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The clearance of senescent and altered red blood cells (RBCs) in the red pulp of the human spleen involves sequential processes of prefiltration, filtration, and postfiltration. While prior work has elucidated the mechanisms underlying the first two processes, biomechanical processes driving the postfiltration phagocytosis of RBCs retained at interendothelial slits (IES) are still poorly understood. We present here a unique computational model of macrophages to study the role of cell biomechanics in modulating the kinetics of phagocytosis of aged and diseased RBCs retained in the spleen. After validating the macrophage model using in vitro phagocytosis experiments, we employ it to probe the mechanisms underlying the kinetics of phagocytosis of mechanically altered RBCs, such as heated RBCs and abnormal RBCs in hereditary spherocytosis (HS) and sickle cell disease (SCD). Our simulations show pronounced deformation of the flexible and healthy RBCs in contrast to minimal shape changes in altered RBCs. Simulations also show that less deformable RBCs are engulfed faster and at lower adhesive strength than flexible RBCs, consistent with our experimental measurements. This efficient sensing and engulfment by macrophages of stiff RBCs retained at IES are expected to temper splenic congestion, a common pathogenic process in malaria, HS, and SCD. Altogether, our combined computational and in vitro experimental studies suggest that mechanical alterations of retained RBCs may suffice to enhance their phagocytosis, thereby adapting the kinetics of their elimination to the kinetics of their mechanical retention, an equilibrium essential for adequately cleaning the splenic filter to preserve its function., Competing Interests: Competing interests statement:The authors declare no competing interest.

We address the challenge of acoustic simulations in three-dimensional (3D) virtual rooms with parametric source positions, which have applications in virtual/augmented reality, game audio, and spatial computing. The wave equation can fully describe wave phenomena such as diffraction and interference. However, conventional numerical discretization methods are computationally expensive when simulating hundreds of source and receiver positions, making simulations with parametric source positions impractical. To overcome this limitation, we propose using deep operator networks to approximate linear wave-equation operators. This enables the rapid prediction of sound propagation in realistic 3D acoustic scenes with parametric source positions, achieving millisecond-scale computations. By learning a compact surrogate model, we avoid the offline calculation and storage of impulse responses for all relevant source/listener pairs. Our experiments, including various complex scene geometries, show good agreement with reference solutions, with root mean squared errors ranging from 0.02 to 0.10 Pa. Notably, our method signifies a paradigm shift as-to our knowledge-no prior machine learning approach has achieved precise predictions of complete wave fields within realistic domains., Competing Interests: Competing interests statement:G.E.K. provides technical advice on direction in machine learning to Anailytica, a private startup company developing AI software products for engineering. He has a very small equity for his work. The rest of the authors declare no competing interest.

Quantifying the flow of cerebrospinal fluid (CSF) is crucial for understanding brain waste clearance and nutrient delivery, as well as edema in pathological conditions such as stroke. However, existing in vivo techniques are limited to sparse velocity measurements in pial perivascular spaces (PVSs) or low-resolution measurements from brain-wide imaging. Additionally, volume flow rate, pressure, and shear stress variation in PVSs are essentially impossible to measure in vivo. Here, we show that artificial intelligence velocimetry (AIV) can integrate sparse velocity measurements with physics-informed neural networks to quantify CSF flow in PVSs. With AIV, we infer three-dimensional (3D), high-resolution velocity, pressure, and shear stress. Validation comes from training with 70% of PTV measurements and demonstrating close agreement with the remaining 30%. A sensitivity analysis on the AIV inputs shows that the uncertainty in AIV inferred quantities due to uncertainties in the PVS boundary locations inherent to in vivo imaging is less than 30%, and the uncertainty from the neural net initialization is less than 1%. In PVSs of N = 4 wild-type mice we find mean flow speed 16.33 ± 11.09 µm/s, volume flow rate 2.22 ± 1.983 × 10 3 µm 3 /s, axial pressure gradient ( - 2.75 ± 2.01)×10 -4 Pa/µm (-2.07 ± 1.51 mmHg/m), and wall shear stress (3.00 ± 1.45)×10 -3 Pa (all mean ± SE). Pressure gradients, flow rates, and resistances agree with prior predictions. AIV infers in vivo PVS flows in remarkable detail, which will improve fluid dynamic models and potentially clarify how CSF flow changes with aging, Alzheimer's disease, and small vessel disease.

The spleen clears altered red blood cells (RBCs) from circulation, contributing to the balance between RBC formation (erythropoiesis) and removal. The splenic RBC retention and elimination occur predominantly in open circulation where RBCs flow through macrophages and inter-endothelial slits (IESs). The mechanisms underlying and interconnecting these processes significantly impact clinical outcomes. In sickle cell disease (SCD), blockage of intrasplenic sickled RBCs is observed in infants splenectomized due to acute splenic sequestration crisis (ASSC). This life-threatening RBC pooling and organ swelling event is plausibly triggered or enhanced by intra-tissular hypoxia. We present an oxygen-mediated spleen-on-a-chip platform for in vitro investigations of the homeostatic balance in the spleen. To demonstrate and validate the benefits of this general microfluidic platform, we focus on SCD and study the effects of hypoxia on splenic RBC retention and elimination. We observe that RBC retention by IESs and RBC-macrophage adhesion are faster in blood samples from SCD patients than those from healthy subjects. This difference is markedly exacerbated under hypoxia. Moreover, the sickled RBCs under hypoxia show distinctly different phagocytosis processes from those non-sickled RBCs under hypoxia or normoxia. We find that reoxygenation significantly alleviates RBC retention at IESs, and leads to rapid unsickling and fragmentation of the ingested sickled RBCs inside macrophages. These results provide unique mechanistic insights into how the spleen maintains its homeostatic balance between splenic RBC retention and elimination, and shed light on how disruptions in this balance could lead to anemia, splenomegaly, and ASSC in SCD and possible clinical manifestations in other hematologic diseases.

Understanding the mechanics of blood flow is necessary for developing insights into mechanisms of physiology and vascular diseases in microcirculation. Given the limitations of technologies available for assessing in vivo flow fields, in vitro methods based on traditional microfluidic platforms have been developed to mimic physiological conditions. However, existing methods lack the capability to provide accurate assessment of these flow fields, particularly in vessels with complex geometries. Conventional approaches to quantify flow fields rely either on analyzing only visual images or on enforcing underlying physics without considering visualization data, which could compromise accuracy of predictions. Here, we present artificial-intelligence velocimetry (AIV) to quantify velocity and stress fields of blood flow by integrating the imaging data with underlying physics using physics-informed neural networks. We demonstrate the capability of AIV by quantifying hemodynamics in microchannels designed to mimic saccular-shaped microaneurysms (microaneurysm-on-a-chip, or MAOAC), which signify common manifestations of diabetic retinopathy, a leading cause of vision loss from blood-vessel damage in the retina in diabetic patients. We show that AIV can, without any a priori knowledge of the inlet and outlet boundary conditions, infer the two-dimensional (2D) flow fields from a sequence of 2D images of blood flow in MAOAC, but also can infer three-dimensional (3D) flow fields using only 2D images, thanks to the encoded physics laws. AIV provides a unique paradigm that seamlessly integrates images, experimental data, and underlying physics using neural networks to automatically analyze experimental data and infer key hemodynamic indicators that assess vascular injury., Competing Interests: Competing interest statement: S.C., H.L., M.D., G.E.K., and S.S. have filed a patent application based on the research presented in this paper., (Copyright © 2021 the Author(s). Published by PNAS.)

We have demonstrated the effectiveness of reinforcement learning (RL) in bluff body flow control problems both in experiments and simulations by automatically discovering active control strategies for drag reduction in turbulent flow. Specifically, we aimed to maximize the power gain efficiency by properly selecting the rotational speed of two small cylinders, located parallel to and downstream of the main cylinder. By properly defining rewards and designing noise reduction techniques, and after an automatic sequence of tens of towing experiments, the RL agent was shown to discover a control strategy that is comparable to the optimal strategy found through lengthy systematically planned control experiments. Subsequently, these results were verified by simulations that enabled us to gain insight into the physical mechanisms of the drag reduction process. While RL has been used effectively previously in idealized computer flow simulation studies, this study demonstrates its effectiveness in experimental fluid mechanics and verifies it by simulations, potentially paving the way for efficient exploration of additional active flow control strategies in other complex fluid mechanics applications., Competing Interests: The authors declare no competing interest.

Instrumented indentation has been developed and widely utilized as one of the most versatile and practical means of extracting mechanical properties of materials. This method is particularly desirable for those applications where it is difficult to experimentally determine the mechanical properties using stress-strain data obtained from coupon specimens. Such applications include material processing and manufacturing of small and large engineering components and structures involving the following: three-dimensional (3D) printing, thin-film and multilayered structures, and integrated manufacturing of materials for coupled mechanical and functional properties. Here, we utilize the latest developments in neural networks, including a multifidelity approach whereby deep-learning algorithms are trained to extract elastoplastic properties of metals and alloys from instrumented indentation results using multiple datasets for desired levels of improved accuracy. We have established algorithms for solving inverse problems by recourse to single, dual, and multiple indentation and demonstrate that these algorithms significantly outperform traditional brute force computations and function-fitting methods. Moreover, we present several multifidelity approaches specifically for solving the inverse indentation problem which 1) significantly reduce the number of high-fidelity datasets required to achieve a given level of accuracy, 2) utilize known physical and scaling laws to improve training efficiency and accuracy, and 3) integrate simulation and experimental data for training disparate datasets to learn and minimize systematic errors. The predictive capabilities and advantages of these multifidelity methods have been assessed by direct comparisons with experimental results for indentation for different commercial alloys, including two wrought aluminum alloys and several 3D printed titanium alloys., Competing Interests: Competing interest statement: L.L., M.D., G.E.K., and S.S. have filed a patent application based on the research presented in this paper., (Copyright © 2020 the Author(s). Published by PNAS.)

Polymerization and adhesion, dynamic processes that are hallmarks of sickle cell disease (SCD), have thus far been studied in vitro only separately. Here, we present quantitative results of the simultaneous and synergistic effects of adhesion and polymerization of deoxygenated sickle hemoglobin (HbS) in the human red blood cell (RBC) on the mechanisms underlying vasoocclusive pain crisis. For this purpose, we employ a specially developed hypoxic microfluidic platform, which is capable of inducing sickling and unsickling of RBCs in vitro, to test blood samples from eight patients with SCD. We supplemented these experimental results with detailed molecular-level computational simulations of cytoadherence and biorheology using dissipative particle dynamics. By recourse to image analysis techniques, we characterize sickle RBC maturation stages in the following order of the degree of adhesion susceptibility under hypoxia: sickle reticulocytes in circulation (SRs) → sickle mature erythrocytes (SMEs) → irreversibly sickled cells (ISCs). We show that ( i ) hypoxia significantly enhances sickle RBC adherence; ( ii ) HbS polymerization enhances sickle cell adherence in SRs and SMEs, but not in ISCs; ( iii ) SRs exhibit unique adhesion dynamics where HbS fiber projections growing outward from the cell surface create multiple sites of adhesion; and ( iv ) polymerization stimulates adhesion and vice versa, thereby establishing the bidirectional coupling between the two processes. These findings offer insights into possible mechanistic pathways leading to vasoocclusion crisis. They also elucidate the processes underlying the onset of occlusion that may involve circulating reticulocytes, which are more abundant in hemolytic anemias due to robust compensatory erythropoiesis., Competing Interests: Conflict of interest statement: D.P.P., S.Z.A., M.D., and S.S. have filed a patent based on the work presented in this paper., (Copyright © 2018 the Author(s). Published by PNAS.)

In red blood cell (RBC) diseases, the spleen contributes to anemia by clearing the damaged RBCs, but its unique ability to mechanically challenge RBCs also poses the risk of inducing other pathogenic effects. We have analyzed RBCs in hereditary spherocytosis (HS) and hereditary elliptocytosis (HE), two typical examples of blood disorders that result in membrane protein defects in RBCs. We use a two-component protein-scale RBC model to simulate the traversal of the interendothelial slit (IES) in the human spleen, a stringent biomechanical challenge on healthy and diseased RBCs that cannot be directly observed in vivo. In HS, our results confirm that the RBC loses surface due to weakened cohesion between the lipid bilayer and the cytoskeleton and reveal that surface loss may result from vesiculation of the RBC as it crosses IES. In HE, traversing IES induces sustained elongation of the RBC with impaired elasticity and fragmentation in severe disease. Our simulations thus suggest that in inherited RBC disorders, the spleen not only filters out pathological RBCs but also directly contributes to RBC alterations. These results provide a mechanistic rationale for different clinical outcomes documented following splenectomy in HS patients with spectrin-deficient and ankyrin-deficient RBCs and offer insights into the pathogenic role of human spleen in RBC diseases., Competing Interests: The authors declare no conflict of interest., (Copyright © 2018 the Author(s). Published by PNAS.)

Red blood cells (RBCs) can be cleared from circulation when alterations in their size, shape, and deformability are detected. This function is modulated by the spleen-specific structure of the interendothelial slit (IES). Here, we present a unique physiological framework for development of prognostic markers in RBC diseases by quantifying biophysical limits for RBCs to pass through the IES, using computational simulations based on dissipative particle dynamics. The results show that the spleen selects RBCs for continued circulation based on their geometry, consistent with prior in vivo observations. A companion analysis provides critical bounds relating surface area and volume for healthy RBCs beyond which the RBCs fail the "physical fitness test" to pass through the IES, supporting independent experiments. Our results suggest that the spleen plays an important role in determining distributions of size and shape of healthy RBCs. Because mechanical retention of infected RBC impacts malaria pathogenesis, we studied key biophysical parameters for RBCs infected with Plasmodium falciparum as they cross the IES. In agreement with experimental results, surface area loss of an infected RBC is found to be a more important determinant of splenic retention than its membrane stiffness. The simulations provide insights into the effects of pressure gradient across the IES on RBC retention. By providing quantitative biophysical limits for RBCs to pass through the IES, the narrowest circulatory bottleneck in the spleen, our results offer a broad approach for developing quantitative markers for diseases such as hereditary spherocytosis, thalassemia, and malaria.

We study the biomechanical interactions between the lipid bilayer and the cytoskeleton in a red blood cell (RBC) by developing a general framework for mesoscopic simulations. We treated the lipid bilayer and the cytoskeleton as two distinct components and developed a unique whole-cell model of the RBC, using dissipative particle dynamics (DPD). The model is validated by comparing the predicted results with measurements from four different and independent experiments. First, we simulated the micropipette aspiration and quantified the cytoskeletal deformation. Second, we studied the membrane fluctuations of healthy RBCs and RBCs parasitized to different intraerythrocytic stages by the malaria-inducing parasite Plasmodium falciparum. Third, we subjected the RBC to shear flow and investigated the dependence of its tank-treading frequency on shear rate. Finally, we simulated the bilayer-cytoskeletal detachment in channel flow to quantify the strength of such interactions when the corresponding bonds break. Taken together, these experiments and corresponding systematic DPD simulations probe the governing constitutive response of the cytoskeleton, elastic stiffness, viscous friction, and strength of bilayer-cytoskeletal interactions as well as membrane viscosities. Hence, the DPD simulations and comparisons with available independent experiments serve as validation of the unique two-component model and lead to useful insights into the biomechanical interactions between the lipid bilayer and the cytoskeleton of the RBC. Furthermore, they provide a basis for further studies to probe cell mechanistic processes in health and disease in a manner that guides the design and interpretation of experiments and to develop simulations of phenomena that cannot be studied systematically by experiments alone.

Vasoocclusion crisis is a key hallmark of sickle cell anemia. Although early studies suggest that this crisis is caused by blockage of a single elongated cell, recent experiments have revealed that vasoocclusion is a complex process triggered by adhesive interactions among different cell groups in multiple stages. However, the quantification of the biophysical characteristics of sickle cell anemia remains an open issue. Based on dissipative particle dynamics, we develop a multiscale model for the sickle red blood cells (SS-RBCs), accounting for diversity in both shapes and cell rigidities, to investigate the precise mechanism of vasoocclusion. First, we investigate the adhesive dynamics of a single SS-RBC in shear flow and static conditions, and find that the different cell groups (SS2: young-deformable SS-RBCs, ISCs: rigid-irreversible SS-RBCs) exhibit heterogeneous adhesive behavior due to the diverse cell morphologies and membrane rigidities. We quantify the observed adhesion behavior (in static conditions) in terms of a balance of free energies due to cell adhesion and deformation, and propose a power law that relates the free-energy increase as a function of the contact area. We further simulate postcapillary flow of SS-RBC suspensions with different cell fractions. The more adhesive SS2 cells interact with the vascular endothelium and trap ISC cells, resulting in vasoocclusion in vessels less than 12-14 μm depending on the hematocrit. Under inflammation, adherent leukocytes may also trap ISC cells, resulting in vasoocclusion in even larger vessels.

The viscosity of blood has long been used as an indicator in the understanding and treatment of disease, and the advent of modern viscometers allows its measurement with ever-improving clinical convenience. However, these advances have not been matched by theoretical developments that can yield a quantitative understanding of blood's microrheology and its possible connection to relevant biomolecules (e.g., fibrinogen). Using coarse-grained molecular dynamics and two different red blood cell models, we accurately predict the dependence of blood viscosity on shear rate and hematocrit. We explicitly represent cell-cell interactions and identify the types and sizes of reversible rouleaux structures that yield a tremendous increase of blood viscosity at low shear rates. We also present the first quantitative estimates of the magnitude of adhesive forces between red cells. In addition, our simulations support the hypothesis, previously deduced from experiments, of yield stress as an indicator of cell aggregation. This non-Newtonian behavior is analyzed and related to the suspension's microstructure, deformation, and dynamics of single red blood cells. The most complex cell dynamics occurs in the intermediate shear rate regime, where individual cells experience severe deformation and transient folded conformations. The generality of these cell models together with single-cell measurements points to the future prediction of blood-viscosity anomalies and the corresponding microstructures associated with various diseases (e.g., malaria, AIDS, and diabetes mellitus). The models can easily be adapted to tune the properties of a much wider class of complex fluids including capsule and vesicle suspensions.

The pathogenicity of Plasmodium falciparum (Pf) malaria results from the stiffening of red blood cells (RBCs) and its ability to adhere to endothelial cells (cytoadherence). The dynamics of Pf-parasitized RBCs is studied by three-dimensional mesoscopic simulations of flow in cylindrical capillaries in order to predict the flow resistance enhancement at different parasitemia levels. In addition, the adhesive dynamics of Pf-RBCs is explored for various parameters revealing several types of cell dynamics such as firm adhesion, very slow slipping along the wall, and intermittent flipping. The parasite inside the RBC is modeled explicitly in order to capture phenomena such as "hindered tumbling" motion of the RBC and the sudden transition from firm RBC cytoadherence to flipping on the endothelial surface. These predictions are in quantitative agreement with recent experimental observations, and thus the three-dimensional modeling method presented here provides new capabilities for guiding and interpreting future in vitro and in vivo studies of malaria.

In many stochastic partial differential equations (SPDEs) involving random coefficients, modeling the randomness by spatial white noise may lead to ill-posed problems. Here we consider an elliptic problem with spatial Gaussian coefficients and present a methodology that resolves this issue. It is based on stochastic convolution implemented via generalized Malliavin operators in conjunction with weighted Wiener spaces that ensure the ellipticity condition. We present theoretical and numerical results that demonstrate the fast convergence of the method in the proper norm. Our approach is general and can be extended to other SPDEs and other types of multiplicative noise.

We obtain analytical solutions for the perturbed shock paths induced by time-varying random motions of a piston moving inside an adiabatic tube of constant area. The variance of the shock location grows quadratically with time for early times and switches to linear growth for longer times. The analytical results are confirmed by stochastic numerical simulations, and deviations for large random piston motions are established.