, progression models can be very helpful and should be considered for model building and interpretation of the results. 

Especially for special therapeutic areas where it is unethical to treat patients for a longer time with a placebo, the development of disease progression models is of high interest because they allow a better discernment of the true treatment effect, for example, for these therapeutic areas Alzheimer s disease, Parkinson s disease, Osteoporosis, HIV, diabetes, and cancer. Furthermore, such models can help to differentiate whether the drug has only a symptomatic effect or a disease-modifying effect. The implementation of disease progression models also improves the reliability and acceptance of simulations. 

If the empirical approach is chosen, an empirical disease progression model can also be developed based on data collected during clinical trials or from public databases. A general empirical disease progression model has the following components ... 

Overall, the disease progression models allow a visualization of the time course of diseases under treated and untreated conditions and allow one to investigate in silico the impact of different therapeutic interventions. 

While the observer model operates alongside the process, effectively tracking its progress, modeling can also be used for prediction purposes. A model component called the predictor can calculate the required control values for a process in order to achieve a desired operating status. This is, of course, subject to the bounds of what is physically possible. Naturally, this kind of modeling is subject to limitations because in many processes it is not possible to take all the influences into account in computational form. 

Schneider JS, Pope-Coleman A (1995) Cognitive deficits precede motor deficits in a slowly progressing model of parkinsonism in the monkey. Neurodegeneration 4 245-255... 

On the other hand, on-line information on the process state and on the quality of the products should not be limited to such usual parameters as pressure, temperature, pH and composition, but should extend to more sophisticated characteristics such as colour, smoothness, odour, etc. To produce and to introduce these parameters into the current production in progress, modelling and experimental research must be combined. 

The matter discussed in sec. 2.3 concerned the phenomenology of adsorption from solution. To make further progress, model assumptions have to be made to arrive at isotherm equations for the individual components. These assumptions are similar to those for gas adsorption secs. 1.4-1.7) and Include issues such as is the adsorption mono- or multlmolecular. localized or mobile is the surface homogeneous or heterogeneous, porous or non-porous is the adsorbate ideal or non-ideal and is the molecular cross-section constant over the entire composition range In addition to all of this the solution can be ideal or nonideal, the molecules may be monomers or oligomers and their interactions simple (as in liquid krypton) or strongly associative (as in water). 

The linear disease progress model (Equation 20.2) assumes a constant rate of change of a biomarker or clinical outcome that reflects the disease status (S) at any time, t, from the initial observation of the patient — for example, at the time of entry into a clinical trial. The rate of change can be defined in terms of a baseline disease status (Sq) and a slope (a), which reflects the change from baseline status with time ... 

Finally a disease progress model can reflect more complex drug action. Phenomena such as a drug concentration-effect delay tolerance and rebound to both placebo and active treatments can be made using a linear offset model. These effects can be accounted for by including the appropriate terms. For instance a delay in onset can be accounted for by the addition of an effect compartment and tolerance and rebound... 

As with the offset model for the linear disease progress model, the effect of drug would be expected to disappear on cessation of therapy in this offset model. Again, a delay to the onset of drug effect can be incorporated with the use of an effect compartment component. 

The effects of a therapeutic agent (Ejp) on the progress of a disease may include both an immediate palliative effect and a reduction in the overall recovery time. Equation 20.11 describes the combination of these actions on the zero-asymptote disease progress model ... 

Figure 20.8 illustrates the four basic drug effect patterns when the input or output parameter changes with an exponential time course. As an example of this type of disease progress model, consider postmenopausal osteoporosis reflected by the net loss of bone mass after the menopause. Bone loss may be due to decreased formation or increased resorption of bone. Figure 20.9 illustrates the time course of bone mass change due to increased bone loss and the effect of administering a drug to reduce that loss. For example, raloxifene has been shown to be beneficial in women with postmenopausal osteoporosis (11). The pattern of increase in bone mineral density observed after treatment with raloxifene or placebo resembles the curves shown in Figure 20.10. However, the treatment duration in this dataset was too short to identify the actual mechanism of raloxifene effect on disease progress.

Within the past decade there has been significant interest in determining whether the use of clinical modeling and simulation software would increase the probability of conducting successful clinical trials (43). This approach incorporates the technique of pharmacokinetic-pharmacodynamic modeling that was discussed in Chapter 19 with the disease progression models described in Chapter 20. Although this type of a clinical development tool has considerable potential, the outcomes to date have been mixed. For example, this approach has identified the placebo-response rate for various disease states as an... 

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