Simulation Based Analysis of Nanocarrier Internalization: Exciting Challenges with a New Computational Tool - Intracellular Delivery: Fundamentals and Applications - page 134

network routes. However, starting in the early 1960s, the very innovative Petri
Net (Petri 1962 ) and the subsequent General Net Theory (e.g. Brauer 1980 )
proposed a net model for the description of discrete process structures that
inspired other avenues for representation of dynamic processes. In the past
decade, extensive efforts have been devoted towards the implementation of
the quantitative functionalities in the structural model, e.g. in the form of the
Quantitative Petri Nets (Chen and Hofestaedt 1999 ; Peleg et al. 2005 ).
Nevertheless, the execution of the hybrid, discrete/continuous and optionally
multiscale models is a difficult question, because the usual integrators do not toler-
ate the discrete events, while the usual representation of the continuous processes
cannot be embedded into the discrete models conveniently (Meier-Schellersheim
et al. 2009 ). Another challenge is the effective combination of quantitative models
with rule-based qualitative knowledge. Moreover, a multiscale approach is neces-
sary to treat the hierarchy of interactions ranging from molecular (nm, ns) to signal-
ing (mm, ms) length and time scales, which necessitates the development and
application of specialized modeling tools (Shih et al. 2008 ).
Having recognized the problem discussed above, in Direct Computer Mapping
(Csukas and Perez Uriza 1995 ; Csukas et al. 1996 ; Csukas and Balogh 1998 ), the
natural building blocks of the balance based (conservational) and rule based (infor-
mational) processes are mapped onto the state and transition elements of an executable
program. The discrete or continuous, as well as quantitative or qualitative functioning
are described by expert defined program prototypes. These brief programs are asso-
ciated with the structural elements and executed by a general kernel (Csukas 2001 ;
Csukas et al. 2005 ). The idea of DCM is illustrated in Fig. 2 .
Related to the above approaches, the new methodology can be interpreted as a
“naturally structured” Kalman model or a “very high order” Petri net of prototyped
programs. As illustrated in Fig. 3 , the methodology describes the essential structure
of the processes, as well as the structured distribution and optionally parallel execu-
tion of the distributed elementary functionalities.
The generic structure of the process models can be characterized by a feedback struc-
ture of the “passive” state elements (P) and of the “active” elementary transitions (A).

Mathematical construct

Decomposition

Abstraction

Numericalmethod

Simple equations or rules

Executable
program

Problem to be
solved

Fig. 2 Idea of direct computer mapping