Xiaoxu Zhong

All Publications

• Diffusion-aware compartment model of the cellular uptake of ^{18}F-fluorodeoxyglucose. Physical review. E Zhong, X., Nguyen, H. T., Takematsu, E., Pratx, G. 2025; 111 (4-1): 044409

  Abstract

  Compartment models are widely used in fields such as epidemiology and biomedicine to describe the exchange of uniformly distributed materials between interconnected compartments. However, their application in biological fluids is limited by the assumption of infinitely large diffusivity, especially in environments such as tumors or subcutaneous tissue, where diffusion is considerably lower. To address this, we develop a diffusion-aware compartment model that maintains the simplicity of traditional compartment models while offering greater accuracy. We conducted experiments on the uptake of ^{18}F-fluorodeoxyglucose (FDG), a radionuclide, by cells grown in culture plates and found a good agreement between the measured and predicted cellular radioactivity. We identify two critical dimensionless parameters that compare the amount of FDG (i) replenished by diffusion and (ii) available in the culture medium to the amount of FDG taken up by cells. We demonstrate that the diffusion-aware compartment model reduces to the three-compartment model when FDG diffusion is fast relative to cellular uptake, and it further simplifies to the two-compartment model when sufficient FDG is available in the culture medium. The semianalytic solutions of the diffusion-aware compartment model can be easily extended to study other scenarios, such as drug transport and bubble growth dynamics.

  View details for DOI 10.1103/PhysRevE.111.044409

  View details for PubMedID 40411104

• Spatial transcriptomic analysis drives PET imaging of tight junction protein expression in pancreatic cancer theranostics. Nature communications Wang, J., Seo, J. W., Kare, A. J., Schneider, M., Pandrala, M., Tumbale, S. K., Raie, M. N., Engudar, G., Zhang, N., Guo, Y., Zhong, X., Ferreira, S., Wu, B., Attardi, L. D., Pratx, G., Iagaru, A., Brunsing, R. L., Charville, G. W., Park, W. G., Ferrara, K. W. 2024; 15 (1): 10751

  Abstract

  Molecular imaging using positron emission tomography (PET) provides sensitive detection and mapping of molecular targets. While cancer-associated fibroblasts and integrins have been proposed as targets for imaging of pancreatic ductal adenocarcinoma (PDAC), herein, spatial transcriptomics and proteomics of human surgical samples are applied to select PDAC targets. We find that selected cancer cell surface markers are spatially correlated and provide specific cancer localization, whereas the spatial correlation between cancer markers and immune-related or fibroblast markers is low. Claudin-4 expression increases ~16 fold in cancer as compared with normal pancreas, and tight junction localization confers low background for imaging in normal tissue. We develop a peptide-based molecular imaging agent targeted to claudin-4 with accumulation to ~25% injected activity per cubic centimeter (IA/cc) in metastases and ~18% IA/cc in tumors. Our work motivates a data-driven approach to selection of molecular targets.

  View details for DOI 10.1038/s41467-024-54761-6

  View details for PubMedID 39737976

  View details for PubMedCentralID 10236159

• Efficient radiolabeling of mesoporous silica nanoparticles for single-cell PET imaging. European journal of nuclear medicine and molecular imaging Khan, S., Zhong, X., Das, N., Yu, J. H., Natarajan, A., Anders, D., Pratx, G. 2024

  Abstract

  Nanoparticles are highly efficient vectors for ferrying contrast agents across cell membranes, enabling ultra-sensitive in vivo tracking of single cells with positron emission tomography (PET). However, this approach must be fully characterized and understood before it can be reliably implemented for routine applications.We developed a Langmuir adsorption model that accurately describes the process of labeling mesoporous silica nanoparticles (MSNP) with 68Ga. We compared the binding efficiency of three different nanoparticle systems by fitting the model to experimental data. We then chose the MSNP with the highest affinity for 68Ga to study uptake and efflux kinetics in cancer cells. After intracardiac injection of 50-100 cells in mice, PET imaging was performed to test the effectiveness of cellular radiolabeling.We found that highly porous mesoporous nanoparticles (d = 100 nm) with MCM-41 pore structures can achieve radiolabeling efficiency > 30 GBq/mg using 68Ga, without the need for any chelator. These 68Ga conjugated particles showed strong serum stability in vitro. In mice, the 68Ga-MSNPs predominantly accumulated in the liver with a high signal-to-background ratio and no bladder signal, indicating excellent stability of the labeled nanoparticles in vivo. Additionally, these MSNPs were efficiently taken up by B16F10 and MDA-MB-231 cancer cells, as confirmed by confocal imaging, flow cytometry analysis, and gamma counting. Finally, cardiac injection of < 100 68Ga-MSNP-labeled cells allowed PET/CT tracking of these cells in various organs in mice.We characterized the critical parameters of MSNP-mediated direct cellular radiolabeling to improve the use of these nanoparticles as cellular labels for highly sensitive preclinical PET imaging.

  View details for DOI 10.1007/s00259-024-07027-8

  View details for PubMedID 39729092

  View details for PubMedCentralID 5260938

• The role of initial lymphatics in the absorption of monoclonal antibodies after subcutaneous injection. Computers in biology and medicine Rahimi, E., Li, C., Zhong, X., Shi, G. H., Ardekani, A. M. 2024; 183: 109193

  Abstract

  The subcutaneous injection is the most common method of administration of monoclonal antibodies (mAbs) due to the patient's comfort and cost-effectiveness. However, the available knowledge about the transport and absorption of this type of biotherapeutics after subcutaneous injection is limited. Here, a mathematical framework to study the subcutaneous drug delivery of mAbs from injection to lymphatic uptake is presented. A poro-hyperelastic model of the tissue is exploited to find the biomechanical response of the tissue together with a transport model based on an advection-diffusion equation in large-deformation poro-hyperelastic Media. The process of mAbs transport to the lymphatic system has two major parts. First is the initial phase, where mAbs are dispersed in the tissue due to momentum exerted by injection. This stage lasts for only a few minutes after the injection. Then there is the second stage, which can take tens of hours, and as a result, mAb molecules are transported from the subcutaneous layer towards initial lymphatics in the dermis to enter the lymphatic system. In this study, we investigate both stages. The process of plume formation, interstitial pressure, and velocity development is explored. Then, the effect of the injection delivery parameters, injection site, and sensitivity of long-term lymphatic uptake due to variability in permeability, diffusivity, viscosity, and binding of mAbs are investigated. Finally, we study two different injection scenarios with variable injection volume and drug concentration inside the syringe and evaluate them based on the rate of lymphatic uptake. We use our results to find an equivalent lymphatic uptake coefficient similar to the coefficient widely used in pharmacokinetic (PK) models to study the absorption of mAbs. Ultimately, we validate our computational model against available experiments in the literature.

  View details for DOI 10.1016/j.compbiomed.2024.109193

  View details for PubMedID 39423704

• A multi-scale numerical study of monoclonal antibodies uptake by initial lymphatics after subcutaneous injection. International journal of pharmaceutics Li, C., Zhong, X., Rahimi, E., Ardekani, A. M. 2024: 124419

  Abstract

  This paper studies the transport of monoclonal antibodies through skin tissue and initial lymphatics, which impacts the pharmacokinetics of monoclonal antibodies. Our model integrates a macroscale representation of the entire skin tissue with a mesoscale model that focuses on the papillary dermis layer. Our results indicate that it takes hours for the drugs to disperse from the injection site to the papillary dermis before entering the initial lymphatics. Additionally, we observe an inhomogeneous drug distribution in the interstitial space of the papillary dermis, with higher drug concentrations near initial lymphatics and lower concentrations near blood capillaries. To validate our model, we compared our numerical simulation results with experimental data, finding a good alignment. Our parametric studies on the drug molecule properties and injection parameters suggest that a higher diffusion coefficient increases the transport and uptake rate while binding slows down these processes. Furthermore, shallower injection depths lead to faster lymphatic uptake, whereas the size of the injection plume has a minor effect on the uptake rate. These findings advance our understanding of drug transport and lymphatic absorption after subcutaneous injection, offering valuable insights for optimizing drug delivery strategies and the design of biotherapeutics.

  View details for DOI 10.1016/j.ijpharm.2024.124419

  View details for PubMedID 38972522

• Ultrasensitive and multiplexed tracking of single cells using whole-body PET/CT. Science advances Nguyen, H. T., Das, N., Ricks, M., Zhong, X., Takematsu, E., Wang, Y., Ruvalcaba, C., Mehadji, B., Roncali, E., Chan, C. K., Pratx, G. 2024; 10 (24): eadk5747

  Abstract

  In vivo molecular imaging tools are crucially important for elucidating how cells move through complex biological systems; however, achieving single-cell sensitivity over the entire body remains challenging. Here, we report a highly sensitive and multiplexed approach for tracking upward of 20 single cells simultaneously in the same subject using positron emission tomography (PET). The method relies on a statistical tracking algorithm (PEPT-EM) to achieve a sensitivity of 4 becquerel per cell and a streamlined workflow to reliably label single cells with over 50 becquerel per cell of 18F-fluorodeoxyglucose (FDG). To demonstrate the potential of the method, we tracked the fate of more than 70 melanoma cells after intracardiac injection and found they primarily arrested in the small capillaries of the pulmonary, musculoskeletal, and digestive organ systems. This study bolsters the evolving potential of PET in offering unmatched insights into the earliest phases of cell trafficking in physiological and pathological processes and in cell-based therapies.

  View details for DOI 10.1126/sciadv.adk5747

  View details for PubMedID 38875333

  View details for PubMedCentralID PMC11177933

• A compartment model for subcutaneous injection of monoclonal antibodies. International journal of pharmaceutics Zhong, X., Liu, Y., Ardekani, A. M. 2023: 123687

  Abstract

  Despite the growing popularity of subcutaneous (SC) administration for monoclonal antibodies (mAbs), there remains a limited understanding of the significance of mAb transport rate constants within the interstitial space and the lymphatic system on their pharmacokinetics. To bridge this knowledge gap, we introduce a compartmental model for subcutaneously administered mAbs. Our model differentiates FcRn-expressing cells across various sites, and the model predictions agree with experimental data from both human and rat studies. Our findings indicate that the time to reach the maximum mAb concentration in the plasma, denoted by Tmax, displays a weak positive correlation with mAb half-life and a negligible correlation with bioavailability. In contrast, the half-life of mAbs exhibits a strong positive correlation with bioavailability. Moreover, the rate of mAb transport from lymph to plasma significantly affects the mAb half-life. Increasing the transport rates of mAbs from the injection site to the lymph or from lymph to plasma enhances bioavailability. These insights, combined with our compartmental model, contribute to a deeper understanding of the pharmacokinetics of subcutaneously administered mAbs.

  View details for DOI 10.1016/j.ijpharm.2023.123687

  View details for PubMedID 38103705

• Numerical studies of the lymphatic uptake rate. Computers in biology and medicine Li, C., Zhong, X., Ardekani, A. M. 2023; 165: 107380

  Abstract

  Lymphatic uptake is essential for transporting nutrients, wastes, immune cells, and therapeutic proteins. Despite its importance, the literature lacks a quantitative analysis of the factors that affect lymphatic uptake, including interstitial pressure, downstream pressure, and tissue deformation. In this paper, we present a coupled model of a poroelastic tissue with initial lymphatics and quantify the impact of these factors on the rate of lymphatic uptake. Our results indicate that the lymphatic uptake increases with the amplitude of the oscillating downstream pressure when the amplitude exceeds a threshold. Additionally, the cross-sectional area of initial lymphatics increases with the volumetric strain of the tissue, while the interstitial pressure increases when the strain rate becomes negative. Therefore, the lymphatic uptake reaches its maximum when the tissue has positive volumetric strain while being compressed. We have also investigated the effect of intersection angles and positions of two initial lymphatics and concluded that they have minor impacts on lymphatic uptake. However, the lymphatic uptake per unit length of initial lymphatics decreases with their total length. These findings advance our understanding of lymphatic uptake and can guide the development of strategies to accelerate the transport of therapeutics.

  View details for DOI 10.1016/j.compbiomed.2023.107380

  View details for PubMedID 37634464

• Accurate solutions of a thin rectangular plate deflection under large uniform loading APPLIED MATHEMATICAL MODELLING Liu, L., Zhong, X., Liao, S. 2023; 123: 241-258

  View details for DOI 10.1016/j.apm.2023.06.037

  View details for Web of Science ID 001036893000001

• Hydrodynamic considerations for spring-driven autoinjector design INTERNATIONAL JOURNAL OF PHARMACEUTICS Zhong, X., Veilleux, J., Shi, G., Collins, D. S., Vlachos, P., Ardekani, A. M. 2023; 640: 122975

  Abstract

  In recent years, significant progress has been made in the studies of the spring-driven autoinjector, leading to an improved understanding of this device and its interactions with tissue and therapeutic proteins. The development of simulation tools that have been validated against experiments has also enhanced the prediction of the performance of spring-driven autoinjectors. This paper aims to address critical hydrodynamic considerations that impact the design of spring-driven autoinjectors, with a specific emphasis on sloshing and cavitation. Additionally, we present a framework that integrates simulation tools to predict the performance of spring-driven autoinjectors and optimize their design. This work is valuable to the pharmaceutic industry, as it provides crucial insights into the development of spring-driven autoinjectors and therapeutic proteins. This work can also enhance the efficacy and safety of the delivery of therapeutic proteins, ultimately improving patient outcomes.

  View details for DOI 10.1016/j.ijpharm.2023.122975

  View details for Web of Science ID 000998657900001

  View details for PubMedID 37116602

• Optimizing autoinjector devices using physics-based simulations and Gaussian processes JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Sree, V., Zhong, X., Bilionis, I., Ardekani, A., Tepole, A. 2023; 140: 105695

  Abstract

  Autoinjectors are becoming a primary drug delivery option to the subcutaneous space. These devices need to work robustly and autonomously to maximize drug bio-availability. However, current designs ignore the coupling between autoinjector dynamics and tissue biomechanics. Here we present a Bayesian framework for optimization of autoinjector devices that can account for the coupled autoinjector-tissue biomechanics and uncertainty in tissue mechanical behavior. The framework relies on replacing the high fidelity model of tissue insertion with a Gaussian process (GP). The GP model is accurate yet computationally affordable, enabling a thorough sensitivity analysis that identified tissue properties, which are not part of the autoinjector design space, as important variables for the injection process. Higher fracture toughness decreases the crack depth, while tissue shear modulus has the opposite effect. The sensitivity analysis also shows that drug viscosity and spring force, which are part of the design space, affect the location and timing of drug delivery. Low viscosity could lead to premature delivery, but can be prevented with smaller spring forces, while higher viscosity could prevent premature delivery while demanding larger spring forces and increasing the time of injection. Increasing the spring force guarantees penetration to the desired depth, but it can result in undesirably high accelerations. The Bayesian optimization framework tackles the challenge of designing devices with performance metrics coupled to uncertain tissue properties. This work is important for the design of other medical devices for which optimization in the presence of material behavior uncertainty is needed.

  View details for DOI 10.1016/j.jmbbm.2023.105695

  View details for Web of Science ID 000994378900001

  View details for PubMedID 36739826

• The role of liquid rheological properties on the injection process of a spring-driven autoinjector INTERNATIONAL JOURNAL OF PHARMACEUTICS Zhong, X., Mitra, H., Veilleux, J., Simmons, E., Shi, G., Ardekani, A. M. 2022; 628: 122296

  Abstract

  Accurate injection time prediction is essential in developing spring-driven autoinjector devices since the drug delivery is expected to finish within seconds to bring convenience, reduce the risk for early lift-off, and provide a consistent experience to users. The Carreau model captures the liquid's shear-dependent viscosity measured in our experiments. Thus, a quasi-steady model, which uses the Carreau model to describe the liquid's viscosity, is developed to predict the injection time of spring-driven autoinjectors. Analytical relations between the flow rate and the pressure drop in the needle are also obtained. The Carreau number in the spring-driven autoinjector is greater than one and smaller than a critical value; in this region, using the power-law model to describe the liquid viscosity accurately predicts the injection time, which agrees with the current literature findings. Additionally, a force threshold is identified for the friction force between the plunger and the syringe barrel, beyond which the injection time is infinite. Appreciation of this force threshold can help avoid device stalling and reduce the risk of underdosing. Moreover, the role of liquid's shear-thinning index on the injection time of spring-driven autoinjectors is quantified. Understanding the shear-thinning index allows formulators to experiment with excipients and pH to enhance confidence in drug/device combination product design and integration. Our experimental and theoretical results can help drug product and device developers with integrated product design and improve the patient experience.

  View details for DOI 10.1016/j.ijpharm.2022.122296

  View details for Web of Science ID 000882068800007

  View details for PubMedID 36280217

• A framework to optimize spring-driven autoinjectors INTERNATIONAL JOURNAL OF PHARMACEUTICS Zhong, X., Bilionis, I., Ardekani, A. M. 2022; 617: 121588

  Abstract

  The major challenges in the optimization of autoinjectors lie in developing an accurate model and meeting competing requirements. We have developed a computational model for spring-driven autoinjectors, which can accurately predict the kinematics of the syringe barrel, needle displacement (travel distance) at the start of drug delivery, and injection time. This paper focuses on proposing a framework to optimize the single-design of autoinjectors, which deliver multiple drugs with different viscosity. We replace the computational model for spring-driven autoinjectors with a surrogate model, i.e., a deep neural network, which improves computational efficiency 1,000 times. Using this surrogate, we perform Sobol sensitivity analysis to understand the effect of each model input on the quantities of interest. Additionally, we pose the design problem within a multi-objective optimization framework. We use our surrogate to discover the corresponding Pareto optimal designs via Pymoo, an open source library for multi-objective optimization. After these steps, we evaluate the robustness of these solutions and finally identify two promising candidates. This framework can be effectively used for device design optimization as the computation is not demanding, and decision-makers can easily incorporate their preferences into this framework.

  View details for DOI 10.1016/j.ijpharm.2022.121588

  View details for Web of Science ID 000819877200001

  View details for PubMedID 35218897

• A model for bubble dynamics in a protein solution JOURNAL OF FLUID MECHANICS Zhong, X., Ardekani, A. M. M. 2022; 935

  View details for DOI 10.1017/jfm.2022.20

  View details for Web of Science ID 000889262600001

• An experimentally validated dynamic model for spring-driven autoinjectors INTERNATIONAL JOURNAL OF PHARMACEUTICS Zhong, X., Guo, T., Vlachos, P., Veilleux, J., Shi, G., Collins, D. S., Ardekani, A. M. 2021; 594: 120008

  Abstract

  This study focuses on developing a predictive dynamic model for spring-driven autoinjectors. The values of unknown physical parameters, such as the heat convection coefficient and the friction force between the plunger and the syringe barrel, are obtained by fitting the experimentally measured displacements of the plunger and the syringe barrel. The predicted kinematics of the components, such as the displacement and velocity of the syringe barrel, agree well with the experiments with a l2-norm error smaller than 10%. The predictions of the needle displacement at the start of drug delivery agree with the experimental measurements with a l2-norm error of 20%. The maximum air gap pressure and temperature decrease with the initial air gap height but increase with the elasticity and viscosity of the plunger and the mechanical stop. The proposed experimentally validated dynamic model can be effectively used for device design optimization as it is not computationally demanding.

  View details for DOI 10.1016/j.ijpharm.2020.120008

  View details for Web of Science ID 000609878200002

  View details for PubMedID 33189808

• A model for a laser-induced cavitation bubble INTERNATIONAL JOURNAL OF MULTIPHASE FLOW Zhong, X., Eshraghi, J., Vlachos, P., Dabiri, S., Ardekani, A. M. 2020; 132

  View details for DOI 10.1016/j.ijmultiphaseflow.2020.103433

  View details for Web of Science ID 000601052700013

• Analytic solutions of the rise dynamics of liquid in a vertical cylindrical capillary EUROPEAN JOURNAL OF MECHANICS B-FLUIDS Zhong, X., Sun, B., Liao, S. 2019; 78: 1-10

  View details for DOI 10.1016/j.euromechflu.2019.05.011

  View details for Web of Science ID 000491300800001

• On the limiting Stokes wave of extreme height in arbitrary water depth JOURNAL OF FLUID MECHANICS Zhong, X., Liao, S. 2018; 843: 653-679

  View details for DOI 10.1017/jfm.2018.171

  View details for Web of Science ID 000428219100001

• Analytic approximations of Von Karman plate under arbitrary uniform pressure-equations in integral form SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY Zhong, X., Liao, S. 2018; 61 (1)

  View details for DOI 10.1007/s11433-017-9096-1

  View details for Web of Science ID 000419734600010

• On the homotopy analysis method for backward/forward-backward stochastic differential equations NUMERICAL ALGORITHMS Zhong, X., Liao, S. 2017; 76 (2): 487-519

  View details for DOI 10.1007/s11075-017-0268-2

  View details for Web of Science ID 000411622000011

• Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure - Equations in Differential Form STUDIES IN APPLIED MATHEMATICS Zhong, X. X., Liao, S. J. 2017; 138 (4): 371-400

  View details for DOI 10.1111/sapm.12158

  View details for Web of Science ID 000400335800001