Mathematical Model of Forgetting and amnesia

Memory Intensity(time)=acquiredintensity×intensitydecline(time)×cuequality

The Ribot Gradient



 r1(t) refers to the intensity of the hippocampal process (as a function of time) and r2(t) to that of the neocortical process.  In the Memory Chain Model the total memory intensity is simply the sum of the intensities of the individual processes: r(t) = r1(t) + r2(t). A full lesion at time tl of the hippocampus translates to removing the contribution of r1(tl) from the total intensity r(tl). What remains in such a case is the neocortical intensity, r2(tl), which reflects the result of the consolidation process until the lesioning time tl. It, thus, immediately follows that the shape of the Ribot gradient with a full hippocampal lesion at time tl is identical to the expression for r2(tl). Tests of retrograde amnesia do not measure intensity directly but they rather measure recall probability. The predicted shape of these test gradients is, therefore, given by pRibot(t)=1−e−r2(t1) (see Appendix)


If the hippocampus is lesioned at time tl, then there no more memories will be formed after that. There will also be no more consolidation from hippocampus-to-cortex. That means that if the intensity of a particular memory at the time of the lesion is r(tl), then after that will only follow a decline of the memory intensity with neocortical decline rate a2, the equation of which is given by r(tl)e−a2(τ) where τ is the time elapsed since the lesion. We have not been able to find data of high enough quality on such post-lesion forgetting curves, though in principle they could be fitted. Hence, we will drop the subscript l in tl and continue to write t in equations for the Ribot gradient, assuming that in the data considered post-lesion forgetting is negligible.


We often find that neocortical decline (parameter a2) is close to zero for the material and time periods used in the experiments tested here, for example, because the time period is too short for any neocortical decline to become prominent. Equations for the normal forgetting curve and the Ribot gradient equation are derived in Appendix and listed in Table 1 for the case of no neocortical forgetting and a full lesion of the hippocampal area.


In some lesion studies discussed below, we leave the size of the lesion as a free parameter. The lesion parameter is denoted as λ, with 0 ≤ λ ≤ 1. If the lesion parameter is 0, no lesion is present and if λ = 1 we have a 100% lesion. In case of a partial lesion, the Ribot gradient is equal to pRibot(t)=1−e−[(1−λ)r1(t)+r2(t)]. The effects of full and partial lesions of the hippocampal process are illustrated in Figure 4.

Hermann Ebbinghaus forgetting curve

Collective  Memories

Episodic Memory


summary records of sensory-perceptual-conceptual-affective processing deprived from working memory


Patterns of activation/inhibition over long periods


Predominantly represented in the form of (visual) images


always have a perspective



Provide a short-term record of progress in current goal processing

Represent short-time slices, determined by changes in goal processing

Represented roughly in order of occurrence, temporal dimension

In human they are only retained in a durable form if they become linked to conceptual autobiographical knowledge (rapid forgetting)


Mental representations from which concepts are formed.


Recollectively experienced when accessed.

When included as part of an AM construction they provide specificity.



Brain basis


Neuroanatomically they may be represented in brain regions separate from other AM knowledge networks.




Phylogenetically episodic memory may be a species-general evolutionary old memory system.


Ontogenetically the ability to form episodic memories may be present early in development.

(Chapter 1.2 table 1 Handbook of Episodic Memory by Martin A. Conway)

Semantic Memory