International Journal for Numerical Methods in Biomedical Engineering最新文献

{"title":"Direct Numerical Simulations of Inhalation in a 23-Generation Lung Model","authors":"Marco Atzori,&nbsp;Emanuele Gallorini,&nbsp;Ciro Cottini,&nbsp;Andrea Benassi,&nbsp;Maurizio Quadrio","doi":"10.1002/cnm.70208","DOIUrl":"https://doi.org/10.1002/cnm.70208","url":null,"abstract":"<p>The air flows in the proximal and distal portions of the human lungs are interconnected: the lower Reynolds number in the deeper generations causes a progressive flow regularization, but mass conservation requires flow rate oscillations to propagate through the airway bifurcations. To explain how these competing effects shape the flow state in the deeper generations, we have performed the first high-fidelity numerical simulation of the air flow in a lung model that includes 23 successive bifurcations of a single planar airway. Turbulence modeling or assumptions on flow regimes are not required. The chosen flow rate is steady on average, and representative of the peak inspiratory flow reached by adult patients breathing through therapeutic inhalers. As expected, advection becomes progressively less important after each bifurcation, until a time-dependent Stokes regime governed solely by viscous diffusion is established in the smallest generations. However, fluctuations in this regime are relatively fast and large with respect to the mean flow, which is in contrast with the commonly agreed picture that only the breathing frequency is relevant at the scale of the alveoli. We demonstrate that the characteristic frequency and amplitude of these fluctuations are linked to the flow in the upper part of the bronchial tree, as they originate from the time-dependent flow splitting in the upper bifurcations. Even though these fluctuations are observed here in an idealized, rigid lung model, our findings suggest that the assumptions usually adopted in many of the current lung models might need to be revised.</p>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 8","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cnm.70208","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148784418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling Perforator Occlusion After Flow Diversion","authors":"Laurel Marsh,&nbsp;Fernando Mut,&nbsp;Esref Bayraktar,&nbsp;Daying Dai,&nbsp;Julien Ognard,&nbsp;Jonathan Cortese,&nbsp;David Kallmes,&nbsp;Ramanathan Kadirvel,&nbsp;Juan R. Cebral","doi":"10.1002/cnm.70207","DOIUrl":"https://doi.org/10.1002/cnm.70207","url":null,"abstract":"<p>Endoluminal flow diverters are increasingly used to treat cerebral aneurysms. Despite good aneurysm occlusion efficacy, delayed ischemic complications due to side branch or perforator occlusion remain a serious concern. However, the mechanisms leading to side branch occlusion are poorly understood. To investigate these mechanisms, a combination of animal and computational models was utilized. Flow diverters were deployed in four rabbit superior mesenteric artery (SMA) and studied with computational fluid dynamics (CFD) and a previously developed fibrin dynamics model. Subject-specific vascular models were reconstructed from 3D rotational angiography images and flow conditions were derived from Doppler ultrasound velocity measurements. Flow diverting devices were virtually deployed within the vascular models under guidance from angiography images. Coupled flow and fibrin production, transport, and adhesion simulations were carried out and the effects of fibrin accumulation at the origin of jailed side branches after flow diverter implantation were analyzed. The results of the computational models suggest significant fibrin accumulation across the struts of all flow diverting devices jailing side branches. Larger accumulation was observed at the more distal branches. However, minor flow alterations were produced which were not detectable in angiography sequences. These results were in agreement with experimental observations. On the other hand, fibrin accumulation alone did not explain complete side branch occlusions, which are likely the result of the interaction between initial fibrin accumulation and subsequent cell migration from the peripheral parent artery.</p>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 8","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cnm.70207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Closed-Loop Cardiovascular Model of the Supine-To-Stand Manoeuvre: Implications for Falls","authors":"Joeri A. van de Sande,&nbsp;Valeria Krzhizhanovskaya,&nbsp;Lex M. van Loon,&nbsp;Nathalie van der Velde,&nbsp;Eveline P. van Poelgeest,&nbsp;Marjolein Klop,&nbsp;Jurgen A. H. R. Claassen,&nbsp;Alfons G. Hoekstra","doi":"10.1002/cnm.70206","DOIUrl":"https://doi.org/10.1002/cnm.70206","url":null,"abstract":"<p>The risk of falling increases with age and orthostatic hypotension (OH) is a common cardiovascular contributor. Current OH diagnostics rely on intermittent blood pressure measurements, which may not adequately characterise haemodynamic responses during orthostatic stress. We developed a closed-loop cardiovascular lumped-parameter model and fitting pipeline for continuous beat-to-beat blood pressure and heart rate data during a supine-to-stand manoeuvre, enabling model-based evaluation of orthostatic haemodynamic responses in older adults. Our 23-compartment lumped model included baroreflex and cardiopulmonary reflex regulation and was calibrated using Finapres data from older adults (Nijmegen Radboud University PROHEALTH study). Using a stochastic ranking evolutionary strategy, we fitted 31 parameters to averaged cohort data, classifying participants as with or without a history of falls (≥ 1 fall in the previous year). The model reproduced systolic and diastolic blood pressure and heart rate responses at the population level, with normalised root mean squared errors of 10.6% and 9.6% for participants with and without a history of falls, respectively. Four model parameters differed significantly between the two population-average fits: baroreflex reference heart rate, a baroreflex transfer function parameter, transient external muscle pressure during standing, and total blood volume. These results demonstrate that a physiologically structured cardiovascular model can reproduce population-level orthostatic responses in older adults and highlight model-based parameter differences associated with fall history.</p>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 8","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cnm.70206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Biofidelic Simulations of the Ross Procedure: Arterial Growth and Remodeling in an Anatomical Context","authors":"Myléna Audenay,&nbsp;Thibault Vervenne,&nbsp;Lucas Van Hoof,&nbsp;Justina Ghebryal,&nbsp;Patrick Segers,&nbsp;Sandra Loerakker,&nbsp;Filip Rega,&nbsp;Nele Famaey","doi":"10.1002/cnm.70204","DOIUrl":"10.1002/cnm.70204","url":null,"abstract":"<div>\u0000 \u0000 <p>The Ross procedure represents a promising alternative to conventional valve replacement techniques in young patients with aortic valve disease. Unlike mechanical or bioprosthetic substitutes, the pulmonary autograft retains living properties allowing growth and remodeling to systemic blood pressures. However, in aortic position, the mechanobiological adaptation processes of the pulmonary tissue can be unpredictable. Long-term failure of the Ross procedure is frequently associated with autograft dilation, inducing valve leakage and possible reoperation. The present work develops an image-based finite element pipeline to predict autograft growth and remodeling and its impact on leaflet closure. Realistic geometries are reconstructed from preoperative sheep MRI scans using automated scripts. Meshed autografts are combined with experimentally determined material properties to simulate the evolution of the pulmonary root under pulsatile systemic pressure conditions. The time-varying autograft diameter is then coupled with leaflet simulations to compute the regurgitant orifice area over time, a quantitative indicator of valve competence. Results demonstrate the ability of the model to reproduce in vivo autograft dilation in sheep, capturing both geometrical and biomechanical aspects. The predicted evolution of leaflet coaptation provides new insights into valve dysfunction after the Ross procedure. This framework has the potential to support surgical decision-making and optimize long-term outcomes by tailoring operative strategies to patient-specific physiology.</p>\u0000 </div>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 8","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148690177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Comprehensive Numerical Simulation on the Safety and Efficacy of Circular-Versus Trapezoidal-Shaped Intravascular Drug-Eluting Stents","authors":"Ramprosad Saha,&nbsp;Akash Pradip Mandal","doi":"10.1002/cnm.70205","DOIUrl":"10.1002/cnm.70205","url":null,"abstract":"<div>\u0000 \u0000 <p>In modern days, drug-eluting stent (DES) acts as a kingpin for the treatment of coronary artery disease (CAD) and it has a dramatic reduction rate of in-stent restenosis (ISR) in compare to a bare metal stent (BMS). To replicate the drug release from therapeutic devices and its corresponding transportation in the physiological atmosphere, mathematical and computational simulations have become an effective technique. The present article is developed by a thorough comparative analysis of drug transport mechanisms between half-embedded trapezoidal-shaped and circular-shaped struts and also its optimality in stent-based drug delivery. The geometry of the implanted struts (trapezoidal-shaped and circular-shaped) is modeled in a two-dimensional axi-symmetric environment and the target lesion is considered as a single homogeneous layer with identical diffusivity. Due to the hydrostatic pressure of blood, plasma filtration is allowed through the blood-tissue interface along the transmural direction and the flow of interstitial fluid within the porous arterial wall is governed by the unsteady Navier–Stokes equation and the equation of continuity. While the drug is distributed within the arterial wall, tissue receptors grip the drug molecules, so the present study includes the binding of drug along with free drug. An unsteady convection-diffusion–reaction process demonstrates the transportation of free drug, but only reaction process manifests the transportation of bound drug. The mathematical equations of interstitial fluid flow and the transportation of drug along with pertinent initial and boundary conditions are penciled by using a two-dimensional (2D) cylindrical polar coordinate system. A staggered grid generation technique is also leveraged to discretize all the governing equations and boundary conditions, which are then successfully solved numerically by using Marker-and-Cell (MAC) method. The coefficient of variance (CV), a statistical parameter, is introduced in this present drug delivery system to access the consistency of the drug distribution. The study incorporates several necessary factors, such as drug efficacy, tissue drug content, and therapeutic effectiveness to optimize the choice of strut shape and the overall performance of the stent. To achieve the best possible outcomes, a robust sensitivity analysis of several perturbed parameters is carried out by implementing one-way ANOVA. The results highlight that, for long-term safety and efficacy, trapezoidal-shaped struts may be a good choice in compared to circular ones. Furthermore, the tailored combination of strut shape and drug delivery strategy presented herein offers a significant advancement in designing the next-generation DES.</p>\u0000 </div>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 8","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148674585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of Design-Phase Digital Twin for Structural Optimization of a Biomedical Device","authors":"Tanguy René Pinol,&nbsp;Leon Hugh Prentice,&nbsp;Kate Fox,&nbsp;Toh Yen Pang","doi":"10.1002/cnm.70203","DOIUrl":"10.1002/cnm.70203","url":null,"abstract":"<p>Digital twins have transformed design and verification workflows in engineering, yet their adoption within medical device development remains limited. Conventional build-and-test approaches restrict design space exploration and often delay identification of mechanically critical risks. This paper presents a case study on the development of a calibrated, design-phase behavioral digital twin for a capsule-based biomedical delivery system used in dentistry, with the annular snap-fit nozzle-to-body interface selected as a representative mechanically sensitive feature. Empirical testing, analytical snap-fit theory and nonlinear Finite Element Analysis (FEA) were integrated to characterize mating force, strain and structural safety during assembly. Strong pre-calibration agreement was observed between the analytical and numerical models and back-calculation of an effective polymer-to-polymer coefficient of friction (<i>μ</i> = 0.12) reduced prediction error relative to empirical measurements to within experimental repeatability, establishing a validated behavioral digital twin. Design optimization employed a Taguchi orthogonal array to efficiently explore strain-constrained geometric variation. Results identified undercut depth, governed by nozzle inner diameter, as the dominant contributor to retention strength. An optimized configuration achieved a 65%–75% increase in mating force relative to the baseline design while remaining within permissible strain limits. Numerical verification predicted peak mating force of 190 N and identified localized stress concentrations in the nozzle neck region, highlighting reinforcement requirements before production tooling. Physical verification and validation of the optimized system confirmed the predicted increase in structural performance. Consistent with the digital twin maturity continuum, the framework is positioned as a design-phase, behavioral digital twin. It operates with offline one-way physical-to-digital data flow during the product realization stage, with automated bidirectional synchronization identified as the next stage of development. These findings demonstrate how digital twins can shift biomedical device development from reactive validation towards predictive, manufacturability-aware design, strengthening patient safety, clinician confidence and regulatory assurance in Class II medical devices.</p>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 8","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13433137/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148671157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fracture Patterns of an Osteolytic Hole Involved Lumbar Vertebra, Assessed for a Case Study by Computational Models","authors":"A. R. Nazari","doi":"10.1002/cnm.70202","DOIUrl":"10.1002/cnm.70202","url":null,"abstract":"<div>\u0000 \u0000 <p>Osteolytic vertebrae containing central lesions are associated with a high risk of burst fracture, as the presence of such lesions indicates substantial bone destruction. The present study aimed to investigate fracture patterns in a clinically relevant case of a lumbar vertebra with an osteolytic cavity under various loading conditions using a computational modeling approach. Osteolytic damage progression was simulated through a virtual thermal flux approach, while stiffness degradation was represented using a continuum damage mechanics framework. Potential crack locations within the vertebra were defined based on an established clinical classification, and crack propagation was evaluated using the Virtual Crack Closure Technique (VCCT). The results demonstrated that the mechanical competence and fracture patterns of the osteolytic vertebra were strongly dependent on the intensity of osteolytic damage and the applied loading conditions. The earliest onset of instability occurred under lateral bending loading when the average osteolytic damage reached approximately 50%. Under kyphotic loading, vertical cracks propagated around the osteolytic cavity and could significantly compromise vertebral stability when combined with compressive and bending loads associated with daily activities. Such loading conditions may promote the connection of horizontal endplate cracks with vertical cracks, resulting in a burst fracture pattern. Therefore, vertebrae containing osteolytic cavities should be carefully protected against lateral bending loads during the treatment period, and exposure to heavy loading postures should be strictly avoided. Future studies should investigate the sensitivity of vertebral load-carrying capacity to variations in the size, shape, and location of osteolytic lesions.</p>\u0000 </div>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 8","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Mathematical Model for Chemo-Mechanically Induced Collective Cell Motility on Planar Elastic Substrates","authors":"Riham K. Ahmed,&nbsp;Tamer Abdalrahman,&nbsp;Neil H. Davies,&nbsp;Fred Vermolen,&nbsp;Thomas Franz","doi":"10.1002/cnm.70201","DOIUrl":"https://doi.org/10.1002/cnm.70201","url":null,"abstract":"<p>Cells interact with mechanical and chemical environmental cues, such as mechanical cues from other cells and chemical signals from growth factors. The current study aims to develop a mathematical model for combined chemically and mechanically induced collective cell motility on planar substrates. The mechanically induced cell motility is simulated using strain energy density gradients generated in an elastic substrate by cellular traction forces. For chemotaxis, Green's function and Duhamel's principle are used to solve the diffusion equation that describes the distribution of a growth factor and to represent chemo-mechanically induced deterministic collective cell motility on planar elastic substrates. Chemically induced motility of cells towards a growth factor source is predicted for different growth factor production and diffusion rates. Chemo-mechanical cues with varying growth factor production and diffusion rates are explored for the motility of four cells and one motile cell in the presence of one stationary cell. The developed model describes the chemo-mechanically induced motility of individual cells on planar substrates. The model provides valuable information for in vivo or in vitro studies due to its suitability for extension to other chemical source shapes, mobilised sources, many sources, and soluble concentration gradients.</p>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 8","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cnm.70201","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148617354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hemodynamic Metrics and Arterial Dysfunction: Insights From a Novel Microfluidic Device","authors":"Yash Doshi,&nbsp;Jaywant Arakeri,&nbsp;Namrata Gundiah","doi":"10.1002/cnm.70196","DOIUrl":"10.1002/cnm.70196","url":null,"abstract":"<div>\u0000 \u0000 <p>Hemodynamic metrics provide critical insights into the interplay between flow physics and endothelial cell (EC) function in arterial pathologies. Among these, wall shear stress (WSS) is a central regulator of EC function and a key determinant of vascular disease progression. In this study, we review 35 hemodynamic metrics and assess their association with hypertension and atherosclerosis, aneurysms, and thrombosis. Metrics are categorized by magnitude, direction, energy, stagnation time and flow rate to identify those most relevant to specific pathological conditions. We simulate disturbed flow in a novel microfluidic endothelium-on-chip platform using computational fluid dynamics (CFD) and analyze 16 key hemodynamic metrics. The most comprehensive description of the complex flow environments is provided by shear rosettes, polar plots of WSS magnitude and direction over the cardiac cycle. The anisotropy ratio (AR) metric, derived from the shear rosette, offers a robust characterization of the multidirectional secondary flow but cannot distinguish steady from unidirectional oscillatory flows. The R-Ratio and minimized transverse WSS (TransWSSmin) metrics effectively quantify bidirectional WSS when computed along principal flow directions. In contrast, transWSS and directional OSI (DOSI) are limited in their ability to quantify bidirectional WSS in regions of low mean WSS or stagnation. A unified metric integrating WSS magnitude and flow bidirectionality is currently lacking. Combining AR with magnitude-sensitive metrics, such as TAWSS, TransWSS_min, or |TAWSS_SC|, may address these limitations. Together, CFD and microfluidic platforms provide a powerful framework to assess EC responses to disturbed flows and advance understanding of vascular disease progression.</p>\u0000 </div>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 7","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148450477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Analysis of Postoperative Rehabilitation of Femoral Neck Fracture: Coupling of Vascular Growth, Bone Remodeling, and the Effect of Electrical Stimulation","authors":"Qian Wang,&nbsp;Chuanyong Qu","doi":"10.1002/cnm.70199","DOIUrl":"10.1002/cnm.70199","url":null,"abstract":"<div>\u0000 \u0000 <p>Cannulated screws are often used for internal fixation after a femoral neck fracture to ensure the smooth rehabilitation of patients. Patients frequently have various complications, such as avascular necrosis, during the recovery period. Reasonable rehabilitation training after surgery is necessary for patient rehabilitation. Multiple studies have proved a relationship between bone growth repair and blood vessel growth, and the blood supply system provides various oxygen and nutrients for bone remodeling to promote the smooth progress of bone remodeling. As a new therapeutic method, electrical stimulation has been widely used in osteoporosis, bone nonunion, and other diseases, and has achieved good therapeutic effects. Therefore, the internal fixation model of femoral neck fracture was established in this paper, and the influence of load training on postoperative rehabilitation was discussed. At the same time, the blood supply system was coupled with bone remodeling analysis, and electrical stimulation was added to investigate the change in bone density. The simulation results demonstrate a novel method for simulating bone remodeling during postoperative rehabilitation that incorporates electrical stimulation. In this method, mechanical loading promotes an increase in bone density; the addition of angiogenic factors leads to a diminished increase in bone density, whereas the inclusion of electrical stimulation results in an enhanced increase in bone density.</p>\u0000 </div>","PeriodicalId":50349,"journal":{"name":"International Journal for Numerical Methods in Biomedical Engineering","volume":"42 7","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148450452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}