In order to simulate the entire system from drug to patient, the three elements presented above must be integrated and linked. depicts a multiscale computational framework for model-based simulation of the entire system from drug design to patient physical and pathological conditions. In this framework, the system consists of three components: the drug, the delivery system and the patient. Information from these components is gathered and compiled by means of mechanistic approaches into a multiscale mathematical model. The challenge of multiscale modeling is the transition from one space-time scale to another. With respect to spatial scale this can be from nano to micro or micro to macro and with respect to time from picoseconds (eg, such as in MD) to seconds or minutes, for instance. For mechanistic models, the nature of coupling of the physical, chemical and biological processes at each scale determines how the computational methods should be linked.
A framework for multiscale modeling of entire drug delivery systems using information from drug and vehicle properties, disease pathology, and patient characteristics.
Of particular interest to the interaction of the delivery system at the biological interface is discrete-to-continuum coupling including two main categories: information-passing (sequential, serial, hierarchical, parameter passing) and concurrent (embedded, integrated, hand-shake) (Fish and Chen 2004a
In the information-passing approach, the information gained in the lower scale is transferred on to the higher scale. For example, molecular dynamics may be used to predict physical parameters, such as diffusivity (eg, of a drug molecule in the carrier material or across a lipid bi-layer) or solubility (eg, of the carrier or drug at the biological interface as a function of physiological pH) that may be employed to compute higher level or scale continuum transport models. It is noteworthy that this approach is valid as long as the information obtained from the lower space-time scale can be summarized into a finite set of parameters and represent the rigorous reduction of the enormous degrees of freedom of the lower length (space or time) of scale. In the context of discrete-to-continuum coupling, the Generalized Mathematical Homogenization (GMH) theory (Chen and Fish 2006
) can be mentioned among the information passing bridging techniques. The GMH constructs an equivalent continuum description directly from discrete (such as MD) equations. In general the mathematical homogenization theory makes the assumption that the fine scale is locally periodic and is composed of four steps (Chen and Fish 2006
): (i) solving a sequence (various orders) of unit cell problems; (ii) computing effective coarse-scale properties; (iii) solving the coarse-scale problem; and (iv) localizing (or post-processing) the fine scale data.
In the concurrent or embedded approach, the multiple scales are resolved simultaneously in different portions of the domain of interest. More theoretical and computational effort is required in this approach than the former. The information between the different hierarchical models is communicated via the domain decomposition methods where the system response is separated into local (discrete) and global (continuum) effects. Among the concurrent bridging techniques the space-time multilevel method (Fish and Chen 2004b
) can be mentioned. In the context of drug delivery this approach can be applied, for example, to the prediction of biodegradable polymer delivery devices where the polymer is degraded until a critical molecular weight is reached before solvation begins. The bond breaking at the solvent-polymer interface can be described by quantum mechanical model of bonding while the rest of the domain is described with empirical potential.
Given that mechanisms at each level in the drug delivery design process form a vast and complex network of dynamically interacting heterogeneous components, the multiscale modeling can involve other multiscale approaches such as continuum-to-continuum coupling between different time scales.
The next sections will introduce and summarize three basic modeling approaches and their applicability to the different scales relevant to oral drug delivery, including examples of nanoparticle processes. This review is by no means exhaustive, but rather representative of the variety of approaches at each scale, which can be integrated into the multiscale framework. A case study will then provide a specific example of this integration.