Modeling Cerebral Blood Flow Velocity During Orthostatic Stress

Hemodynamics of thrombus formation in intracranial aneurysms: An in silico observational study

How prevalent is spontaneous thrombosis in a population containing all sizes of intracranial aneurysms? How can we calibrate computational models of thrombosis based on published data? How does spontaneous thrombosis differ in normo- and hypertensive subjects? We address the first question through a thorough analysis of published datasets that provide spontaneous thrombosis rates across different aneurysm characteristics. This analysis provides data for a subgroup of the general population of aneurysms, namely, those of large and giant size (>10 mm). Based on these observed spontaneous thrombosis rates, our computational modeling platform enables the first in silico observational study of spontaneous thrombosis prevalence across a broader set of aneurysm phenotypes. We generate 109 virtual patients and use a novel approach to calibrate two trigger thresholds: residence time and shear rate, thus addressing the second question. We then address the third question by utilizing this calibrated model to provide new insight into the effects of hypertension on spontaneous thrombosis. We demonstrate how a mechanistic thrombosis model calibrated on an intracranial aneurysm cohort can help estimate spontaneous thrombosis prevalence in a broader aneurysm population. This study is enabled through a fully automatic multi-scale modeling pipeline. We use the clinical spontaneous thrombosis data as an indirect population-level validation of a complex computational modeling framework. Furthermore, our framework allows exploration of the influence of hypertension in spontaneous thrombosis. This lays the foundation for in silico clinical trials of cerebrovascular devices in high-risk populations, e.g., assessing the performance of flow diverters in aneurysms for hypertensive patients.

Parameter inference in a computational model of haemodynamics in pulmonary hypertension

Pulmonary hypertension (PH), defined by a mean pulmonary arterial pressure (mPAP) greater than 20 mmHg, is characterized by increased pulmonary vascular resistance and decreased pulmonary arterial compliance. There are few measurable biomarkers of PH progression, but a conclusive diagnosis of the disease requires invasive right heart catheterization (RHC). Patient-specific cardiovascular systems-level computational models provide a potential non-invasive tool for determining additional indicators of disease severity. Using computational modelling, this study quantifies physiological parameters indicative of disease severity in nine PH patients. The model includes all four heart chambers, the pulmonary and systemic circulations. We consider two sets of calibration data: static (systolic and diastolic values) RHC data and a combination of static and continuous, time-series waveform data. We determine a subset of identifiable parameters for model calibration using sensitivity analyses and multi-start inference and perform posterior uncertainty quantification. Results show that additional waveform data enables accurate calibration of the right atrial reservoir and pump function across the PH cohort. Model outcomes, including stroke work and pulmonary resistance-compliance relations, reflect typical right heart dynamics in PH phenotypes. Lastly, we show that estimated parameters agree with previous, non-modelling studies, supporting this type of analysis in translational PH research.

Modelling physiology of haemodynamic adaptation in short-term microgravity exposure and orthostatic stress on Earth

Cardiovascular haemodynamics alters during posture changes and exposure to microgravity. Vascular auto-remodelling observed in subjects living in space environment causes them orthostatic intolerance when they return on Earth. In this study we modelled the human haemodynamics with focus on head and neck exposed to different hydrostatic pressures in supine, upright (head-up tilt), head-down tilt position, and microgravity environment by using a well-developed 1D-0D haemodynamic model. The model consists of two parts that simulates the arterial (1D) and brain-venous (0D) vascular tree. The cardiovascular system is built as a network of hydraulic resistances and capacitances to properly model physiological parameters like total peripheral resistance, and to calculate vascular pressure and the related flow rate at any branch of the tree. The model calculated 30.0 mmHg (30%), 7.1 mmHg (78%), 1.7 mmHg (38%) reduction in mean blood pressure, intracranial pressure and central venous pressure after posture change from supine to upright, respectively. The modelled brain drainage outflow percentage from internal jugular veins is 67% and 26% for supine and upright posture, while for head-down tilt and microgravity is 65% and 72%, respectively. The model confirmed the role of peripheral veins in regional blood redistribution during posture change from supine to upright and microgravity environment as hypothesized in literature. The model is able to reproduce the known haemodynamic effects of hydraulic pressure change and weightlessness. It also provides a virtual laboratory to examine the consequence of a wide range of orthostatic stresses on human haemodynamics.

Rude mechanicals in brain haemodynamics: non-neural actors that influence blood flow

Fluctuations in blood oxygenation and flow are widely used to infer brain activity during resting-state functional magnetic resonance imaging (fMRI). However, there are strong systemic and vascular contributions to resting-state signals that are unrelated to ongoing neural activity. Importantly, these non-neural contributions to haemodynamic signals (or 'rude mechanicals') can be as large as or larger than the neurally evoked components. Here, we review the two broad classes of drivers of these signals. One is systemic and is tied to fluctuations in external drivers such as heart rate and breathing, and the robust autoregulatory mechanisms that try to maintain a constant milieu in the brain. The other class comprises local, active fluctuations that appear to be intrinsic to vascular tissue and are likely similar to active local fluctuations seen in vasculature all over the body. In this review, we describe these non-neural fluctuations and some of the tools developed to correct for them when interpreting fMRI recordings. However, we also emphasize the links between these vascular fluctuations and brain physiology and point to ways in which fMRI measurements can be used to exploit such links to gain valuable information about neurovascular health and about internal brain states. This article is part of the theme issue 'Key relationships between non-invasive functional neuroimaging and the underlying neuronal activity'.

Sensitivity analysis methods in the biomedical sciences

Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before applying each method to a simple model. Also included is a summary of current software packages, as well as a modeller's guide for carrying out sensitivity analyses. Finally, we apply the popular Morris and Sobol methods to two models with biomedical applications, with the intention of providing a deeper understanding behind both the principles of these methods and the presentation of their results.

Population-specific modelling of between/within-subject flow variability in the carotid arteries of the elderly

Computational fluid dynamics models are increasingly proposed for assisting the diagnosis and management of vascular diseases. Ideally, patient-specific flow measurements are used to impose flow boundary conditions. When patient-specific flow measurements are unavailable, mean values of flow measurements across small cohorts are used as normative values. In reality, both the between-subjects and within-subject flow variabilities are large. Consequently, neither one-shot flow measurements nor mean values across a cohort are truly indicative of the flow regime in a given person. We develop models for both the between-subjects and within-subject variability of internal carotid flow. A log-linear mixed effects model is combined with a Gaussian process to model the between-subjects flow variability, while a lumped parameter model of cerebral autoregulation is used to model the within-subject flow variability in response to heart rate and blood pressure changes. The model parameters are identified from carotid ultrasound measurements in a cohort of 103 elderly volunteers. We use the models to study intracranial aneurysm flow in 54 subjects under rest and exercise and conclude that OSI, a common wall shear-stress derived quantity in vascular CFD studies, may be too sensitive to flow fluctuations to be a reliable biomarker.

Cerebral Artery Vasospasm Detection Using Transcranial Doppler Signal Analysis

OBJECTIVES

Silent cerebral artery vasospasm in aneurysmal subarachnoid hemorrhage causes serious complications such as cerebral ischemia and death. A transcranial Doppler (TCD) ultrasound system is a noninvasive device that can effectively detect cerebral artery vasospasm as soon as it sets in, even before and in the absence of clinical deterioration. Continuous or even daily TCD monitoring is challenging because of the operator expertise and certification required in the form of a trained sonographer and interpretive experience required in the form of an additionally trained and certified physician to perform these studies. This barrier exists because of a lack of automation for detection (without human intervention) of cerebral artery vasospasm using TCD ultrasound. To overcome this barrier, we present an algorithm that automates detection of cerebral artery vasospasm.

METHODS

We extracted features such as the energy, energy entropy, zero-crossing rate, spectral centroid, spectral speed, spectral entropy, spectral flux, spectral roll-off, harmonic ratio, chroma, and Mel frequency cepstral coefficients for signal classification. Then we applied principal component analysis to reduce the data dimensionality.

RESULTS

All of the chosen features were used for training a decision-tree classifier. The algorithm had high accuracy for cerebral artery vasospasm detection, with overall sensitivity of 87.5% and specificity of 89.74%.

CONCLUSIONS

The algorithm has the potential for development into a continuous cerebral artery vasospasm monitor.

A model-based analysis of autonomic nervous function in response to the Valsalva maneuver

The Valsalva maneuver (VM) is a diagnostic protocol examining sympathetic and parasympathetic activity in patients with autonomic dysfunction (AD) impacting cardiovascular control. Because direct measurement of these signals is costly and invasive, AD is typically assessed indirectly by analyzing heart rate and blood pressure response patterns. This study introduces a mathematical model that can predict sympathetic and parasympathetic dynamics. Our model-based analysis includes two control mechanisms: respiratory sinus arrhythmia (RSA) and the baroreceptor reflex (baroreflex). The RSA submodel integrates an electrocardiogram-derived respiratory signal with intrathoracic pressure, and the baroreflex submodel differentiates aortic and carotid baroreceptor regions. Patient-specific afferent and efferent signals are determined for 34 control subjects and 5 AD patients, estimating parameters fitting the model output to heart rate data. Results show that inclusion of RSA and distinguishing aortic/carotid regions are necessary to model the heart rate response to the VM. Comparing control subjects to patients shows that RSA and baroreflex responses are significantly diminished. This study compares estimated parameter values from the model-based predictions to indices used in clinical practice. Three indices are computed to determine adrenergic function from the slope of the systolic blood pressure in phase II [α (a new index)], the baroreceptor sensitivity (β), and the Valsalva ratio (γ). Results show that these indices can distinguish between normal and abnormal states, but model-based analysis is needed to differentiate pathological signals. In summary, the model simulates various VM responses and, by combining indices and model predictions, we study the pathologies for 5 AD patients.NEW & NOTEWORTHY We introduce a patient-specific model analyzing heart rate and blood pressure during a Valsalva maneuver (VM). The model predicts autonomic function incorporating the baroreflex and respiratory sinus arrhythmia (RSA) control mechanisms. We introduce a novel index (α) characterizing sympathetic activity, which can distinguish control and abnormal patients. However, we assert that modeling and parameter estimation are necessary to explain pathologies. Finally, we show that aortic baroreceptors contribute significantly to the VM and RSA affects early VM.

Subject-specific multi-poroelastic model for exploring the risk factors associated with the early stages of Alzheimer's disease

There is emerging evidence suggesting that Alzheimer's disease is a vascular disorder, caused by impaired cerebral perfusion, which may be promoted by cardiovascular risk factors that are strongly influenced by lifestyle. In order to develop an understanding of the exact nature of such a hypothesis, a biomechanical understanding of the influence of lifestyle factors is pursued. An extended poroelastic model of perfused parenchymal tissue coupled with separate workflows concerning subject-specific meshes, permeability tensor maps and cerebral blood flow variability is used. The subject-specific datasets used in the modelling of this paper were collected as part of prospective data collection. Two cases were simulated involving male, non-smokers (control and mild cognitive impairment (MCI) case) during two states of activity (high and low). Results showed a marginally reduced clearance of cerebrospinal fluid (CSF)/interstitial fluid (ISF), elevated parenchymal tissue displacement and CSF/ISF accumulation and drainage in the MCI case. The peak perfusion remained at 8 mm s⁻¹ between the two cases.

Screening for Cognitive Impairment by Model-Assisted Cerebral Blood Flow Estimation

OBJECTIVE

Alzheimer's disease (AD) is a progressive and debilitating neurodegenerative disease; a major health concern in the ageing population with an estimated prevalence of 46 million dementia cases worldwide. Early diagnosis is therefore crucial so mitigating treatments can be initiated at an early stage. Cerebral hypoperfusion has been linked with blood-brain barrier dysfunction in the early stages of AD, and screening for chronic cerebral hypoperfusion in individuals has been proposed for improving the early diagnosis of AD. However, ambulatory measurements of cerebral blood flow are not routinely carried out in the clinical setting. In this study, we combine physiological modeling with Holter blood pressure monitoring and carotid ultrasound imaging to predict 24-h cerebral blood flow (CBF) profiles in individuals. One hundred and three participants [53 with mild cognitive impairment (MCI) and 50 healthy controls] underwent model-assisted prediction of 24-h CBF. Model-predicted CBF and neuropsychological tests were features in lasso regression models for MCI diagnosis.

RESULTS

A CBF-enhanced classifier for diagnosing MCI performed better, area-under-the-curve (AUC) = 0.889 (95%-CI: 0.800 to 0.978), than a classifier based only on the neuropsychological test scores, AUC = 0.818 (95%-CI: 0.643 to 0.992). An additional cohort of 25 participants (11 MCI and 14 healthy) was recruited to perform model validation by arterial spin-labeling magnetic resonance imaging, and to establish a link between measured CBF that predicted by the model.

CONCLUSION

Ultrasound imaging and ambulatory blood pressure measurements enhanced with physiological modeling can improve MCI diagnosis accuracy.

Increased blood pressure variability upon standing up improves reproducibility of cerebral autoregulation indices

Dynamic cerebral autoregulation, that is the transient response of cerebral blood flow to changes in arterial blood pressure, is currently assessed using a variety of different time series methods and data collection protocols. In the continuing absence of a gold standard for the study of cerebral autoregulation it is unclear to what extent does the assessment depend on the choice of a computational method and protocol. We use continuous measurements of blood pressure and cerebral blood flow velocity in the middle cerebral artery from the cohorts of 18 normotensive subjects performing sit-to-stand manoeuvre. We estimate cerebral autoregulation using a wide variety of black-box approaches (including the following six autoregulation indices ARI, Mx, Sx, Dx, FIR and ARX) and compare them in the context of reproducibility and variability. For all autoregulation indices, considered here, the intra-class correlation was greater during the standing protocol, however, it was significantly greater (Fisher's Z-test) for Mx (p < 0.03), Sx (p < 0.003) and Dx (p < 0.03). In the specific case of the sit-to-stand manoeuvre, measurements taken immediately after standing up greatly improve the reproducibility of the autoregulation coefficients. This is generally coupled with an increase of the within-group spread of the estimates.

A model for generating synthetic arterial blood pressure

A new model capable of simulating many important aspects of human arterial blood pressure (ABP) is proposed. Both data-driven approach and physiological principles have been applied to describe the time series of diastolic, systolic, dicrotic notch and dicrotic peak pressure points. Major static and dynamic features of the model can be prescribed by the user, including heart rate, mean systolic and diastolic pressure, and the corresponding physiological control quantities, such as baroreflex sensitivity coefficient and Windkessel time constant. A realistic ABP generator can be used to compile a virtual database of signals reflecting individuals with different clinical conditions and signals containing common artefacts. The ABP model permits to create a platform to assess a wide range of biomedical signal processing approaches and be used in conjunction with, e.g. Kalman filters to improve the quality of ABP signals.

A stochastic delay differential model of cerebral autoregulation

Mathematical models of the cardiovascular system and of cerebral autoregulation (CAR) have been employed for several years in order to describe the time course of pressures and flows changes subsequent to postural changes. The assessment of the degree of efficiency of cerebral auto regulation has indeed importance in the prognosis of such conditions as cerebro-vascular accidents or Alzheimer. In the quest for a simple but realistic mathematical description of cardiovascular control, which may be fitted onto non-invasive experimental observations after postural changes, the present work proposes a first version of an empirical Stochastic Delay Differential Equations (SDDEs) model. The model consists of a total of four SDDEs and two ancillary algebraic equations, incorporates four distinct delayed controls from the brain onto different components of the circulation, and is able to accurately capture the time course of mean arterial pressure and cerebral blood flow velocity signals, reproducing observed auto-correlated error around the expected drift.