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Polymers are extensively used for the realization of drug delivery systems across multiple scales, from nanomedicines to microparticles and macroscopic implantable devices, for their favorable biodegradation profiles and tunable physicochemical features. The accurate quantification of the polymer content is key to finely controlling drug loading and release and ensuring reproducibility, yet it continues to be a major challenge in the design and development of delivery systems. In this study, we introduce a novel protocol based on the PULCON technique to quantify, with a routine NMR spectroscopy analysis, the precise concentration of polymers in various delivery systems. Specifically, the PULCON protocol is applied to characterize the physicochemical and pharmaceutical properties of nanoparticles, microparticles, and implantable devices realized by combining three extensively used polymers, namely, poly(lactic-co-glycolic acid) (PLGA), poly(vinyl alcohol) (PVA), and poly(ethylene glycol) (PEG). Without using internal calibration procedures, in a single step, the PULCON protocol precisely quantifies the concentration of each polymer and the drug content. This approach can be readily implemented on standard NMR spectrometers, enabling accurate characterization of drug delivery systems and facilitating their effective development.

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A fundamental step in the rational design of vascular targeted particles is the firm adhesion at the blood vessel walls. Here, a combined lattice Boltzmann-immersed boundary model is presented for predicting the near-wall dynamics of circulating particles. A moving least squares algorithm is used to reconstruct the forcing term accounting for the immersed particle, whereas ligand-receptor binding at the particle-wall interface is described via forward and reverse probability distributions. First, it is demonstrated that the model predicts with good accuracy the rolling velocity of tumor cells over an endothelial layer in a microfluidic channel. Then, particle-wall interactions are systematically analyzed in terms of particle geometries (circular, elliptical with aspect ratios 2 and 3), surface ligand densities (0.3, 0.5, 0.7 and 0.9), ligand-receptor bond strengths (1 and 2) and Reynolds numbers (Re = 0.01, 0.1 and 1.0). Depending on these conditions, four different particle-wall interaction regimens are identified, namely not adhering, rolling, sliding and firmly adhering particles. The proposed computational strategy can be efficiently used for predicting the near-wall dynamics of particles with arbitrary geometries and surface properties and represents a fundamental tool in the rational design of particles for the specific delivery of therapeutic and imaging agents.

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We derive a sophisticated mathematical model for coupled heat and mass transport in the tumour microenvironment and we apply it to study nanoparticle delivery and hyperthermic treatment of cancer. The model has the unique ability of combining the following features: (i) realistic vasculature; (ii) coupled capillary and interstitial flow; (iii) coupled capillary and interstitial mass transfer applied to nanoparticles; and (iv) coupled capillary and interstitial heat transfer, which are the fundamental mechanisms governing nano-based hyperthermic treatment. This is an improvement with respect to previous modelling approaches, where the effect of blood perfusion on heat transfer is modelled in a spatially averaged form. We analyse the time evolution and the spatial distribution of particles and temperature in a tumour mass treated with superparamagnetic nanoparticles excited by an alternating magnetic field. By means of numerical experiments, we synthesize scaling laws that illustrate how nano-based hyperthermia depends on tumour size and vascularity. In particular, we identify two distinct mechanisms that regulate the distribution of particle and temperature, which are characterized by perfusion and diffusion, respectively.

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Malignancies of the lungs, both primary and metastatic, are the leading cause of death worldwide. Over 1.5 million new cases of primary lung cancer are diagnosed annually worldwide with a dismal five-year survival rate of approximately 15%, which remains unchanged despite major efforts and medical advances. As expected, survival for patients with lung metastases is even worse at about 5%. Early detection and staging are fundamental in improving survival rates and selecting the most effective treatment strategies. Recently, nanoparticles have been developed for imaging and treating various cancers, including pulmonary malignancies. In this work, three different examples of nanoparticle configurations for cancer theranosis are presented, namely conventional spherical polymeric nanoparticles with a diameter of ~ 150 nm; and discoidal mesoporous silicon nanoconstructs and discoidal polymeric nanoconstructs with a diameter of ~ 1,000 nm and a height of 400 and 500 nm, respectively. The spherical nanoparticles accumulate in tumors by means of the well-known enhanced permeation and retention effect, whereas sub-micrometer discoidal nanoconstructs are rationally designed to adhere firmly to the tortuous tumor vasculature. All three nanoparticles are characterized for their in vivo performance in terms of magnetic resonance, positron-emission tomography (PET), and optical imaging. Preliminary data on the in vivo and ex vivo PET/CT imaging of breast cancer metastasis in the lungs using discoidal nanoconstructs is presented. In conclusion, opportunities for nanoparticle-based theranosis in primary lung cancer and pulmonary metastasis are presented and discussed.

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Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution.

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Several mathematical formulations have analyzed the time-dependent behaviour of a tumor mass. However, most of these propose simplifications that compromise the physical soundness of the model. Here, multiphase porous media mechanics is extended to model tumor evolution, using governing equations obtained via the Thermodynamically Constrained Averaging Theory (TCAT). A tumor mass is treated as a multiphase medium composed of an extracellular matrix (ECM); tumor cells (TC), which may become necrotic depending on the nutrient concentration and tumor phase pressure; healthy cells (HC); and an interstitial fluid (IF) for the transport of nutrients. The equations are solved by a Finite Element method to predict the growth rate of the tumor mass as a function of the initial tumor-to-healthy cell density ratio, nutrient concentration, mechanical strain, cell adhesion and geometry. Results are shown for three cases of practical biological interest such as multicellular tumor spheroids (MTS) and tumor cords. First, the model is validated by experimental data for time-dependent growth of an MTS in a culture medium. The tumor growth pattern follows a biphasic behaviour: initially, the rapidly growing tumor cells tend to saturate the volume available without any significant increase in overall tumor size; then, a classical Gompertzian pattern is observed for the MTS radius variation with time. A core with necrotic cells appears for tumor sizes larger than 150 µm, surrounded by a shell of viable tumor cells whose thickness stays almost constant with time. A formula to estimate the size of the necrotic core is proposed. In the second case, the MTS is confined within a healthy tissue. The growth rate is reduced, as compared to the first case - mostly due to the relative adhesion of the tumor and healthy cells to the ECM, and the less favourable transport of nutrients. In particular, for tumor cells adhering less avidly to the ECM, the healthy tissue is progressively displaced as the malignant mass grows, whereas tumor cell infiltration is predicted for the opposite condition. Interestingly, the infiltration potential of the tumor mass is mostly driven by the relative cell adhesion to the ECM. In the third case, a tumor cord model is analyzed where the malignant cells grow around microvessels in a 3D geometry. It is shown that tumor cells tend to migrate among adjacent vessels seeking new oxygen and nutrient. This model can predict and optimize the efficacy of anticancer therapeutic strategies. It can be further developed to answer questions on tumor biophysics, related to the effects of ECM stiffness and cell adhesion on tumor cell proliferation.

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Multiphase porous media mechanics is used for modeling tumor growth, using governing equations obtained via the thermodynamically constrained averaging theory (TCAT). This approach incorporates the interaction of more phases than legacy tumor growth models. The tumor is treated as a multiphase system composed of an extracellular matrix, tumor cells which may become necrotic depending on nutrient level and pressure, healthy cells and an interstitial fluid which transports nutrients. The governing equations are numerically solved within a Finite Element framework for predicting the growth rate of the tumor mass, and of its individual components, as a function of the initial tumor-to-healthy cell ratio, nutrient concentration, and mechanical strain. Preliminary results are shown.

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Understanding how size and shape can affect the biodistribution of intravascularly injected particles is of fundamental importance both for the rational design of delivery systems and from a standardization and regulatory view point. In this work, uncoated silica spherical beads, with a diameter ranging from 700 nm to 3 microm, and uncoated non-spherical silicon-based particles, with quasi-hemispherical, cylindrical and discoidal shapes, have been injected into tumor bearing mice. The number of particles accumulating in the major organs and within the tumor mass has been measured through elemental silicon (Si) analysis. For the spherical beads, it has been found that the number of particles accumulating in the non-RES organs reduces monotonically as the diameter d increases, suggesting the use of smaller particles to provide a more uniform tissue distribution. However, discoidal particles have been observed to accumulate more than others in most of the organs but the liver, where cylindrical particles are deposited at a larger extent. These preliminary results support the notion of using sub-micrometer discoidal particles as intravascular carriers to maximize accumulation in the target organ whilst reducing sequestration by the liver.

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The margination dynamics of microparticles with different shapes has been analyzed within a laminar flow mimicking the hydrodynamic conditions in the microcirculation. Silica spherical particles, quasi-hemispherical and discoidal silicon particles have been perfused in a parallel plate flow chamber. The effect of the shape and density on their margination propensity has been investigated at different physiologically relevant shear rates S. Simple scaling laws have been derived showing that the number n of marginating particles scales as S(-0.63) for the spheres; S(-0.85) for discoidal and S(-1) for quasi-hemispherical particles, regardless of their density and size. Within the range considered for the shear rate, discoidal particles marginate in a larger number compared to quasi-hemispherical and spherical particles. These results may be of interest in drug delivery and bio-imaging applications, where particles are expected to drift towards and interact with the walls of the blood vessels.

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Enveloped viruses and nanosized biomimetic particles for drug and gene delivery enter target cells mainly through receptor-mediated endocytosis. A few models have been presented to elucidate the mechanics of particle engulfment by the cell membrane, showing how size and surface chemico-physical properties favor or oppose internalization. In this work, the effect of particle nonsphericity is addressed considering elliptical cylindrical particles with aspect ratio Gamma. Using a continuum energetic approach, three different conditions have been identified: for sufficiently small Gamma, the particle is not even wrapped by the cell membrane; for sufficiently large Gamma, the particle is partially wrapped ("frustrated endocytosis"); and for intermediate values of Gamma, the particle is fully wrapped and eventually internalized. Given the pleomorphism of viruses and the broad spectrum of shapes for nanosized biomimetic particles, the results presented may be of interest to virologists, pharmacologists, toxicologists, and nanotechnologists.

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The role of specific and non-specific interactions in the receptor-mediated endocytosis of nanoparticles is analyzed. The characteristic time tau(w), the threshold R(th) and optimal R(opt) radii for particle endocytosis are estimated as a function of the binding energy factor C, bond elasticity factor G, and non-specific attractive/repulsive factor F at the cell-particle interface. It is shown that the contribution of F is as important as that of C and G. General and ready to use formulas are presented that can be a guide in designing nanoparticles with controlled endocytic performances.

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The non-specific adhesion of spherical micro- and nano-particles to a cell substrate is investigated in a parallel plate flow chamber. Differently from prior in-vitro analyses, the total volume of the particles injected into the flow chamber is kept fixed whilst the particle diameter is changed in the range 0.5-10 microm. It is shown that: (i) the absolute number of particles adherent to the cell layer per unit surface decreases with the size of the particle as d(-1.7); (ii) the volume of the particles adherent per unit surface increases with the size of the particles as d(+1.3). From these results and considering solely non-specific particles, the following hypothesis are generated (i) use the smallest possible particles in biomedical imaging and (ii) use the largest possible particles in drug delivery.

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The specific adhesive interaction between a non-spherical particle and a cell layer under a linear shear flow is analyzed. The effect of the characteristic particle size, expressed in terms of the volume V, and shape, expressed in terms of the aspect ratio gamma, on the adhesive strength is investigated. It is shown that for a fixed shape, there exists an optimal volume V(opt) for which the adhesive strength has a maximum. A surprisingly accurate relationship has been derived between the optimal volume V(opt) and the ratio microS/m(r) (wall shear stress to the receptors surface density) having the form V(opt)=alpha(m(r)/microS)(beta). Also, oblate particles have been shown to adhere more effectively to the biological substrate than classical spherical particles for the same volume V. As a consequence, non-spherical particles can carry a larger amount of drugs and contrast agents than classical spherical particles with the same adhesive strength, improving the therapeutic and imaging efficacy. The formulae and the procedures described in the present work can guide the optimal design of intravascularly injectable micro/nano carriers.

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The effective longitudinal diffusion of nanovectors along non-permeable and permeable capillaries has been studied considering the contribution of molecular and convective diffusion based on the Taylor's theory of shear dispersion. The problem is of importance in the transport of nanovectors used for the intravascular delivery of drugs and contrast agents. It has been shown that for a given capillary size and hemodynamic conditions a critical radius acr exists for which the effective longitudinal diffusion along the capillary has a minimum: Nanovectors with a < acr diffuse mainly by Brownian diffusion whereas nanovectors with a < acr diffuse mainly by convection and the effective diffusion coefficient grows with a. In permeable conduits, the effective diffusion reduces significantly compared to normal non-leaky vessels and it has been derived that acr grows almost linearly with the hydraulic permeability Lp of blood vessels. It has been shown that the blood conduits with the largest effective longitudinal diffusivity could be preferentially targeted by the circulating vectors. Based on these findings, the following strategies are proposed to increase the number of nanovectors targeting the tumor vessels: (i) The use of nanovectors with a critical radius for normal vessels, (ii) the injecting of bolus of nanovectors with different radii, and (iii) the normalization of the tumor vasculature. Finally, it has been emphasized that the size of the vector should be selected depending on the body district where the tumoral mass is developing and on the type, malignancy, and state of the tumor.

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The margination of a particle circulating in the blood stream has been analyzed. The contribution of buoyancy, hemodynamic forces, van der Waals, electrostatic and steric interactions between the circulating particle and the endothelium lining the vasculature has been considered. For practical applications, the contribution of buoyancy, hemodynamic forces and van der Waals interactions should be only taken into account, whilst the effect of electrostatic and steric repulsion becomes important only at very short distances from the endothelium (1-10 nm). The margination speed and the time for margination t(s) have been estimated as a function of the density of the particle relative to blood delta rho, the Hamaker constant A and radius R of the particle. A critical radius Rc exists for which the margination time t(s) has a maximum, which is influenced by both delta rho and A: the critical radius decreases as the relative density increases and the Hamaker constant decreases. Therefore, particles used for drug delivery should have a radius smaller than the critical value (in the range of 100 nm) to facilitate margination and interaction with the endothelium. While particles used as nanoharvesting agents in proteomics or genomics analysis should have a radius close to the critical value to minimize margination and increase their circulation time.

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