Quantitative Hemodynamics using Magnetic Resonance Imaging, Computational Fluid Dynamics and Physics-informed Neural Network

Indoor airflow field reconstruction using physics-informed neural network

3D concrete printing (3DCP) is an innovative construction method that extrudes cementitious materials layer-by-layer to fabricate building components based on a digital model. 3DCP has gained increasing adoption globally for projects like buildings, bridges, retaining walls, and stormwater management systems. However, 3DCP places stringent demands on the rheological properties of the printable cementitious materials. Rheology is critical for the flow and buildability of fresh concrete during extrusion. The mixture must have a low yield stress for pumping, moderate viscosity to hold its shape after deposition, minimal bleeding and segregation of aggregates, as well as responsive rheology that can transition from fluid to solid state as layers are printed sequentially. In this dissertation, we aim to solve the challenges mentioned above including: (1) accurate and efficient quantification of rheological and thixotropic properties of cementitious materials, (2) evaluation of flow behavior of fresh concrete during extrusion. Using traditional experimental methods to evaluate rheological properties of cement paste is labor-intensive and time-consuming. Numerical simulations like Finite Element Method (FEM) or Computational Fluid Dynamics (CFD) can help increase the speed of finding the most suitable material for 3DCP. However, these simulation methods are costly in computing power, making them less desirable for simulating the dynamic and complex process of 3DCP. Moreover, mesh-based approaches are not suitable for complex geometries as the mesh generation would be challenging with curved boundaries, small features, holes or thin regions. Physics-Informed Neural Network (PINN) is introduced in the work as an innovative solution to simulate and model the whole process of 3DCP. It can leverage the flexibility and computational efficiency of data-based neural networks, which can accelerate the learning and convergence speed. At the same time, Partial Differential Equations (PDEs) would be embedded in the network structure to increase the accuracy of its prediction. The integrated governing physical laws can help the neural network understanding the underlying physics of the 3DCP process, potentially increasing the accuracy and reliability of simulations. A significant part of the research is dedicated to understanding the rheological and thixotropic behavior of cementitious materials, which is critical for the material design in 3DCP. We developed a Rheology-informed Neural Network, RheologyNet, where we embedded the rheological constitutive laws into the loss function. These physical laws can help the network focus on simulating the rheological properties of cementitious materials. Moreover, a thixotropic evaluation system has been established based on the proposed model to evaluate the thixotropic property of cement paste. This study is presented in Chapter 2. Then, we proposed a Navier-Stokes Informed Neural Network (NSINN) to study the flow behavior of cement paste in the 3DCP barrel and nozzle since it involves complicated Multiscale or Multiphysics behaviors, such as anisotropy and non-uniform shear rate distribution. The Navier Stokes Equation and the rheological constitutive equations are coupled and embedded into the NSINN architecture to simulate the flow behavior in the barrel during 3D-printing extrusion process. This approach demonstrates the potential of PINNs to provide high-accuracy simulations of velocity and pressure fields in a computationally efficient manner compared to traditional mesh-based models. Also, we used the NSINN to learn the relationship between the nozzle size and the printing quality. The details of the study are presented in Chapter 3. At last, a multi-subnetwork PINN architecture (MultiSubPINN) is proposed to address the limitations of traditional PINNs. This is because traditional PINNs used Fully-connected Neural Network (FNN) as main bone. It has problems like different outputs must share parameters within the network structure. However, this parameter sharing nature might lead to potential errors and decrease the model performance. The main architecture of this network is consisted of multiple separated sub-networks and the loss function of each sub-network is calculated separately to update the parameters in each sub-network. By doing this, we can ensure that the optimization for one output doesn't negatively impact others, therefore providing a more flexible, scalable, and potentially more accurate alternative for the evaluation. Besides, using randomly distributed training points in the computational domain for PINNs is a common way. However, many physical problems exhibit non-uniform behavior, with certain regions of the domain having more complex dynamics or sharper gradients than others. Randomly distributed training points might not adequately capture these regions, leading to a model that misrepresents the underlying physics in critical areas. We proposed a Physical-based sampling strategy to optimize the training of the PINNs. This study is presented in Chapter 4. In summary, this dissertation has established a new platform that is enabled by interpretable NN to accurately quantify cement paste’s rheological properties and simulate the flow behavior of 3D concrete printing process. The findings suggest that PINNs can not only improve the efficiency and accuracy of simulations but also provide a more profound understanding of the material behaviors and process dynamics critical to 3DCP. The novel PINN structure developed from this dissertation is a powerful general platform that could be applicable to a variety of material domains for complex rheological behavior predictions.

Aim Comprehensive evaluation of blood flow in the thoracic aorta using a software for 4D processing of magnetic resonance (MR) images of the heart and blood vessels (4D Flow) in patients with aortic coarctation in the late postoperative period.Materials and methods The MR study of the heart was performed for 10 patients (7 boys and 3 girls) aged 8 to 13 years (median, 9.5 [8.3; 10.8] years) who underwent resection with end-to-end anastomosis for aortic coarctation at age of 2 weeks to 10 months. MR tomography was performed on a 1.5 T MR scanner using a multichannel surface coil for scanning, electrocardiographic synchronization, and a specialized package of pulse sequences for scanning of the heart. Blood flow was evaluated with a 4D data handling software for processing of MR images of heart and blood vessels (4D Flow). The following blood flow parameters were analyzed: blood flow volume per second, peak blood flow velocity, peak and minimum blood flow area at the levels of ascending aorta, arch, isthmus, and descending aorta, and pressure gradient at the level of maximum narrowing of the aorta. 3D-MR images were used for evaluation of aortic geometry. Blood flow formation, distribution, and trajectories were analyzed by maps of vectors, particle trace, and stream lines. Statistical analysis was performed with a Statistica (v. 6.0 StatSoft Inc.) package.Results Accelerated flow in the region of residual aortic stenosis in systole was observed in all patients; 4 patients had an additional vortex flow below the aortic stenosis and a spiral flow in the descending aorta. The pressure gradient on the aortic isthmus was directly correlated with the left ventricular myocardial mass index (r=0.65; р=0.04) and indexes of blood flow in the ascending and descending aorta (р=0.03; р=0.026). No significant correlation was found for blood flow indexes and geometry of the aortic arch (H / L). Delayed contrast enhancement MR imaging did not detect any fibrotic changes in the myocardium in only one patient. The fibrosis severity inversely correlated with the right ventricular ejection fraction (r=0.65; р=0.04) and directly correlated with the pressure gradient at the aortic isthmus (r=0.63; p=0.05).Conclusion The 4D MR image processing software for the heart and blood vessels allows studying the blood flow in detail under natural conditions, provides potential advantages in comprehensive evaluation of patients with aortic coarctation during a dynamic follow-up. For a definitive conclusion about the relationship between the altered blood flow in the thoracic aorta and markers of residual, post-correction pathology, larger studies are required as well as long-term follow-up of patients with documented pathological patterns of blood flow (changes in blood flow velocity and volume throughout the entire thoracic aorta in combination with disorders in the normal flow geometry during the cardiac cycle).

Atrial fibrillation (AF) promotes blood stasis and thrombus formation, most often within the left atrial appendage (LAA), and can lead to stroke or transient ischemic attack (TIA). Time-resolved contrast-enhanced computed tomography (4D CT) captures left atrial (LA) opacification and washout, but it does not directly provide quantitative stasis metrics such as blood residence time. Patient-specific computational fluid dynamics (CFD) can quantify LA/LAA residence time, yet routine clinical use is limited by computational cost and sensitivity to patient-specific boundary conditions. Here, we present two complementary approaches to infer time-resolved 3D residence time fields directly from contrast dynamics. First, a physics-informed neural network (PINN) treats contrast as a passive scalar and jointly reconstructs velocity and residence time by enforcing the incompressible Navier-Stokes equations and transport equations for contrast concentration and residence time in moving, patient-specific LA anatomies. Second, an indicator dilution theory (IDT) formulation computes voxelwise, time-resolved residence time maps from contrast time curves alone by constructing a PV-referenced impulse response and modeling transport with a tank-in-series model with spatially dependent parameters. Both methods are benchmarked against patient-specific CFD in six cases spanning diverse LA function, including three patients with TIA or thrombus in the LAA and three patients free of events. Both approaches reproduce expected spatial and temporal trends, with higher residence time in the distal LAA and higher LAA residence time in cases with TIA or thrombus. IDT demonstrates the closest agreement with CFD across the full range of residence times and produces maps in seconds, facilitating clinical translation. In contrast, the PINN additionally recovers phase-dependent atrial flow structures, but tends to smooth and underestimate the highest residence-time regions and requires hours of training. Together, these results support a scalable workflow in which IDT enables rapid stasis screening from contrast CT, and PINNs provide a complementary pathway for detailed, patient-specific hemodynamic inference when full-field flow information is needed.

We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of dilute polymer solutions. In this framework the training of the neural network is guided by an evolution equation for the conformation tensor, which is GENERIC-compliant. We compare two training methodologies for the data-driven PINN constitutive models: one trained on data from the analytical solution of the Oldroyd-B (OB) model under steady-state rheometric flows (PINN-rheometric), and another trained on in silico data generated from computational fluid dynamics (CFD) simulations of complex flow around a cylinder that use the OB model (PINN-complex). The capacity of the PINN models to provide good predictions is evaluated by comparison with CFD simulations using the underlying OB model as a reference. Both models are capable of predicting flow behaviour in transient and complex conditions; however, the PINN-complex model, trained on a broader range of mixed-flow data, outperforms the PINN-rheometric model in complex flow scenarios. The geometry agnostic character of our methodology allows us to apply the learned PINN models to flows with topologies different from those used for training.

Physics-informed neural networks (PINNs) are emerging as a promising artificial intelligence approach for solving complex two-phase flow simulations. A critical challenge in these simulations is an accurate representation of the gas–liquid interface using interface tracking methods. While numerous studies in conventional computational fluid dynamics (CFD) have addressed this issue, there remains a notable absence of research within the context of PINNs-based two-phase flow simulations. Therefore, this study aims to develop a robust and generic PINNs for two-phase flow by incorporating the governing equations with three advanced interface tracking methods—specifically, the Volume of Fluid, Level Set, and Phase-Field method—into an improved PINN framework that has been previously proposed and validated. To further enhance the performance of the PINNs in simulating two-phase flow, the phase field constraints, residual connection and the time divide-and-conquer strategies are employed for restricting neural network training within the scope of physical laws. This self-adaptive and time divide-and-conquer (AT) PINNs is then optimized by minimizing both the residual and loss terms of partial differential equation. By incorporating the three different interface tracking methods, it efficiently handles high-order derivative terms and captures the phase interface. The case of single rising bubble in two-phase flow is simulated to validate the robustness and accuracy of the AT PINNs. The simulation's accuracy is evaluated by comparing its performance in terms of velocity, pressure, phase field, center of mass, and rising velocity with that of conventional PINNs and CFD benchmarks. The results indicate that the AT PINNs coupled with these interface tracking methods offers a satisfactory performance in simulating rising bubble phenomenon.

BackgroundFour dimensional (4D) flow magnetic resonance imaging (MRI) enables both visualisation and quantification of hemodynamics in abdominal aortic aneurysms (AAAs). However, its clinical implementation remains limited due to time-consuming and cumbersome post-processing, as well as a lack of standardisation. While previous work has proposed automated solutions for thoracic and intracranial cases, applications in the abdominal region, particularly for AAAs, remain underexplored. The aim of this study was to develop an automated post-processing pipeline for 4D flow MRI in AAA patients, incorporating aneurysm identification, via automated segmentation, blood flow visualisation and hemodynamic parameter quantification.Methods4D flow MRI and three dimensional (3D) cine balanced steady state free precession (bSSFP) scans were acquired from 16 patients with an AAA in the same field of view and with an isotropic resolution of 1 mm. Using 5-fold cross-validation, an nnU-Net was trained to segment the aorta based on 3D cine bSSFP MRI. The automated post-processing pipeline was built using MATLAB. Wall shear stress (WSS) values were assessed within the extracted aneurysm. nnU-Net performance was assessed with the Dice-similarity coefficient (DSC), 95% percentile Hausdorff distance (HD95) and by calculating the Pearson correlation coefficients between WSS values obtained in the aneurysm based on segmentation with both methods.ResultsThe resulting post-processing pipeline demonstrated robustness to anatomical variability, including tortuosity and intraluminal thrombus (ILT), both characteristic of AAA, and consistently produced output without user-interference. The nnU-Net performance was excellent for lumen segmentation and good for ILT segmentation, with DSCs of 0.93 (0.05) and 0.80 (0.26) respectively. The HD95 was 4.87 (8.59) mm and 6.04 (3.71) mm for respectively lumen and thrombus segmentation. Significant correlations (ρ =0.92 or higher) were found between WSS values derived using the manual and nnU-Net segmentations.ConclusionsAn automated post-processing pipeline was developed specifically for 4D flow MRI in patients with AAA. The pipeline is robust for varying anatomies and may facilitate 4D flow MRI implementation in the clinical workflow.

BackgroundChanges in blood flow after brain aneurysm treatment are linked to treatment success. While 4D flow magnetic resonance imaging (MRI) can measure these changes, it is sensitive to metal artifacts from implants. Black-blood MRI, less affected by artifacts, may complement 4D flow MRI. We investigated whether changes in black-blood signal reflect reductions in blood flow and could indicate the success of aneurysm treatment.MethodsWe performed 22 flow experiments using 3D printed models of two patient-derived brain aneurysms and two straight vessels. Flow-modulating devices, including flow-diverter stents and intrasaccular devices, were inserted into 15 aneurysm models, while untreated models served as controls. All models were imaged with 4D flow and black-blood MRI on a 3 T clinical system. Numerical flow simulations were also performed. Blood flow velocity and black-blood signal were compared between treated and untreated models using non-parametric statistical tests, and their relationship was evaluated with correlation analysis.ResultsHere we show that the black-blood signal in straight vessels decreases with increasing velocity (rho = −0.92, p-value = 3.29E-04). Implanted devices reduce blood flow within aneurysms while leaving flow in the parent vessels essentially unchanged. Treated aneurysms exhibit a significant increase in black-blood signal, which correlates inversely with measured velocity (rho = −0.82, p-value = 6.24E-04). The experimentally observed flow reductions match the numerical simulations. Metal artifacts are more pronounced on 4D flow compared to black-blood MRI.ConclusionsBlack-blood MRI may serve as a surrogate marker of blood flow reduction after aneurysm treatment, particularly in cases where metal artifacts limit conventional imaging.

Objective To perform the virtual Fontan operations on patients who had undergone the bilateral bidirectional Glenn procedure, and to simulate the blood flow in different types of opera-tive strategies by the method of computational fluid dynamics (CFD). Methods Three-dimensional re-construction was performed with Mimics 12. 0(R) according to the results of magnetic resonance imaging (MRI). Virtual operations were performed by changing the virtual anastomotic sites of bilateral supe-rior vena cava (SVC) and pulmonary arteries (PAs), and by connecting the inferior vena cava (IVC) to different sites of PAs. Numerical simulations were established to analyze the CFD of blood flows in patients undergoing 4 different types of virtual operative strategies at different predetermined flow split distribution ratios of left pulmonary artery (LPA) to right pulmonary artery (RPA) (at 30: 70,40 : 60, 50:50,60:40 and 70:30, respectively). Results When the distance between the anastomotic sites of the bilateral SVCs to the PAs was relatively long and the anastomotic site of IVC and PAs was in the middle of the SVC-PA anastomotic sites, the control volume power loss (CVPL) was lower than any other three operative strategies at all predetermined LPA/RPA flow split distribution ratios. The CV-PL achieved a minimal value of 23.60 mW at the ratio of 50/50. Conclusions For Fontan operations, it may be the optimal operative strategy to anastomose bilateral SVCs to the homolateral PA separately and to connect the IVC in the middle of the SVC-PA anastomotic sites. Key words: Computational fluid dynamics; Fontan procedure; Virtual operation; Energy me-tabolism

The article "Assessment of superior mesenteric vascular flow quantitation in children using four-dimensional flow magnetic resonance imaging" suggests to use of four-dimensional (4D) flow magnetic resonance imaging (MRI) which is also to measure the blood flow in the superior mesenteric vein (SMV) in pediatric patients over the traditional method. The study focuses on assessing the potential of SMV and superior mesenteric artery (SMA) flow quantification in children utilizing 4D flow MRI. It included 9 pediatric patients aged 18 years and below where 5 were male and 4 were female patients, on whom magnetic resonance enterorrhaphy (MRE) with 4D flow MRI protocol was used. Statistical analysis was performed using MedCalc. Measurements of SMV and SMA between two readers were calculated using Bland-Altman analysis. The results stated that six patients showed no MRE evidence of active inflammatory bowel disease, two patients showed unmarkable bowel appearance on MRI and one patient showed normal MRE without endoscopy performed at the same timeframe. The study utilized available 4D flow MRI sequences in this study aiming to show the feasibility of 4D flow quantitation of SMA and SMV flow in pediatric patients. The study also discovered good agreement for both peak velocity and peak speed measurements of SMA and SMV.

Computational modeling of left ventricular flow using PC-CMR-derived four-dimensional wall motion

Aim: Insufficient assessment of post-surgical organ perfusion in hepatobiliopancreatic surgery can lead to serious complications. Consequently, various technological solutions have been developed to achieve non-invasive and accurate blood flow assessment. This article aims to evaluate the current state of four-dimensional flow magnetic resonance imaging (4D-flow MRI) and computational fluid dynamics (CFD) technologies in assessing vascular blood flow within this surgical field. Methods: A comprehensive literature search using ClinicalTrials.gov and PubMed/MEDLINE was performed; articles published between 2015 and 2025 were included. Broad search terms, including “blood flow measurement”, “4D-flow MRI”, or “computational fluid dynamics” and “abdomen” or “liver”, were utilized. Results: Twenty-two studies were analyzed in detail. Nineteen focused on vascular conditions surrounding the liver, with 15 assessing venous flow and five evaluating the hepatic artery. Additional hemodynamic features analyzed included blood velocity, pressure, and particle distribution. The clinical applications investigated were: portal vein embolization (1), venous anastomosis (3), liver resection (2), portal hypertension (2), transarterial radioembolization (2), transjugular intrahepatic portosystemic shunt (4), and liver fibrosis (1). Notably, only CFD facilitated the simulation of prospective hemodynamic conditions (2). Conclusion: Both 4D-flow MRI and CFD technologies facilitate the accurate study of blood flow dynamics within the supramesocolic compartment. Furthermore, CFD enables the simulation of prospective vascular conditions, establishing its potential as a preoperative planning tool. However, further research is required to fully validate the clinical utility of CFD in this surgical context.

Determining brain hemodynamics plays a critical role in the diagnosis and treatment of various cerebrovascular diseases. In this work, we put forth a physics-informed deep learning framework that augments sparse clinical measurements with one-dimensional (1D) reduced-order model (ROM) simulations to generate physically consistent brain hemodynamic parameters with high spatiotemporal resolution. Transcranial Doppler (TCD) ultrasound is one of the most common techniques in the current clinical workflow that enables noninvasive and instantaneous evaluation of blood flow velocity within the cerebral arteries. However, it is spatially limited to only a handful of locations across the cerebrovasculature due to the constrained accessibility through the skull's acoustic windows. Our deep learning framework uses in vivo real-time TCD velocity measurements at several locations in the brain combined with baseline vessel cross-sectional areas acquired from 3D angiography images and provides high-resolution maps of velocity, area, and pressure in the entire brain vasculature. We validate the predictions of our model against in vivo velocity measurements obtained via four-dimensional (4D) flow magnetic resonance imaging (MRI) scans. We then showcase the clinical significance of this technique in diagnosing cerebral vasospasm (CVS) by successfully predicting the changes in vasospastic local vessel diameters based on corresponding sparse velocity measurements. We show this capability by generating synthetic blood flow data after cerebral vasospasm at various levels of stenosis. Here, we demonstrate that the physics-based deep learning approach can estimate and quantify the subject-specific cerebral hemodynamic variables with high accuracy despite lacking knowledge of inlet and outlet boundary conditions, which is a significant limitation for the accuracy of the conventional purely physics-based computational models.

ABSTRACTObjectiveTo characterize the fetoplacental response to acute maternal hyperoxygenation (AMH) in fetuses with suspected coarctation of the aorta (CoA) using fetal cardiac magnetic resonance imaging (MRI).MethodsPregnant women carrying a fetus with suspected CoA were recruited prospectively from a tertiary fetal cardiology center as part of the Fetal Imaging with Maternal Oxygen (FIMOx) study between February 2019 and April 2022. MRI included phase‐contrast flow measurements and oxygen‐sensitive T2* sequences to assess placental and fetal brain oxygenation. Results were analyzed on a groupwise basis, comparing true‐positive CoA cases (requiring surgical CoA repair ≤ 28 days after birth) to false positives.ResultsFetal MRI with AMH was performed in 20 pregnancies (mean ± SD gestational age, 33.0 ± 1.3 weeks), of which five had CoA and 15 were false positives. In both groups, AMH significantly increased the placental T2* signal but had no effect on cerebral T2*. Increased pulmonary blood flow with AMH was associated with reduced right–left shunting at the foramen ovale (r = −0.74, P < 0.001), but not with increased ascending aortic flow (r = 0.36, P = 0.177). Compared with baseline, AMH increased anterograde flow at the aortic isthmus from −2 (interquartile range (IQR), −57 to 10) mL/kg/min to 32 (IQR, −14 to 48) mL/kg/min (P < 0.001); however, this was associated with a reduction in superior vena cava flow (median, −29% (IQR, −41% to 0%); P < 0.001) and not with changes in ascending aortic flow. No differences in baseline or AMH phase‐contrast or T2* values usefully distinguished true‐ and false‐positive cases in this pilot study.ConclusionsAMH leads to a significant reduction in cerebral blood flow in fetuses with suspected CoA, which is the primary driver of changes in flow at the aortic isthmus. Future studies should consider the effects of maternal oxygen on the entirety of fetoplacental circulation, particularly for cases in which chronic maternal hyperoxygenation administration is being considered. © 2025 The Author(s). Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of International Society of Ultrasound in Obstetrics and Gynecology.

Atherosclerosis involves an inflammatory response due to plaque formation within the arteries, which can lead to ischemic stroke and heart disease. It is one of the leading causes of death worldwide, with various contributing factors such as hyperlipidemia, hypertension, obesity, diabetes, and smoking. Wall shear stress (WSS) is also known as a contributing factor of the formation of atherosclerotic plaques. Since the causes of atherosclerosis cannot be attributed to a single factor, clearly understanding the mechanisms and causes of its occurrence is crucial for preventing the disease and developing effective treatment strategies. To better understand atherosclerosis and define the correlation between various contributing factors, computational fluid dynamics (CFD) analysis is primarily used. CFD simulates WSS, the frictional force caused by blood flow on the vessel wall with various hemodynamic changes. Using apolipoprotein E knockout (ApoE-KO) mice subjected to partial ligation and a high-fat diet at 1-week, 2-week, and 4-week intervals as an atherosclerosis model, CFD analysis was conducted along with the reconstruction of carotid artery blood flow via magnetic resonance imaging (MRI) and compared to the inflammatory factors and pathological staining. In this experiment, a comparative analysis of the effects of high WSS and low WSS was conducted by comparing the standard deviation of time-averaged wall shear stress (TAWSS) at each point within the vessel wall. As a novel approach, the standard deviation of TAWSS within the vessel was analyzed with the staining results and pathological features. Since the onset of atherosclerosis cannot be explained by a single factor, the aim was to find the correlation between the thickness of atherosclerotic plaques and inflammatory factors through standard deviation analysis. As a result, the gap between low WSS and high WSS widened as the interval between weeks in the atherosclerosis mouse model increased. This finding not only linked the occurrence of atherosclerosis to WSS differences but also provided a connection to the causes of vulnerable plaques.