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Vascular targeted nanoparticles have been developed for the delivery of therapeutic and imaging agents in cancer and cardiovascular diseases. However, at authors' knowledge, a comprehensive systematic analysis on their delivery efficiency is still missing. Here, a computational model is developed to predict the vessel wall accumulation of agents released from vascular targeted nanoconstructs. The transport problem for the released agent is solved using a finite volume scheme in terms of three governing parameters: the local wall shear rate $$S$$ S , ranging from $$10$$ 10 to $$200\,\mathrm{s}^{-1}$$ 200 s - 1 ; the wall filtration velocity $$V_f$$ V f , varying from $$10^{-9}$$ 10 - 9 to $$10^{-7}\,\mathrm{m}/\mathrm{s}$$ 10 - 7 m / s ; and the agent diffusion coefficient $$D$$ D , ranging from $$10^{-12}$$ 10 - 12 to $$10^{-9}\,\mathrm{m}^2/\mathrm{s}$$ 10 - 9 m 2 / s . It is shown that the percentage of released agent adsorbing on the vessel walls in the vicinity of the vascular targeted nanoconstructs reduces with an increase in shear rate $$S$$ S , and with a decrease in filtration velocity $$V_f$$ V f and agent diffusivity $$D$$ D . In particular, in tumor microvessels, characterized by lower shear rates ( $$S = 10\,\mathrm{s}^{-1}$$ S = 10 s - 1 ) and higher filtration velocities ( $$V_f=10^{-7}\,\mathrm{m}/\mathrm{s}$$ V f = 10 - 7 m / s ), an agent with a diffusivity $$D = 10^{-12}\,\mathrm{m}^2/\mathrm{s}$$ D = 10 - 12 m 2 / s (i.e. a 50 nm particle) is predicted to deposit on the vessel wall up to $$30~\%$$ 30 % of the total released dose. Differently, drug molecules, exhibiting a smaller size and much higher diffusion coefficient ( $$D = 10^{-9}\,\mathrm{m}^2/\mathrm{s}$$ D = 10 - 9 m 2 / s ), are predicted to accumulate up to $$70~\%$$ 70 % . In healthy vessels, characterized by higher $$S$$ S and lower $$V_f$$ V f , the largest majority of the released agent is redistributed directly in the circulation. These data suggest that drug molecules and small nanoparticles only can be efficiently released from vascular targeted nanoconstructs towards the diseased vessel walls and tissue.

The complex vascular dynamics and wall deposition of systemically injected nanoparticles is regulated by their geometrical properties (size, shape) and biophysical parameters (ligand---receptor bond type and surface density, local shear rates). Although sophisticated computational models have been developed to capture the vascular behavior of nanoparticles, it is increasingly recognized that purely deterministic approaches, where the governing parameters are known a priori and conclusively describe behaviors based on physical characteristics, may be too restrictive to accurately reflect natural processes. Here, a novel computational framework is proposed by coupling the physics dictating the vascular adhesion of nanoparticles with a stochastic model. In particular, two governing parameters (i.e. the ligand---receptor bond length and the ligand surface density on the nanoparticle) are treated as two stochastic quantities, whose values are not fixed a priori but would rather range in defined intervals with a certain probability. This approach is used to predict the deposition of spherical nanoparticles with different radii, ranging from 750 to 6,000 nm, in a parallel plate flow chamber under different flow conditions, with a shear rate ranging from 50 to 90 $$\text {s}^{-1}$$ s - 1 . It is demonstrated that the resulting stochastic model can predict the experimental data more accurately than the original deterministic model. This approach allows one to increase the predictive power of mathematical models of any natural process by accounting for the experimental and intrinsic biological uncertainties.

Existing tumor models generally consider only a single pressure for all the cell phases. Here, a three-fluid model originally proposed by the authors is further developed to allow for different pressures in the host cells (HC), the tumor cells (TC) and the interstitial fluid (IF) phases. Unlike traditional mixture theory models, this model developed within the thermodynamically constrained averaging theory contains all the necessary interfaces. Appropriate constitutive relationships for the pressure difference among the three fluid phases are introduced with respect to their relative wettability and fluid---fluid interfacial tensions, resulting in a more realistic modeling of cell adhesion and invasion. Five different tumor cases are studied by changing the interfacial tension between the three liquid phases, adhesion and dynamic viscosity. Since these parameters govern the relative velocities of the fluid phases and the adhesion of the phases to the extracellular matrix significant changes in tumor growth are observed. High interfacial tensions at the TC---IF and TC---HC interface support the lateral displacement of the healthy tissue in favor of a rapid growth of the malignant mass, with a relevant amount of HC which cannot be pushed out by TC and remain in place. On the other hand, lower TC---IF and TC---HC interfacial tensions tend to originate a more compact and dense tumor mass with a slower growth rate of the overall size. This novel computational model emphasizes the importance of characterizing the TC---HC interfacial properties to properly predict the temporal and spatial pattern evolution of tumor.

Nanoparticle (NP)-mediated drug/gene delivery involves phenomena at broad range spatial and temporal scales. The interplay between these phenomena makes the NP-mediated drug/gene delivery process very complex. In this paper, we have identified four key steps in the NP-mediated drug/gene delivery: (i) design and synthesis of delivery vehicle/platform; (ii) microcirculation of drug carriers (NPs) in the blood flow; (iii) adhesion of NPs to vessel wall during the microcirculation and (iv) endocytosis and exocytosis of NPs. To elucidate the underlying physical mechanisms behind these four key steps, we have developed a multiscale computational framework, by combining all-atomistic simulation, coarse-grained molecular dynamics and the immersed molecular electrokinetic finite element method (IMEFEM). The multiscale computational framework has been demonstrated to successfully capture the binding between nanodiamond, polyethylenimine and small inference RNA, margination of NP in the microcirculation, adhesion of NP to vessel wall under shear flow, as well as the receptor-mediated endocytosis of NPs. Moreover, the uncertainties in the microcirculation of NPs has also been quantified through IMEFEM with a Bayesian updating algorithm. The paper ends with a critical discussion of future opportunities and key challenges in the multiscale modeling of NP-mediated drug/gene delivery. The present multiscale modeling framework can help us to optimize and design more efficient drug carriers in the future.