Disease System Analysis: Evaluate the structural properties and the physiological implications of an indirect physiologic response model describing the degenerative progression of Alzheimer’s disease using a closed-form solution
Monica Simeoni(1), Michael Gold(2), Marina Zvartau-Hind(3), Michael Irizarry(4), Daren Austin(1), Roberto Gomeni(5)
(1)Clinical Pharmacology and Discovery Biometrics (Stockley Park, UK), (2)Neurosciences Medicine Development Centre (RTP, USA), (3)Neurosciences Medicine Development Centre (Stockley Park, UK), (4)WW Epidemiology (RTP, USA), (5)Pharmacometrics (Verona, Italy), GlaxoSmithKline
Objectives: In a previous communication [1] a novel Disease System Analysis approach has been proposed to describe the degenerative process in Alzheimer's disease (AD) and to account for drug action using indirect physiologic response models [2]. The objectives of the present effort were to derive a closed-form solution of this indirect-response model with a time-varying impairment of the cognitive function, and to evaluate the physiological implication of this mechanistic model.
Methods: Disease System Analysis: The best performing mechanistic model was:
dADAS(t)/dt=kin(t)-kout(t)·ADAS(t) (1)
kin(t)=k0+k1·t; kout(t)=kout; ADAS(0)=ADAS0
where: ADAS(t) is the time-varying level of cognitive function expressed by the cognitive portion of the AD Assessment Scale (ADAS-cog), ranging from 0 to 70, with higher scores indicating greater cognitive impairment, kin(t) is the time-varying impairment rate of ADAS(t), k0 is the deterioration rate of cognitive function at baseline, k1 is a constant characterising the time-varying rate describing the loss of cognition in patients with AD and kout is the first order constant controlling the compensatory regulatory response performed by homeostatic control systems.
Results: The closed-form solution of the equation (1) was derived using the Laplace transform method:
ADAS(t)=(k0/kout-k1/(kout2))+(k1/kout)·t+(ADAS0-k0/kout+ k1/(kout2))·exp(-kout·t) (2)
The analysis of the first derivative of equation (2) indicates that ADAS(t) will be monotonically increasing (impairment in cognitive functions) when:
ADAS0<k0/kout
This relationship discriminates subjects with a transient improvement on cognitive degenerative process (for which this relation does not hold) from subjects where the process is purely degenerative. The degenerative process occurs when the ratio between the loss of cognition (kin) and the homeostatic controlling process (kout) becomes greater than the current disease status (ADAS0) and the system is no longer able to compensate for the natural fluctuations in cognitive functioning.
When k0=k1/kout, the model takes the reduced form:
ADAS(t)=k1/kout·t+ADAS0·exp(-kout·t) (4)
a simplified empirical model to describe AD progression [3].
Conclusions: An explicit solution of the indirect-response model with a time-varying impairment of cognitive function was derived. This equation was used to evaluate the physiological meaning of the model parameters and for discriminating subjects with a transient improvement on cognitive degenerative process from subjects where the process is purely degenerative.
References:
[1] Gomeni R. , Gold M., Zvartau-Hind M., Irizarry M., Austin D., Simeoni M., Disease System Analysis approach to describe Alzheimer's Disease progression in patients on stable acetylcholinesterase inhibitor therapy: exploration of alternative mechanistic modelling options. 6th International Symposium on 'Measurement and kinetics of in vivo drug effects', 21-24 April 2010, Noordwijkerhout, The Netherlands.
[2] Post T.M., Freijer J.I., DeJongh J., Danhof M. Disease system analysis: Basic disease progression models in degenerative disease Pharmaceutical Research 2005; 22-7: 1038-1049.
[3]. Simeoni M., Gold M., Zvartau-Hind M., Irizarry M., Austin D., Gomeni R. , Clinical and Genetic factors affecting Alzheimer's disease progression in subjects on stable acetylcholinesterase inhibitor therapy: a comparison between mechanistic and empirical disease progression modelling approaches. Population Approach Group Europe, PAGE 2010, 9-11 June, Berlin, Germany.
