USNCTAM perspectives on mechanics in medicine

Learning reduced-order models for cardiovascular simulations with graph neural networks

Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience loss in accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 3% for pressure and flow rate, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models while maintaining high efficiency at inference time.

Quantum Dots Mediated Imaging and Phototherapy in Cancer Spheroid Models: State of the Art and Perspectives

Quantum Dots (QDs) are fluorescent nanoparticles known for their exceptional optical properties, i.e., high fluorescence emission, photostability, narrow emission spectrum, and broad excitation wavelength. These properties make QDs an exciting choice for bioimaging applications, notably in cancer imaging. Challenges lie in their ability to specifically label targeted cells. Numerous studies have been carried out with QDs coupled to various ligands like peptides, antibodies, aptamers, etc., to achieve efficient targeting. Most studies were conducted in vitro with two-dimensional cell monolayers (n = 8902) before evolving towards more sophisticated models. Three-dimensional multicellular tumor models better recapitulate in vivo conditions by mimicking cell-to-cell and cell-matrix interactions. To date, only few studies (n = 34) were conducted in 3D in vitro models such as spheroids, whereas these models could better represent QDs behavior in tumors compared to monolayers. Thus, the purpose of this review is to present a state of the art on the studies conducted with Quantum Dots on spheroid models for imaging and phototherapy purposes.

Tuning cellular uptake of nanoparticles via ligand density: Contribution of configurational entropy

The bioactivity of nanoparticles (NPs) crucially depends on their ability to cross biological membranes. A fundamental understanding of cell-NP interaction is hence essential to improve the performance of the NP-based biomedical applications. Although extensive studies of cellular uptake have converged upon the idea that the uptake process is mainly regulated by the elastic deformation of the cell membrane or NP, recent experimental observations indicate the ligand density as another critical factor in modulating NP uptake into cells. In this study, we propose a theoretical model of the wrapping of an elastic vesicle NP by a finite lipid membrane to depict the relevant energetic and morphological evolutions during the wrapping process driven by forming receptor-ligand bonds. In this model, the deformations of the membrane and the vesicle NP are assumed to follow the continuum Canham-Helfrich framework, whereas the change of configurational entropy of receptors is described from statistical thermodynamics. Results show that the ligand density strongly affects the binding energy and configurational entropy of free receptors, thereby altering the morphology of the vesicle-membrane system in the steady wrapping state. For the wrapping process by the finite lipid membrane, we also find that there exists optimal ligand density for the maximum wrapping degree. These predictions are consistent with relevant experimental observations reported in the literature. We have further observed that there are transitions of various wrapping phases (no wrapping, partial wrapping, and full wrapping) in terms of ligand density, membrane tension, and molecular binding energy. In particular, the ligand and receptor shortage regimes for the small and high ligand density are, respectively, identified. These results may provide guidelines for the rational design of nanocarriers for drug delivery.

Role of Ligand Distribution in the Cytoskeleton-Associated Endocytosis of Ellipsoidal Nanoparticles

Nanoparticle (NP)–cell interaction mediated by receptor–ligand bonds is a crucial phenomenon in pathology, cellular immunity, and drug delivery systems, and relies strongly on the shape of NPs and the stiffness of the cell. Given this significance, a fundamental question is raised on how the ligand distribution may affect the membrane wrapping of non-spherical NPs under the influence of cytoskeleton deformation. To address this issue, in this work we use a coupled elasticity–diffusion model to systematically investigate the role of ligand distribution in the cytoskeleton-associated endocytosis of ellipsoidal NPs for different NP shapes, sizes, cytoskeleton stiffness, and the initial receptor densities. In this model, we have taken into account the effects of receptor diffusion, receptor–ligand binding, cytoskeleton and membrane deformations, and changes in the configuration entropy of receptors. By solving this model, we find that the uptake process can be significantly influenced by the ligand distribution. Additionally, there exists an optimal state of such a distribution, which corresponds to the fastest uptake efficiency and depends on the NP aspect ratio and cytoskeleton stiffness. We also find that the optimal distribution usually needs local ligand density to be sufficiently high at the large curvature region. Furthermore, the optimal state of NP entry into cells can tolerate slight changes to the corresponding optimal distribution of the ligands. The tolerance to such a change is enhanced as the average receptor density and NP size increase. These results may provide guidelines to control NP–cell interactions and improve the efficiency of target drug delivery systems.

Model order reduction of flow based on a modular geometrical approximation of blood vessels

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g., straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by Proper Orthogonal Decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier-Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton-Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.

The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations

We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the generalized-α scheme. The spatiotemporal discretization leads to a block structure of the resulting consistent tangent matrix in the Newton-Raphson procedure. As a generalization of the conventional block preconditioners, a three-level nested block preconditioner is introduced to attain a better representation of the Schur complement, which plays a key role in the overall algorithm robustness and efficiency. This approach provides a flexible, algorithmic way to handle the Schur complement for problems involving multiscale and multiphysics coupling. The solution method is implemented and benchmarked against experimental data from the nozzle challenge problem issued by the US Food and Drug Administration. The robustness, efficiency, and parallel scalability of the proposed technique are then examined in several settings, including moderately high Reynolds number flows and physiological flows with strong resistance effect due to coupled downstream vasculature models. Two patient-specific hemodynamic simulations, covering systemic and pulmonary flows, are performed to further corroborate the efficacy of the proposed methodology.

Progress in ligand design for monolayer-protected nanoparticles for nanobio interfaces

Ligand-functionalized inorganic nanoparticles, also known as monolayer-protected nanoparticles, offer great potential as vehicles for in vivo delivery of drugs, genes, and other therapeutics. These nanoparticles offer highly customizable chemistries independent of the size, shape, and functionality imparted by the inorganic core. Their success as drug delivery agents depends on their interaction with three major classes of biomolecules: nucleic acids, proteins, and membranes. Here, the authors discuss recent advances and open questions in the field of nanoparticle ligand design for nanomedicine, with a focus on atomic-scale interactions with biomolecules. While the importance of charge and hydrophobicity of ligands for biocompatibility and cell internalization has been demonstrated, ligand length, flexibility, branchedness, and other properties also influence the properties of nanoparticles. However, a comprehensive understanding of ligand design principles lies in the cost associated with synthesizing and characterizing diverse ligand chemistries and the ability to carefully assess the structural integrity of biomolecules upon interactions with nanoparticles.

Anomalous Vascular Dynamics of Nanoworms within Blood Flow

Nanomaterials have been widely used in the design of drug delivery platforms. This work computationally explores the vascular dynamics of nanoworms as drug carriers within blood flow by considering the effects of nanoworm length, stiffness, and local physiological conditions such as hematocrit. We found that nanoworms with length of 8 μm and moderate stiffness are the optimal choice as drug carriers for circulating within normal vascular network due to their lower near wall margination. Compared to those of spherical rigid particles, these nanoworms demonstrate significant demargination behaviors at hematocrit 20%, induced by the local hydrodynamic interactions. Specifically, the interactions between nanoworms and red blood cells create asymmetrical local flow fields, resulting in the demargination of nanoworms. In addition, the flexibility of nanoworms enables them to conform to the deformed shape of red blood cells under shear flow, leading to their high concentration within the core region of vessels. Therefore, the long blood circulation time of nanoworms can be partially attributed to their demargination behaviors and intertwinement with red blood cells. According to these simulation results, tuning the length and stiffness of nanoworms is the key to design drug carries with reduced near wall margination within normal vascular networks and extend their blood circulation time.

Capture of microparticles by bolus flow of red blood cells in capillaries

Previous studies have concluded that microparticles (MPs) can more effectively approach the microvessel wall than nanoparticles because of margination. In this study, however, we show that MPs are not marginated in capillaries where the vessel diameter is comparable to that of red blood cells (RBCs). We numerically investigated the behavior of MPs with a diameter of 1 μm in various microvessel sizes, including capillaries. In capillaries, the flow mode of RBCs shifted from multi-file flow to bolus (single-file) flow, and MPs were captured by the bolus flow of the RBCs instead of being marginated. Once MPs were captured, they rarely escaped from the vortex-like flow structures between RBCs. These capture events were enhanced when the hematocrit was decreased, and reduced when the shear rate was increased. Our results suggest that microparticles may be rather inefficient drug carriers when targeting capillaries because of capture events, but nanoparticles, which are more randomly distributed in capillaries, may be more effective carriers.

Effects of ligand distribution on receptor-diffusion-mediated cellular uptake of nanoparticles

Biophysical-factor-dependent cellular uptake of nanoparticles (NPs) through receptor-diffusion-mediated endocytosis bears significance in pathology, cellular immunity and drug-delivery systems. Advanced nanotechnology of NP synthesis provides methods for modifying NP surface with different ligand distributions. However, no report discusses effects of ligand distribution on NP surface on receptor-diffusion-mediated cellular uptake. In this article, we used a statistical dynamics model of receptor-diffusion-mediated endocytosis to examine ligand-distribution-dependent cellular uptake dynamics by considering that ligand-receptor complexes drive engulfing to overcome resistance to membrane deformation and changes in configuration entropy of receptors. Results showed that cellular internalization of NPs strongly depended on ligand distribution and that cellular-uptake efficiency of NPs was high when ligand distribution was within a range around uniform distribution. This feature of endocytosis ensures robust infection ability of viruses to enter host cells. Interestingly, results also indicated that optimal ligand distribution associated with highest cellular-uptake efficiency slightly depends on distribution pattern of ligands and density of receptors, and the optimal distribution becomes uniform when receptor density is sufficiently large. Position of initial contact point is also a factor affecting dynamic wrapping. This study explains why most enveloped viruses present almost homogeneous ligand distribution and is useful in designing controlled-release drug-delivery systems.

Improved Targeting of Cancers with Nanotherapeutics

Targeted cancer nanotherapeutics offers numerous opportunities for the selective uptake of toxic chemotherapies within tumors and cancer cells. The unique properties of nanoparticles, such as their small size, large surface-to-volume ratios, and the ability to achieve multivalency of targeting ligands on their surface, provide superior advantages for nanoparticle-based drug delivery to a variety of cancers. This review highlights various key concepts in the design of targeted nanotherapeutics for cancer therapy, and discusses physicochemical parameters affecting nanoparticle targeting, along with recent developments for cancer-targeted nanomedicines.

A computational study of cancer hyperthermia based on vascular magnetic nanoconstructs

The application of hyperthermia to cancer treatment is studied using a novel model arising from the fundamental principles of flow, mass and heat transport in biological tissues. The model is defined at the scale of the tumour microenvironment and an advanced computational scheme called the embedded multiscale method is adopted to solve the governing equations. More precisely, this approach involves modelling capillaries as one-dimensional channels carrying flow, and special mathematical operators are used to model their interaction with the surrounding tissue. The proposed computational scheme is used to analyse hyperthermic treatment of cancer based on systemically injected vascular magnetic nanoconstructs carrying super-paramagnetic iron oxide nanoparticles. An alternating magnetic field is used to excite the nanoconstructs and generate localized heat within the tissue. The proposed model is particularly adequate for this application, since it has a unique capability of incorporating microvasculature configurations based on physiological data combined with coupled capillary flow, interstitial filtration and heat transfer. A virtual tumour model is initialized and the spatio-temporal distribution of nanoconstructs in the vascular network is analysed. In particular, for a reference iron oxide concentration, temperature maps of several different hypothesized treatments are generated in the virtual tumour model. The observations of the current study might in future guide the design of more efficient treatments for cancer hyperthermia.

Decorating Nanoparticle Surface for Targeted Drug Delivery: Opportunities and Challenges

The size, shape, stiffness (composition) and surface properties of nanoparticles (NPs) have been recognized as key design parameters for NP-mediated drug delivery platforms. Among them, the surface functionalization of NPs is of great significance for targeted drug delivery. For instance, targeting moieties are covalently coated on the surface of NPs to improve their selectively and affinity to cancer cells. However, due to a broad range of possible choices of surface decorating molecules, it is difficult to choose the proper one for targeted functions. In this work, we will review several representative experimental and computational studies in selecting the proper surface functional groups. Experimental studies reveal that: (1) the NPs with surface decorated amphiphilic polymers can enter the cell interior through penetrating pathway; (2) the NPs with tunable stiffness and identical surface chemistry can be selectively accepted by the diseased cells according to their stiffness; and (3) the NPs grafted with pH-responsive polymers can be accepted or rejected by the cells due to the local pH environment. In addition, we show that computer simulations could be useful to understand the detailed physical mechanisms behind these phenomena and guide the design of next-generation NP-based drug carriers with high selectivity, affinity, and low toxicity. For example, the detailed free energy analysis and molecular dynamics simulation reveals that amphiphilic polymer-decorated NPs can penetrate into the cell membrane through the "snorkeling" mechanism, by maximizing the interaction energy between the hydrophobic ligands and lipid tails. We anticipate that this work will inspire future studies in the design of environment-responsive NPs for targeted drug delivery.

Magnetic resonance imaging-based computational modelling of blood flow and nanomedicine deposition in patients with peripheral arterial disease

Peripheral arterial disease (PAD) is generally attributed to the progressive vascular accumulation of lipoproteins and circulating monocytes in the vessel walls leading to the formation of atherosclerotic plaques. This is known to be regulated by the local vascular geometry, haemodynamics and biophysical conditions. Here, an isogeometric analysis framework is proposed to analyse the blood flow and vascular deposition of circulating nanoparticles (NPs) into the superficial femoral artery (SFA) of a PAD patient. The local geometry of the blood vessel and the haemodynamic conditions are derived from magnetic resonance imaging (MRI), performed at baseline and at 24 months post intervention. A dramatic improvement in blood flow dynamics is observed post intervention. A 500% increase in peak flow rate is measured in vivo as a consequence of luminal enlargement. Furthermore, blood flow simulations reveal a 32% drop in the mean oscillatory shear index, indicating reduced disturbed flow post intervention. The same patient information (vascular geometry and blood flow) is used to predict in silico in a simulation of the vascular deposition of systemically injected nanomedicines. NPs, targeted to inflammatory vascular molecules including VCAM-1, E-selectin and ICAM-1, are predicted to preferentially accumulate near the stenosis in the baseline configuration, with VCAM-1 providing the highest accumulation (approx. 1.33 and 1.50 times higher concentration than that of ICAM-1 and E-selectin, respectively). Such selective deposition of NPs within the stenosis could be effectively used for the detection and treatment of plaques forming in the SFA. The presented MRI-based computational protocol can be used to analyse data from clinical trials to explore possible correlations between haemodynamics and disease progression in PAD patients, and potentially predict disease occurrence as well as the outcome of an intervention.

Cell and nanoparticle transport in tumour microvasculature: the role of size, shape and surface functionality of nanoparticles

Through nanomedicine, game-changing methods are emerging to deliver drug molecules directly to diseased areas. One of the most promising of these is the targeted delivery of drugs and imaging agents via drug carrier-based platforms. Such drug delivery systems can now be synthesized from a wide range of different materials, made in a number of different shapes, and coated with an array of different organic molecules, including ligands. If optimized, these systems can enhance the efficacy and specificity of delivery compared with those of non-targeted systems. Emerging integrated multiscale experiments, models and simulations have opened the door for endless medical applications. Current bottlenecks in design of the drug-carrying particles are the lack of knowledge about the dispersion of these particles in the microvasculature and of their subsequent internalization by diseased cells (Bao et al. 2014 J. R. Soc. Interface 11, 20140301 (doi:10.1098/rsif.2014.0301)). We describe multiscale modelling techniques that study how drug carriers disperse within the microvasculature. The immersed molecular finite-element method is adopted to simulate whole blood including blood plasma, red blood cells and nanoparticles. With a novel dissipative particle dynamics method, the beginning stages of receptor-driven endocytosis of nanoparticles can be understood in detail. Using this multiscale modelling method, we elucidate how the size, shape and surface functionality of nanoparticles will affect their dispersion in the microvasculature and subsequent internalization by targeted cells.

Design of Nanoparticle-Based Carriers for Targeted Drug Delivery

Nanoparticles have shown promise as both drug delivery vehicles and direct antitumor systems, but they must be properly designed in order to maximize efficacy. Computational modeling is often used both to design new nanoparticles and to better understand existing ones. Modeled processes include the release of drugs at the tumor site and the physical interaction between the nanoparticle and cancer cells. In this article, we provide an overview of three different targeted drug delivery methods (passive targeting, active targeting and physical targeting), compare methods of action, advantages, limitations, and the current stage of research. For the most commonly used nanoparticle carriers, fabrication methods are also reviewed. This is followed by a review of computational simulations and models on nanoparticle-based drug delivery.

Shape effect in cellular uptake of PEGylated nanoparticles: comparison between sphere, rod, cube and disk

The size, shape, surface property and material composition of polymer-coated nanoparticles (NPs) are four important parameters in designing efficient NP-based carriers for targeted drug delivery. However, due to the complex interplay between size, shape and surface property, most studies lead to ambiguous descriptions of the relevance of shape. To clarify its influence on the cellular uptake of PEGylated NPs, large scale molecular simulations have been performed to study differently shaped convex NPs, such as sphere, rod, cube and disk. Comparing systems with identical NP surface area, ligand-receptor interaction strength, and grafting density of the polyethylene glycol, we find that the spherical NPs exhibit the fastest internalization rate, followed by the cubic NPs, then rod- and disk-like NPs. The spherical NPs thus demonstrate the highest uptake among these differently shaped NPs. Based on a detailed free energy analysis, the NP shape effect is found to be mainly induced by the different membrane bending energies during endocytosis. The spherical NPs need to overcome a minimal membrane bending energy barrier, compared with the non-spherical counterparts, while the internalization of disk-like NPs involves a strong membrane deformation, responsible for a large free energy barrier. Besides, the free energy change per tethered chain is about a single kBT regardless of NP shape, as revealed by our self-consistent field theory calculations, where kB and T denote Boltzmann constant and temperature, respectively. Thus, the NP shape only plays the secondary role in the free energy change of grafted PEG polymers during internalization. We also find that star-shaped NPs can be quickly wrapped by the cell membrane, similar to their spherical counterparts, indicating star-shaped NPs can be used for drug delivery with high efficacy. Our findings seem to provide useful guidance in the molecular design of PEGylated NPs for controllable cellular uptake and help establish quantitatively rules in designing NP-based vectors for targeted drug delivery.

The Incompatibility of Living Systems: Characterizing Growth-Induced Incompatibilities in Expanded Skin

Skin expansion is a common surgical technique to correct large cutaneous defects. Selecting a successful expansion protocol is solely based on the experience and personal preference of the operating surgeon. Skin expansion could be improved by predictive computational simulations. Towards this goal, we model skin expansion using the continuum framework of finite growth. This approach crucially relies on the concept of incompatible configurations. However, aside from the classical opening angle experiment, our current understanding of growth-induced incompatibilities remains rather vague. Here we visualize and characterize incompatibilities in living systems using skin expansion in a porcine model: We implanted and inflated two expanders, crescent, and spherical, and filled them to 225 cc throughout a period of 21 days. To quantify the residual strains developed during this period, we excised the expanded skin patches and subdivided them into smaller pieces. Skin growth averaged 1.17 times the original area for the spherical and 1.10 for the crescent expander, and displayed significant regional variations. When subdivided into smaller pieces, the grown skin patches retracted heterogeneously and confirmed the existence of incompatibilities. Understanding skin growth through mechanical stretch will allow surgeons to improve-and ultimately personalize-preoperative treatment planning in plastic and reconstructive surgery.