Table 2.

Selected studies featuring multiscale modeling of drug transport.

Application	Model Scale				Remarks	Reference
	ML	MS	TL	SL
Calculation of effective diffusion coefficient and development of a tumor transport model that accounts for the heterogenous tumor tissue-blood vessel network	+	+	+		Using numerical homogenization, the microstructural diffusivity analysis is extended to the equivalent continuum diffusion coefficient. Fictitious elements that contain nodes from both tumor tissue and vasculature are used for information transfer from lower to higher scales.	(74,183)
Margination of NPs in microvascular network	+		+		RBCs tend to accumulate to the mid-part of the vessel. As a result, NP radial distribution is maximum at regions close to the vessel wall and it gets higher with increasing NP size.	(60)
Uncertainty quantification using Bayesian statistical framework and Immersed Finite Element (IFEM)	+		+		The Immersed Finite Element (IFEM) is employed for simulating both solid and fluid phases, i.e., RBCs, NPs and blood plasma. The study employs computer simulations to explore the blood flow in the microvasculature and particle dispersion characteristics. Considering the wide variations of the key flow characterizing parameters, i.e., microvascular uncertainty, these simulations are extrapolated using Bayesian updating algorithm to acquire computational prediction. It shows that dispersion of NPs is relatively slower than natural diffusion.	(57)
Development of a multi-scale PK/PD model capable of preclinical to clinical translation to analyze antibody drug conjugates (ADCs)		+	+	+	PK and PD models in cellular and tissue levels are used to obtain the parameters that affect ADC distribution in a multi-scale, multicompartmental PK/PD model.	(81)
Estimation of doxorubicin cyto/cardiotoxicity from system to cellular scale		+	+	+	PBPK model having tissue compartments with vascular, interstitial, intracellular and nucleus sub-compartments is utilized to assess doxorubicin cyto/cardiotoxicity. Model predictions agree with rat and human concentration-time profile data.	(79)
Migration of NPs within micro-vessels		+	+		LB for fluid phase is coupled with Spectrin-Link to investigate red blood cell (RBC) - membrane interactions. Langevin Dynamics (LD) approach is used to capture NP motion. The study is particularly critical for transport of large NPs.	(56)
Analysis of drug induced perturbations		+		+	A coupled PBPK-GSMN model is developed to predict drug induced perturbations using cellular scale metabolism and system level pharmacokinetics information.	(80)
Investigation of drug combination effectiveness in realistic brain tumor model		+	+		Efficacy of combination drug treatment is investigated in a realistic brain tumor model, obtained using MR images. Drug concentration in extracellular matrix to intracellular space is described using the mathematical model. Results show that inclusion of anti-angiogenic drug enhances the effect of doxorubicin the most.	(173)
Modelling drug delivery to solid tumor using a 2D computational field reconstructed from tumor image		+	+		A bisected tumor imaged with standard means is utilized to construct the computational domain with heterogeneous tumor vasculature. Results show that circular tumors are easier to eliminate than elliptical tumors and that usage of adjuvant therapy is more effective in eliminating small sized tumors.	(172)
Micro-macro scale governing equations are coupled by homogenization technique		+	+		Capillary and interstitial compartments are modelled on microscale, by local periodicity and smoothing out the macroscopic variations, i.e., using a homogenized domain on the macro-scale to obtain hydraulic conductivity and diffusivities. These tensors are then used in macro-scale equations.	(73)
Study of dissolution, transport, adsorption, distribution, metabolism and elimination (DTADME) of orally administered drugs			+	+	The gastrointestinal tract (GIT) is modelled as a connection of quasi-3D (Q3D) volumes that are made of 1D tubes with annular layers. The model successfully predicts drug concentration at personal and population levels.	(78)

¹ML: molecular, MS: microstructural, TL: tissue-level, SL: system-level