Cardiovascular models for personalised medicine: Where now and where next?

Age and sex-dependent sensitivity analysis of a common carotid artery model

The common carotid artery (CCA) is an accessible and informative site for assessing cardiovascular function which makes it a prime candidate for clinically relevant computational modelling. The interpretation of supplemental information possible through modelling is encumbered by measurement uncertainty and population variability in model parameters. The distribution of model parameters likely depends on the specific sub-population of interest and delineation based on sex, age or health status may correspond to distinct ranges of typical parameter values. To assess this impact in a 1D-CCA-model, we delineated specific sub-populations based on age, sex and health status and carried out uncertainty quantification and sensitivity analysis for each sub-population. We performed a structured literature review to characterize sub-population-specific variabilities for eight model parameters without consideration of health status; variations for a healthy sub-populations were based on previously established references values. The variabilities of diameter and distensibility found in the literature review differed from those previously established in a healthy population. Model diameter change and pulse pressure were most sensitive to variations in distensibility, while pressure was most sensitive to resistance in the Windkessel model for all groups. Uncertainties were lower when variabilities were based on a healthy sub-population; however, the qualitative distribution of sensitivity indices was largely similar between the healthy and general population. Average sensitivity of the pressure waveform showed a moderate dependence on age with decreasing sensitivity to distal resistance and increasing sensitivity to distensibility and diameter. The female population was less sensitive to variations in diameter but more sensitive to distensibility coefficient than the male population. Overall, as hypothesized input variabilities differed between sub-populations and resulted in distinct uncertainties and sensitivities of the 1D-CCA-model outputs, particularly over age for the pressure waveform and between males and females for pulse pressure.

Evaluation of models of sequestration flow in coronary arteries-Physiology versus anatomy?

BACKGROUND

Myocardial ischaemia results from insufficient coronary blood flow. Computed virtual fractional flow reserve (vFFR) allows quantification of proportional flow loss without the need for invasive pressure-wire testing. In the current study, we describe a novel, conductivity model of side branch flow, referred to as 'leak'. This leak model is a function of taper and local pressure, the latter of which may change radically when focal disease is present. This builds upon previous techniques, which either ignore side branch flow, or rely purely on anatomical factors. This study aimed to describe a new, conductivity model of side branch flow and compare this with established anatomical models.

METHODS AND RESULTS

The novel technique was used to quantify vFFR, distal absolute flow (Qd) and microvascular resistance (CMVR) in 325 idealised 1D models of coronary arteries, modelled from invasive clinical data. Outputs were compared to an established anatomical model of flow. The conductivity model correlated and agreed with the reference model for vFFR (r = 0.895, p < 0.0001; ＋0.02, 95% CI 0.00 to ＋ 0.22), Qd (r = 0.959, p < 0.0001; -5.2 mL/min, 95% CI -52.2 to ＋13.0) and CMVR (r = 0.624, p < 0.0001; ＋50 Woods Units, 95% CI -325 to ＋2549).

CONCLUSION

Agreement between the two techniques was closest for vFFR, with greater proportional differences seen for Qd and CMVR. The conductivity function assumes vessel taper was optimised for the healthy state and that CMVR was not affected by local disease. The latter may be addressed with further refinement of the technique or inferred from complementary image data. The conductivity technique may represent a refinement of current techniques for modelling coronary side-branch flow. Further work is needed to validate the technique against invasive clinical data.

Efficient sensitivity analysis for biomechanical models with correlated inputs

In most variance-based sensitivity analysis (SA) approaches applied to biomechanical models, statistical independence of the model input is assumed. However, often the model inputs are correlated. This might alter the interpretation of the SA results, which may severely impact the guidance provided during model development and personalization. Potential reasons for the infrequent usage of SA techniques that account for input correlation are the associated high computational costs, especially for models with many parameters, and the fact that the input correlation structure is often unknown. The aim of this study was to propose an efficient correlated global sensitivity analysis method by applying a surrogate model-based approach. Furthermore, this article demonstrates how correlated SA should be interpreted and how the applied method can guide the modeler during model development and personalization, even when the correlation structure is not entirely known beforehand. The proposed methodology was applied to a typical example of a pulse wave propagation model and resulted in accurate SA results that could be obtained at a theoretically 27,000× lower computational cost compared to the correlated SA approach without employing a surrogate model. Furthermore, our results demonstrate that input correlations can significantly affect SA results, which emphasizes the need to thoroughly investigate the effect of input correlations during model development. We conclude that our proposed surrogate-based SA approach allows modelers to efficiently perform correlated SA to complex biomechanical models and allows modelers to focus on input prioritization, input fixing and model reduction, or assessing the dependency structure between parameters.

Harnessing the power of synthetic data in healthcare: innovation, application, and privacy

Data-driven decision-making in modern healthcare underpins innovation and predictive analytics in public health and clinical research. Synthetic data has shown promise in finance and economics to improve risk assessment, portfolio optimization, and algorithmic trading. However, higher stakes, potential liabilities, and healthcare practitioner distrust make clinical use of synthetic data difficult. This paper explores the potential benefits and limitations of synthetic data in the healthcare analytics context. We begin with real-world healthcare applications of synthetic data that informs government policy, enhance data privacy, and augment datasets for predictive analytics. We then preview future applications of synthetic data in the emergent field of digital twin technology. We explore the issues of data quality and data bias in synthetic data, which can limit applicability across different applications in the clinical context, and privacy concerns stemming from data misuse and risk of re-identification. Finally, we evaluate the role of regulatory agencies in promoting transparency and accountability and propose strategies for risk mitigation such as Differential Privacy (DP) and a dataset chain of custody to maintain data integrity, traceability, and accountability. Synthetic data can improve healthcare, but measures to protect patient well-being and maintain ethical standards are key to promote responsible use.

Toward precision medicine using a "digital twin" approach: modeling the onset of disease-specific brain atrophy in individuals with multiple sclerosis

Digital Twin (DT) is a novel concept that may bring a paradigm shift for precision medicine. In this study we demonstrate a DT application for estimating the age of onset of disease-specific brain atrophy in individuals with multiple sclerosis (MS) using brain MRI. We first augmented longitudinal data from a well-fitted spline model derived from a large cross-sectional normal aging data. Then we compared different mixed spline models through both simulated and real-life data and identified the mixed spline model with the best fit. Using the appropriate covariate structure selected from 52 different candidate structures, we augmented the thalamic atrophy trajectory over the lifespan for each individual MS patient and a corresponding hypothetical twin with normal aging. Theoretically, the age at which the brain atrophy trajectory of an MS patient deviates from the trajectory of their hypothetical healthy twin can be considered as the onset of progressive brain tissue loss. With a tenfold cross validation procedure through 1000 bootstrapping samples, we found the onset age of progressive brain tissue loss was, on average, 5-6 years prior to clinical symptom onset. Our novel approach also discovered two clear patterns of patient clusters: earlier onset versus simultaneous onset of brain atrophy.

Literature review of digital twin in healthcare

This article aims to make a bibliometric literature review using systematic scientific mapping and content analysis of digital twins in healthcare to know the evolution, domain, keywords, content type, and kind and purpose of digital twin's implementation in healthcare, so a consolidation and future improvement of existing knowledge can be made and gaps for new studies can be identified. The increase in publications of digital twins in healthcare is quite recent and it is still concentrated in the domain of technology sources. The subject is majorly concentrated in patient's digital twin group and in precision medicine and aspects, issues and/or policies subgroups, although the publications keywords mirror it only at the group side. Digital twins in healthcare are probably stepping out of the infancy phase. On the other hand, digital twins in hospital group and the device and facilities management subgroups are more mature with all knowledge gathered from the manufacturing sector. There is an absence of some publication's types in general, device and care subgroup and no whole body or hospital digital twin was reported. Based on the presented arguments, guidelines for future research were presented: advance in the creation of general frameworks, in subgroups not as much explored, and in groups and subgroups already explored, but that need more advancement to achieve the main goals of a whole human or hospital digital twin with the main issues resolved.

Three-dimensional printing in modelling mitral valve interventions

Mitral interventions remain technically challenging owing to the anatomical complexity and heterogeneity of mitral pathologies. As such, multi-disciplinary pre-procedural planning assisted by advanced cardiac imaging is pivotal to successful outcomes. Modern imaging techniques offer accurate 3D renderings of cardiac anatomy; however, users are required to derive a spatial understanding of complex mitral pathologies from a 2D projection thus generating an 'imaging gap' which limits procedural planning. Physical mitral modelling using 3D printing has the potential to bridge this gap and is increasingly being employed in conjunction with other transformative technologies to assess feasibility of intervention, direct prosthesis choice and avoid complications. Such platforms have also shown value in training and patient education. Despite important limitations, the pace of innovation and synergistic integration with other technologies is likely to ensure that 3D printing assumes a central role in the journey towards delivering personalised care for patients undergoing mitral valve interventions.

Rapid virtual fractional flow reserve using 3D computational fluid dynamics

Aims

Over the last ten years, virtual Fractional Flow Reserve (vFFR) has improved the utility of Fractional Flow Reserve (FFR), a globally recommended assessment to guide coronary interventions. Although the speed of vFFR computation has accelerated, techniques utilising full 3D computational fluid dynamics (CFD) solutions rather than simplified analytical solutions still require significant time to compute.

Methods and results

This study investigated the speed, accuracy and cost of a novel 3D-CFD software method based upon a graphic processing unit (GPU) computation, compared with the existing fastest central processing unit (CPU)-based 3D-CFD technique, on 40 angiographic cases. The novel GPU simulation was significantly faster than the CPU method (median 31.7 s (Interquartile Range (IQR) 24.0-44.4s) vs. 607.5 s (490-964 s), P < 0.0001). The novel GPU technique was 99.6% (IQR 99.3-99.9) accurate relative to the CPU method. The initial cost of the GPU hardware was greater than the CPU (£4080 vs. £2876), but the median energy consumption per case was significantly less using the GPU method (8.44 (6.80-13.39) Wh vs. 2.60 (2.16-3.12) Wh, P < 0.0001).

Conclusion

This study demonstrates that vFFR can be computed using 3D-CFD with up to 28-fold acceleration than previous techniques with no clinically significant sacrifice in accuracy.

Sex matters: the frequently overlooked importance of considering sex in computational models

Personalised medicine and the development of a virtual human or a digital twin comprises visions of the future of medicine. To realise these innovations, an understanding of the biology and physiology of all people are required if we wish to apply these technologies at a population level. Sex differences in health and biology is one aspect that has frequently been overlooked, with young white males being seen as the "average" human being. This has not been helped by the lack of inclusion of female cells and animals in biomedical research and preclinical studies or the historic exclusion, and still low in proportion, of women in clinical trials. However, there are many known differences in health between the sexes across all scales of biology which can manifest in differences in susceptibility to diseases, symptoms in a given disease, and outcomes to a given treatment. Neglecting these important differences in the development of any health technologies could lead to adverse outcomes for both males and females. Here we highlight just some of the sex differences in the cardio-respiratory systems with the goal of raising awareness that these differences exist. We discuss modelling studies that have considered sex differences and touch on how and when to create sex-specific models. Scientific studies should ensure sex differences are included right from the study planning phase and results reported using sex as a biological variable. Computational models must have sex-specific versions to ensure a movement towards personalised medicine is realised.

Using the Non-Adoption, Abandonment, Scale-Up, Spread, and Sustainability (NASSS) Framework to Identify Barriers and Facilitators for the Implementation of Digital Twins in Cardiovascular Medicine

A digital twin is a computer-based "virtual" representation of a complex system, updated using data from the "real" twin. Digital twins are established in product manufacturing, aviation, and infrastructure and are attracting significant attention in medicine. In medicine, digital twins hold great promise to improve prevention of cardiovascular diseases and enable personalised health care through a range of Internet of Things (IoT) devices which collect patient data in real-time. However, the promise of such new technology is often met with many technical, scientific, social, and ethical challenges that need to be overcome-if these challenges are not met, the technology is therefore less likely on balance to be adopted by stakeholders. The purpose of this work is to identify the facilitators and barriers to the implementation of digital twins in cardiovascular medicine. Using, the Non-adoption, Abandonment, Scale-up, Spread, and Sustainability (NASSS) framework, we conducted a document analysis of policy reports, industry websites, online magazines, and academic publications on digital twins in cardiovascular medicine, identifying potential facilitators and barriers to adoption. Our results show key facilitating factors for implementation: preventing cardiovascular disease, in silico simulation and experimentation, and personalised care. Key barriers to implementation included: establishing real-time data exchange, perceived specialist skills required, high demand for patient data, and ethical risks related to privacy and surveillance. Furthermore, the lack of empirical research on the attributes of digital twins by different research groups, the characteristics and behaviour of adopters, and the nature and extent of social, regulatory, economic, and political contexts in the planning and development process of these technologies is perceived as a major hindering factor to future implementation.

Wearable technology and the cardiovascular system: the future of patient assessment

The past decade has seen a dramatic rise in consumer technologies able to monitor a variety of cardiovascular parameters. Such devices initially recorded markers of exercise, but now include physiological and health-care focused measurements. The public are keen to adopt these devices in the belief that they are useful to identify and monitor cardiovascular disease. Clinicians are therefore often presented with health app data accompanied by a diverse range of concerns and queries. Herein, we assess whether these devices are accurate, their outputs validated, and whether they are suitable for professionals to make management decisions. We review underpinning methods and technologies and explore the evidence supporting the use of these devices as diagnostic and monitoring tools in hypertension, arrhythmia, heart failure, coronary artery disease, pulmonary hypertension, and valvular heart disease. Used correctly, they might improve health care and support research.

Toward Precision Medicine Using a "Digital Twin" Approach: Modeling the Onset of Disease-Specific Brain Atrophy in Individuals with Multiple Sclerosis

Digital Twin (DT) is a novel concept that may bring a paradigm shift for precision medicine. In this study we demonstrate a DT application for estimating the age of onset of disease-specific brain atrophy in individuals with multiple sclerosis (MS) using brain MRI. We first augmented longitudinal data from a well-fitted spline model derived from a large cross-sectional normal aging data. Then we compared different mixed spline models through both simulated and real-life data and identified the mixed spline model with the best fit. Using the appropriate covariate structure selected from 52 different candidate structures, we augmented the thalamic atrophy trajectory over the lifespan for each individual MS patient and a corresponding hypothetical twin with normal aging. Theoretically, the age at which the brain atrophy trajectory of an MS patient deviates from the trajectory of their hypothetical healthy twin can be considered as the onset of progressive brain tissue loss. With a 10-fold cross validation procedure through 1000 bootstrapping samples, we found the onset age of progressive brain tissue loss was, on average, 5-6 years prior to clinical symptom onset. Our novel approach also discovered two clear patterns of patient clusters: earlier onset vs. simultaneous onset of brain atrophy.

Monitoring variability in parameter estimates for lumped parameter models of the systemic circulation using longitudinal hemodynamic measurements

BACKGROUND

Physics-based cardiovascular models are only recently being considered for disease diagnosis or prognosis in clinical settings. These models depend on parameters representing the physical and physiological properties of the modeled system. Personalizing these parameters may give insight into the specific state of the individual and etiology of disease. We applied a relatively fast model optimization scheme based on common local optimization methods to two model formulations of the left ventricle and systemic circulation. One closed-loop model and one open-loop model were applied. Intermittently collected hemodynamic data from an exercise motivation study were used to personalize these models for data from 25 participants. The hemodynamic data were collected for each participant at the start, middle and end of the trial. We constructed two data sets for the participants, both consisting of systolic and diastolic brachial pressure, stroke volume, and left-ventricular outflow tract velocity traces paired with either the finger arterial pressure waveform or the carotid pressure waveform.

RESULTS

We examined the feasibility of separating parameter estimates for the individual from population estimates by assessing the variability of estimates using the interquartile range. We found that the estimated parameter values were similar for the two model formulations, but that the systemic arterial compliance was significantly different ([Formula: see text]) depending on choice of pressure waveform. The estimates of systemic arterial compliance were on average higher when using the finger artery pressure waveform as compared to the carotid waveform.

CONCLUSIONS

We found that for the majority of participants, the variability of parameter estimates for a given participant on any measurement day was lower than the variability both across all measurement days combined for one participant, and for the population. This indicates that it is possible to identify individuals from the population, and that we can distinguish different measurement days for the individual participant by parameter values using the presented optimization method.

Evaluation of Different Cannulation Strategies for Aortic Arch Surgery Using a Cardiovascular Numerical Simulator

Aortic disease has a significant impact on quality of life. The involvement of the aortic arch requires the preservation of blood supply to the brain during surgery. Deep hypothermic circulatory arrest is an established technique for this purpose, although neurological injury remains high. Additional techniques have been used to reduce risk, although controversy still remains. A three-way cannulation approach, including both carotid arteries and the femoral artery or the ascending aorta, has been used successfully for aortic arch replacement and redo procedures. We developed circuits of the circulation to simulate blood flow during this type of cannulation set up. The CARDIOSIM© cardiovascular simulation platform was used to analyse the effect on haemodynamic and energetic parameters and the benefit derived in terms of organ perfusion pressure and flow. Our simulation approach based on lumped-parameter modelling, pressure-volume analysis and modified time-varying elastance provides a theoretical background to a three-way cannulation strategy for aortic arch surgery with correlation to the observed clinical practice.

Region-dependent mechanical characterization of porcine thoracic aorta with a one-to-many correspondence method to create virtual datasets using uniaxial tensile tests

The simulation of the cardiovascular system and in silico clinical trials have garnered attention in the biomedical engineering field. Physics-based modeling is essential to associate with physical and clinical features. In physics-based constitutive modeling, the identification of the parameters and estimation of their ranges based on appropriate experiments are required. Uniaxial tests are commonly used in the field of vascular mechanics, but they have limitations in fully characterizing the regional mechanical behavior of the aorta. Therefore, this study is aimed at identifying a method to integrate constitutive models with experimental data to elucidate regional aortic behavior. To create a virtual two-dimensional dataset, a pair of uniaxial experimental datasets in the longitudinal and circumferential directions was combined using a one-to-many correspondence method such as bootstrap aggregation. The proposed approach is subsequently applied to three constitutive models, i.e., the Fung model, Holzapfel model, and constrained mixture model, to estimate the material parameters based on the four test regions of the porcine thoracic aorta. Finally, the regional difference in the mechanical behavior of the aorta, the correlation between the experimental characteristics and model parameters, and the inter-correlation of the material parameters are confirmed. This integrative approach will enhance the prediction capability of the model with respect to the regions of the aorta.

The health digital twin to tackle cardiovascular disease-a review of an emerging interdisciplinary field

Potential benefits of precision medicine in cardiovascular disease (CVD) include more accurate phenotyping of individual patients with the same condition or presentation, using multiple clinical, imaging, molecular and other variables to guide diagnosis and treatment. An approach to realising this potential is the digital twin concept, whereby a virtual representation of a patient is constructed and receives real-time updates of a range of data variables in order to predict disease and optimise treatment selection for the real-life patient. We explored the term digital twin, its defining concepts, the challenges as an emerging field, and potentially important applications in CVD. A mapping review was undertaken using a systematic search of peer-reviewed literature. Industry-based participants and patent applications were identified through web-based sources. Searches of Compendex, EMBASE, Medline, ProQuest and Scopus databases yielded 88 papers related to cardiovascular conditions (28%, n = 25), non-cardiovascular conditions (41%, n = 36), and general aspects of the health digital twin (31%, n = 27). Fifteen companies with a commercial interest in health digital twin or simulation modelling had products focused on CVD. The patent search identified 18 applications from 11 applicants, of which 73% were companies and 27% were universities. Three applicants had cardiac-related inventions. For CVD, digital twin research within industry and academia is recent, interdisciplinary, and established globally. Overall, the applications were numerical simulation models, although precursor models exist for the real-time cyber-physical system characteristic of a true digital twin. Implementation challenges include ethical constraints and clinical barriers to the adoption of decision tools derived from artificial intelligence systems.

Characterization of the Microflow Through 3D Synthetic Niche Microenvironments Hosted in a Millifluidic Bioreactor

Background: Development of new medicines is a lengthy process with high risk of failure since drug efficacy measured in vitro is difficult to confirm in vivo. Intended to add a new tool aiding drug discovery, the MOAB-NICHOID device was developed: a miniaturized optically accessible bioreactor (MOAB) housing the 3D engineered scaffold NICHOID. The aim of our study was to characterize the microflow through the 3D nichoid microenvironment hosted in the MOAB-NICHOID device.

Methods: We used computational fluid dynamics (CFD) simulations to compute the flow field inside a very fine grid resembling the scaffold microenvironment.

Results: The microflow inside the multi-array of nichoid blocks is fed and locally influenced by the mainstream flow developed in the perfusion chamber of the device. Here we have revealed a low velocity, complex flow field with secondary, backward, or local recirculation micro-flows induced by the intricate architecture of the nichoid scaffold.

Conclusion: Knowledge of the microenvironment inside the 3D nichoids allows planning of cell experiments, to regulate the transport of cells towards the scaffold substrate during seeding or the spatial delivery of nutrients and oxygen which affects cell growth and viability.

PROTEA, A Southern African Multicenter Congenital Heart Disease Registry and Biorepository: Rationale, Design, and Initial Results

Objectives: The PartneRships in cOngeniTal hEart disease (PROTEA) project aims to establish a densely phenotyped and genotyped Congenital Heart Disease (CHD) cohort for southern Africa. This will facilitate research into the epidemiology and genetic determinants of CHD in the region. This paper introduces the PROTEA project, characterizes its initial cohort, from the Western Cape Province of South Africa, and compares the proportion or "cohort-prevalences" of CHD-subtypes with international findings. Methods: PROTEA is a prospective multicenter CHD registry and biorepository. The initial cohort was recruited from seven hospitals in the Western Cape Province of South Africa from 1 April 2017 to 31 March 2019. All patients with structural CHD were eligible for inclusion. Descriptive data for the preliminary cohort are presented. In addition, cohort-prevalences (i.e., the proportion of patients within the cohort with a specific CHD-subtype) of 26 CHD-subtypes in PROTEA's pediatric cohort were compared with the cohort-prevalences of CHD-subtypes in two global birth-prevalence studies. Results: The study enrolled 1,473 participants over 2 years, median age was 1.9 (IQR 0.4-7.1) years. Predominant subtypes included ventricular septal defect (VSD) (339, 20%), atrial septal defect (ASD) (174, 11%), patent ductus arteriosus (185, 11%), atrioventricular septal defect (AVSD) (124, 7%), and tetralogy of Fallot (121, 7%). VSDs were 1.8 (95% CI, 1.6-2.0) times and ASDs 1.4 (95% CI, 1.2-1.6) times more common in global prevalence estimates than in PROTEA's pediatric cohort. AVSDs were 2.1 (95% CI, 1.7-2.5) times more common in PROTEA and pulmonary stenosis and double outlet right ventricle were also significantly more common compared to global estimates. Median maternal age at delivery was 28 (IQR 23-34) years. Eighty-two percent (347/425) of mothers used no pre-conception supplementation and 42% (105/250) used no first trimester supplements. Conclusions: The cohort-prevalence of certain mild CHD subtypes is lower than for international estimates and the cohort-prevalence of certain severe subtypes is higher. PROTEA is not a prevalence study, and these inconsistencies are unlikely the result of true differences in prevalence. However, these findings may indicate under-diagnosis of mild to moderate CHD and differences in CHD management and outcomes. This reemphasizes the need for robust CHD epidemiological research in the region.

A modular computational framework for medical digital twins

The digital twin paradigm holds great promise for medicine, even though many technical and scientific challenges remain to be overcome, most importantly the efficient integration of many heterogeneous component models. This is an unsolved problem even in industry. It has long been understood that such models need to be built in a modular fashion, connecting together component models of individual biological processes. In conventional implementations, however, the dependency structure of the modules reflects the dependencies among these processes, making it all but impossible to modify or expand the digital twin without breaking it. This paper presents a fundamental reorganization of the internal digital twin architecture into a hub-and-spokes design that completely circumvents this dependency problem.

This paper presents a modular software design for the construction of computational modeling technology that will help implement precision medicine. In analogy to a common industrial strategy used for preventive maintenance of engineered products, medical digital twins are computational models of disease processes calibrated to individual patients using multiple heterogeneous data streams. They have the potential to help improve diagnosis, prognosis, and personalized treatment for a wide range of medical conditions. Their large-scale development relies on both mechanistic and data-driven techniques and requires the integration and ongoing update of multiple component models developed across many different laboratories. Distributed model building and integration requires an open-source modular software platform for the integration and simulation of models that is scalable and supports a decentralized, community-based model building process. This paper presents such a platform, including a case study in an animal model of a respiratory fungal infection.

An integrated lumped-parameter model of the cardiovascular system for the simulation of acute ischemic stroke: description of instantaneous changes in hemodynamics

Acute Ischemic Stroke (AIS) is defined as the acute condition of occlusion of a cerebral artery and is often caused by a Hypertensive Condition (HC). Due to its sudden occurrence, AIS is not observable the right moment it occurs, thus information about instantaneous changes in hemodynamics is limited. This study aimed to propose an integrated Lumped Parameter (LP) model of the cardiovascular system to simulate an AIS and describe instantaneous changes in hemodynamics. In the integrated LP model of the cardiovascular system, heart chambers have been modelled with elastance systems with controlled pressure inputs; heart valves have been modelled with static open/closed pressure-controlled valves; eventually, the vasculature has been modelled with resistor-inductor-capacitor (RLC) direct circuits and have been linked to the rest of the system through a series connection. After simulating physiological conditions, HC has been simulated by changing pressure inputs and constant RLC parameters. Then, AIS occurring in arteries of different sizes have been simulated by considering time-dependent RLC parameters due to the elimination from the model of the occluding artery; instantaneous changes in hemodynamics have been evaluated by Systemic Arteriolar Flow (Qa) and Systemic Arteriolar Pressure (Pa) drop with respect to those measured in HC. Occlusion of arteries of different sizes leaded to an average Qa drop of 0.38 ml/s per cardiac cycle (with minimum and maximum values of 0.04 ml/s and 1.93 ml/s) and average Pa drop of 0.39 mmHg, (with minimum and maximum values of 0.04 mmHg and 1.98 mmHg). In conclusion, hemodynamic variations due to AIS are very small with respect to HC. A direct relation between the inverse of the length of the artery in which the occlusion occurs and the hemodynamic variations has been highlighted; this may allow to link the severity of AIS to the length of the interested artery.

Digital Twins for Multiple Sclerosis

An individualized innovative disease management is of great importance for people with multiple sclerosis (pwMS) to cope with the complexity of this chronic, multidimensional disease. However, an individual state of the art strategy, with precise adjustment to the patient's characteristics, is still far from being part of the everyday care of pwMS. The development of digital twins could decisively advance the necessary implementation of an individualized innovative management of MS. Through artificial intelligence-based analysis of several disease parameters - including clinical and para-clinical outcomes, multi-omics, biomarkers, patient-related data, information about the patient's life circumstances and plans, and medical procedures - a digital twin paired to the patient's characteristic can be created, enabling healthcare professionals to handle large amounts of patient data. This can contribute to a more personalized and effective care by integrating data from multiple sources in a standardized manner, implementing individualized clinical pathways, supporting physician-patient communication and facilitating a shared decision-making. With a clear display of pre-analyzed patient data on a dashboard, patient participation and individualized clinical decisions as well as the prediction of disease progression and treatment simulation could become possible. In this review, we focus on the advantages, challenges and practical aspects of digital twins in the management of MS. We discuss the use of digital twins for MS as a revolutionary tool to improve diagnosis, monitoring and therapy refining patients' well-being, saving economic costs, and enabling prevention of disease progression. Digital twins will help make precision medicine and patient-centered care a reality in everyday life.

Uncertainty propagation and sensitivity analysis: results from the Ocular Mathematical Virtual Simulator

We propose an uncertainty propagation study and a sensitivity analysis with the Ocular Mathematical Virtual Simulator, a computational and mathematical model that predicts the hemodynamics and biomechanics within the human eye. In this contribution, we focus on the effect of intraocular pressure, retrolaminar tissue pressure and systemic blood pressure on the ocular posterior tissue vasculature. The combination of a physically-based model with experiments-based stochastic input allows us to gain a better understanding of the physiological system, accounting both for the driving mechanisms and the data variability.

Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid-dynamics model of the pulmonary circulation

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid-dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient-specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed-form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state-of-the-art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long-term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

Data-driven cardiovascular flow modelling: examples and opportunities

High-fidelity blood flow modelling is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from such investigations remains limited by the presence of uncertainty in parameters, low resolution, and measurement noise. Additionally, extracting useful information from these datasets is challenging. Data-driven modelling techniques have the potential to overcome these challenges and transform cardiovascular flow modelling. Here, we review several data-driven modelling techniques, highlight the common ideas and principles that emerge across numerous such techniques, and provide illustrative examples of how they could be used in the context of cardiovascular fluid mechanics. In particular, we discuss principal component analysis (PCA), robust PCA, compressed sensing, the Kalman filter for data assimilation, low-rank data recovery, and several additional methods for reduced-order modelling of cardiovascular flows, including the dynamic mode decomposition and the sparse identification of nonlinear dynamics. All techniques are presented in the context of cardiovascular flows with simple examples. These data-driven modelling techniques have the potential to transform computational and experimental cardiovascular research, and we discuss challenges and opportunities in applying these techniques in the field, looking ultimately towards data-driven patient-specific blood flow modelling.

Model Verification and Error Sensitivity of Turbulence-Related Tensor Characteristics in Pulsatile Blood Flow Simulations

Model verification, validation, and uncertainty quantification are essential procedures to estimate errors within cardiovascular flow modeling, where acceptable confidence levels are needed for clinical reliability. While more turbulent-like studies are frequently observed within the biofluid community, practical modeling guidelines are scarce. Verification procedures determine the agreement between the conceptual model and its numerical solution by comparing for example, discretization and phase-averaging-related errors of specific output parameters. This computational fluid dynamics (CFD) study presents a comprehensive and practical verification approach for pulsatile turbulent-like blood flow predictions by considering the amplitude and shape of the turbulence-related tensor field using anisotropic invariant mapping. These procedures were demonstrated by investigating the Reynolds stress tensor characteristics in a patient-specific aortic coarctation model, focusing on modeling-related errors associated with the spatiotemporal resolution and phase-averaging sampling size. Findings in this work suggest that attention should also be put on reducing phase-averaging related errors, as these could easily outweigh the errors associated with the spatiotemporal resolution when including too few cardiac cycles. Also, substantially more cycles are likely needed than typically reported for these flow regimes to sufficiently converge the phase-instant tensor characteristics. Here, higher degrees of active fluctuating directions, especially of lower amplitudes, appeared to be the most sensitive turbulence characteristics.

Does the inflow velocity profile influence physiologically relevant flow patterns in computational hemodynamic models of left anterior descending coronary artery?

Patient-specific computational fluid dynamics is a powerful tool for investigating the hemodynamic risk in coronary arteries. Proper setting of flow boundary conditions in computational hemodynamic models of coronary arteries is one of the sources of uncertainty weakening the findings of in silico experiments, in consequence of the challenging task of obtaining in vivo 3D flow measurements within the clinical framework. Accordingly, in this study we evaluated the influence of assumptions on inflow velocity profile shape on coronary artery hemodynamics. To do that, (1) ten left anterior descending coronary artery (LAD) geometries were reconstructed from clinical angiography, and (2) eleven velocity profiles with realistic 3D features such as eccentricity and differently shaped (single- and double-vortex) secondary flows were generated analytically and imposed as inflow boundary conditions. Wall shear stress and helicity-based descriptors obtained prescribing the commonly used parabolic velocity profile were compared with those obtained with the other velocity profiles. Our findings indicated that the imposition of idealized velocity profiles as inflow boundary condition is acceptable as long the results of the proximal vessel segment are not considered, in LAD coronary arteries. As a pragmatic rule of thumb, a conservative estimation of the length of influence of the shape of the inflow velocity profile on LAD local hemodynamics can be given by the theoretical entrance length for cylindrical conduits in laminar flow conditions.

Creation and application of virtual patient cohorts of heart models

Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.