Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation

A sonographic quantitative cutoff value of cerebral venous outflow in neurologic diseases: a blinded study of 115 subjects

BACKGROUND AND PURPOSE

The autonomic nervous system maintains constant cerebral venous blood outflow in changing positions. Alterations in cerebral autoregulation can be revealed by postural changes at quantitative color Doppler sonography. The aim of this study was to reach an optimal cutoff value of the difference between the cerebral venous blood outflow in the supine and seated positions that can discriminate healthy controls from patients with multiple sclerosis and those with other neurologic diseases and to evaluate its specificity, sensitivity, and diagnostic accuracy.

MATERIALS AND METHODS

One hundred fifteen subjects (54 with MS, 31 healthy controls, 30 with other neurologic diseases) underwent a blinded quantitative color Doppler sonography evaluation of cerebral venous blood outflow in the supine and sitting positions. An optimal difference value between the supine and sitting positions of the cerebral venous blood outflow cutoff value was sought.

RESULTS

The difference value between supine and sitting positions of the cerebral venous blood outflow was ≤ 503.24 in 38/54 (70.37%) patients with MS, 9/31 (29.03%) healthy controls, and 13/30 (43.33%) subjects with other neurological diseases. A difference value between supine and sitting positions of the cerebral venous blood outflow at a 503.24 cutoff reached a sensitivity at 70.37%, a 70.96% specificity, a 80.85% positive predictive value, and a 57.89% negative predictive value; the quantitative color Doppler sonography parameters yielded significant differences. The difference value between supine and sitting positions of cerebral venous blood outflow ≤ 503.24 assessed the significant difference between MS versus other neurological diseases.

CONCLUSIONS

Alteration of cerebral venous blood outflow discriminated MS versus other neurologic diseases and MS versus healthy controls. The difference value between supine and sitting positions of cerebral venous blood outflow ≤ 503.24 was statistically associated with MS.

Effect of postural changes on normal and stenosed common carotid artery using FSI

Gravity associated with postural changes has a strong bearing on haemodynamics of blood flow in arteries. Its effect on stenosed cases has not been widely investigated. In the present study, variation observed in blood flow during postural changes is investigated for different conditions like standing, sleeping and head-down position. A fluid structure interaction study is carried out for idealized normal and 75% eccentric and concentric stenosed common carotid normal artery. The results clearly indicate the effects of altered gravity on flow conditions. It was found to be very significant during head-down position and demonstrated very high arterial blood pressure in stenosed common carotid when compared with normal carotid.

A cardiovascular mathematical model of graded head-up tilt

A lumped parameter model of the cardiovascular system has been developed and optimized using experimental data obtained from 13 healthy subjects during graded head-up tilt (HUT) from the supine position to . The model includes descriptions of the left and right heart, direct ventricular interaction through the septum and pericardium, the systemic and pulmonary circulations, nonlinear pressure volume relationship of the lower body compartment, arterial and cardiopulmonary baroreceptors, as well as autoregulatory mechanisms. A number of important features, including the separate effects of arterial and cardiopulmonary baroreflexes, and autoregulation in the lower body, as well as diastolic ventricular interaction through the pericardium have been included and tested for their significance. Furthermore, the individual effect of parameter associated with heart failure, including LV and RV contractility, baseline systemic vascular resistance, pulmonary vascular resistance, total blood volume, LV diastolic stiffness and reflex gain on HUT response have also been investigated. Our fitted model compares favorably with our experimental measurements and published literature at a range of tilt angles, in terms of both global and regional hemodynamic variables. Compared to the normal condition, a simulated congestive heart failure condition produced a blunted response to HUT with regards to the percentage changes in cardiac output, stroke volume, end diastolic volume and effector response (i.e., heart contractility, venous unstressed volume, systemic vascular resistance and heart rate) with progressive tilting.

Why is ABI effective in detecting vascular stenosis? Investigation based on multibranch hemodynamic model

The ankle-brachial index (ABI), defined as the ratio of systolic pressure in the ankle arteries and that in the brachial artery, was a useful noninvasive method to detect arterial stenoses. There had been a lot of researches about clinical regularities of ABI; however, mechanism studies were less addressed. For the purpose of a better understanding of the correlation between vascular stenoses and ABI, a computational model for simulating blood pressure and flow propagation in various arterial stenosis circumstances was developed with a detailed compartmental description of the heart and main arteries. Particular attention was paid to the analysis of effects of vascular stenoses in different large-sized arteries on ABI in theory. Moreover, the variation of ABI during the increase of the stenosis severity was also studied. Results showed that stenoses in lower limb arteries, as well as, brachial artery, caused different variations of blood pressure in ankle and brachial arteries, resulting in a significant change of ABI. Furthermore, the variation of ABI became faster when the severity of the stenosis increased, validating that ABI was more sensitive to severe stenoses than to mild/moderate ones. All these in findings revealed the reason why ABI was an effective index for detecting stenoses, especially in lower limb arteries.

A practical approach to parameter estimation applied to model predicting heart rate regulation

Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The "best" subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets.

Mathematical modeling approaches in the study of glaucoma disparities among people of African and European descents

Open angle glaucoma (OAG) is a severe ocular disease characterized by progressive and irreversible vision loss. While elevated intraocular pressure (IOP) is a well-established risk factor for OAG, the progression of OAG in many cases, despite IOP treatment, suggests that other risk factors must play significant roles in the development of the disease. For example, various structural properties of the eye, ocular blood flow properties, and systemic conditions have been identified as risk factors for OAG. Ethnicity has also been indicated as a relevant factor that affects the incidence and prevalence of OAG; in fact, OAG is the leading cause of blindness among people of African descent. Numerous clinical studies have been designed to examine the possible correlation and causation between OAG and these factors; however, these studies are met with the challenge of isolating the individual role of multiple interconnected factors. Over the last decade, various mathematical modeling approaches have been implemented in combination with clinical studies in order to provide a mechanical and hemodynamical description of the eye in relation to the entire human body and to assess the contribution of single risk factors to the development of OAG. This review provides a summary of the clinical evidence of ocular structural differences, ocular vascular differences and systemic vascular differences among people of African and European descent, describes the mathematical approaches that have been proposed to study ocular mechanics and hemodynamics while discussing how they could be used to investigate the relevance to OAG of racial disparities, and outlines possible new directions of research.

Space physiology IV: mathematical modeling of the cardiovascular system in space exploration

Mathematical modeling represents an important tool for analyzing cardiovascular function during spaceflight. This review describes how modeling of the cardiovascular system can contribute to space life science research and illustrates this process via modeling efforts to study postflight orthostatic intolerance (POI), a key issue for spaceflight. Examining this application also provides a context for considering broader applications of modeling techniques to the challenges of bioastronautics. POI, which affects a large fraction of astronauts in stand tests upon return to Earth, presents as dizziness, fainting and other symptoms, which can diminish crew performance and cause safety hazards. POI on the Moon or Mars could be more critical. In the field of bioastronautics, POI has been the dominant application of cardiovascular modeling for more than a decade, and a number of mechanisms for POI have been investigated. Modeling approaches include computational models with a range of incorporated factors and hemodynamic sophistication, and also physical models tested in parabolic and orbital flight. Mathematical methods such as parameter sensitivity analysis can help identify key system mechanisms. In the case of POI, this could lead to more effective countermeasures. Validation is a persistent issue in modeling efforts, and key considerations and needs for experimental data to synergistically improve understanding of cardiovascular responses are outlined. Future directions in cardiovascular modeling include subject-specific assessment of system status, as well as research on integrated physiological responses, leading, for instance, to assessment of subject-specific susceptibility to POI or effects of cardiovascular alterations on muscular, vision and cognitive function.

Supine-to-standing transcranial Doppler test in patients with multiple system atrophy

BACKGROUND

Supine-to-standing test, a transcranial Doppler (TCD) based technique, has been recently developed to evaluate cardiovascular dysautonomia. We explored the value of supine-to-standing TCD test in predicting the course of multiple system atrophy (MSA) with orthostatic hypotension (OH).

METHODS

By monitoring the signals of middle cerebral artery during supine-to-standing posture changes, the trend curves of cerebral blood flow velocities, pulsatility index and resistance index were obtained from 38 MSA patients with OH and 31 healthy subjects. The correlation between TCD findings and the clinical outcome of the patients, which was determined by follow-up structured phone interview, was analyzed. Adverse outcome was defined if a patient died, was in bed-ridden state or had recurrent syncope (>1 per month).

RESULTS

Two characteristic TCD findings were revealed in the MSA patients but not in the controls, i.e. a blunted cerebral blood flow velocity rebound after standing and/or sustained higher pulsatility index upon standing than supine baseline. Structured phone interview was completed in 31 of the 38 patients (mean follow-up time, 20 ± 11 months). While no subject had recurrent syncope before enrollment, 12 patients developed an adverse outcome during follow-up. The coexistence of two characteristic TCD findings predicted adverse outcomes with positive predictive value 66.7% and negative predictive value 87.5%.

CONCLUSIONS

Supine-to-standing TCD test is valuable in predicting the course of MSA with OH at early stage. We hypothesize baroreflex failure effects and paradoxical cerebral vasoconstriction in response to OH may account for the TCD findings in MSA patients.

Initial orthostatic hypotension and cerebral blood flow regulation: effect of α1-adrenoreceptor activity

We examined the hypothesis that α1-adrenergic blockade would lead to an inability to correct initial orthostatic hypotension (IOH) and cerebral hypoperfusion, leading to symptoms of presyncope. Twelve normotensive humans (aged 25 ± 1 yr; means ± SE) attempted to complete a 3-min upright stand, 90 min after the administration of either α1-blockade (prazosin, 1 mg/20 kg body wt) or placebo. Continuous beat-to-beat measurements of middle cerebral artery velocity (MCAv; Doppler), blood pressure (finometer), heart rate, and end-tidal Pco2were obtained. Compared with placebo, the α1-blockade reduced resting mean arterial blood pressure (MAP) (−15%; P < 0.01); MCAv remained unaltered ( P ≥ 0.28). Upon standing, although the absolute level of MAP was lower following α1-blockade (39 ± 10 mmHg vs. 51 ± 14 mmHg), the relative difference in IOH was negligible in both trials (mean difference in MAP: 2 ± 2 mmHg; P = 0.50). Compared with the placebo trial, the declines in MCAv and PetCO2during IOH were greater in the α1-blockade trial by 12 ± 4 cm/s and 4.4 ± 1.3 mmHg, respectively ( P ≤ 0.01). Standing tolerance was markedly reduced in the α1-blockade trial (75 ± 17 s vs. 180 ± 0 s; P < 0.001). In summary, while IOH was little affected by α1-blockade, the associated decline in MCAv was greater in the blockade condition. Unlike in the placebo trial, the extent of IOH and cerebral hypoperfusion failed to recover toward baseline in the α1-blockade trial leading to presyncope. Although the development of IOH is not influenced by the α1-adrenergic receptor pathway, this pathway is critical in the recovery from IOH to prevent cerebral hypoperfusion and ultimately syncope.

Computational simulation to understand vision changes during prolonged weightlessness

A mathematical model of whole body and cerebral hemodynamics is a useful tool for investigating visual impairment and intracranial pressure (VIIP), a recently described condition associated with space flight. VIIP involves loss of visual acuity, anatomical changes to the eye, and, usually, elevated cerebrospinal fluid pressure. Loss of visual acuity is a significant threat to astronaut health and performance. It is therefore important to understand the pathogenesis of VIIP. Some of the experimental measurements that could lead to better understanding of the pathophysiology are impossible or infeasible on orbit. A computational implementation of a mathematical model of hypothetical pathophysiological processes is therefore valuable. Such a model is developed, and is used to investigate how changes in vascular compliance or pressure can influence intraocular or intracranial pressure.

Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia

This study develops a lumped cardiovascular-respiratory system-level model that incorporates patient-specific data to predict cardiorespiratory response to hypercapnia (increased CO(2) partial pressure) for a patient with congestive heart failure (CHF). In particular, the study focuses on predicting cerebral CO(2) reactivity, which can be defined as the ability of vessels in the cerebral vasculature to expand or contract in response CO(2) induced challenges. It is difficult to characterize cerebral CO(2) reactivity directly from measurements, since no methods exist to dynamically measure vasomotion of vessels in the cerebral vasculature. In this study we show how mathematical modeling can be combined with available data to predict cerebral CO(2) reactivity via dynamic predictions of cerebral vascular resistance, which can be directly related to vasomotion of vessels in the cerebral vasculature. To this end we have developed a coupled cardiovascular and respiratory model that predicts blood pressure, flow, and concentration of gasses (CO(2) and O(2)) in the systemic, cerebral, and pulmonary arteries and veins. Cerebral vascular resistance is incorporated via a model parameter separating cerebral arteries and veins. The model was adapted to a specific patient using parameter estimation combined with sensitivity analysis and subset selection. These techniques allowed estimation of cerebral vascular resistance along with other cardiovascular and respiratory parameters. Parameter estimation was carried out during eucapnia (breathing room air), first for the cardiovascular model and then for the respiratory model. Then, hypercapnia was introduced by increasing inspired CO(2) partial pressure. During eucapnia, seven cardiovascular parameters and four respiratory parameters was be identified and estimated, including cerebral and systemic resistance. During the transition from eucapnia to hypercapnia, the model predicted a drop in cerebral vascular resistance consistent with cerebral vasodilation.

Compromised cerebrovascular modulation in chronic anxiety: evidence from cerebral blood flow velocity measured by transcranial Doppler sonography

OBJECTIVE

Cerebral autoregulation (CA) is the mechanism by which constant cerebral blood flow is maintained despite changes in cerebral perfusion pressure. CA can be evaluated by dynamic monitoring of cerebral blood flow velocity (CBFV) with transcranial Doppler sonography (TCD). The present study aimed to explore CA in chronic anxiety.

METHODS

Subjects with Hamilton anxiety scale scores ≥14 were enrolled and the dynamic changes of CBFV in response to an orthostatic challenge were investigated using TCD.

RESULTS

In both the anxious and the healthy subjects, the mean CBFV was significantly lower in the upright position than when supine. However, the CBFV changes from supine to upright differed between the anxious and the healthy groups. Anxious subjects showed more pronounced decreases in CBFV with abrupt standing.

CONCLUSION

Our results indicate that cerebrovascular modulation is compromised in chronic anxiety; anxious subjects have some insufficiency in maintaining cerebral perfusion after postural change. Given the fact that anxiety and impaired CA are associated with cardiovascular disease, early ascertainment of compromised cerebrovascular modulation using TCD might suggest interventional therapies in the anxious population, and improve the primary prevention of cardiovascular disease.

Maximizing information from space data resources: a case for expanding integration across research disciplines

Regulatory systems are affected in space by exposure to weightlessness, high-energy radiation or other spaceflight-induced changes. The impact of spaceflight occurs across multiple scales and systems. Exploring such interactions and interdependencies via an integrative approach provides new opportunities for elucidating these complex responses. This paper argues the case for increased emphasis on integration, systematically archiving, and the coordination of past, present and future space and ground-based analogue experiments. We also discuss possible mechanisms for such integration across disciplines and missions. This article then introduces several discipline-specific reviews that show how such integration can be implemented. Areas explored include: adaptation of the central nervous system to space; cerebral autoregulation and weightlessness; modelling of the cardiovascular system in space exploration; human metabolic response to spaceflight; and exercise, artificial gravity, and physiologic countermeasures for spaceflight. In summary, spaceflight physiology research needs a conceptual framework that extends problem solving beyond disciplinary barriers. Administrative commitment and a high degree of cooperation among investigators are needed to further such a process. Well-designed interdisciplinary research can expand opportunities for broad interpretation of results across multiple physiological systems, which may have applications on Earth.

Panic disorder and subthreshold panic in the light of comorbidity: a follow-up study

Especially in the presence of agoraphobia and comorbid conditions, panic disorder causes significant impairment in life quality. Although there are several studies about epidemiology and clinical features, subthreshold symptoms and courses of comorbidity have not been studied sufficiently in panic disorder. The current study assessed the courses of panic disorder and subthreshold panic symptoms in consideration of the major and subthreshold comorbid conditions. Patients with Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition-diagnosed panic disorder were assessed using the panic disorder follow-up questionnaire, Panic and Agoraphobia Scale, Hamilton Depression Rating Scale, and State-Trait Anxiety Inventory. Structured Clinical Interview for Diagnostic and Statistical Manual of Mental Disorders was used to determine comorbidity, and all participants were received to 1-year follow-up. Comorbidity assessment showed that the threshold comorbidity decreased, while the subthreshold comorbidity increased at 1-year follow-up. Panic disorder symptom severity was decreased, but subthreshold panic symptoms continued to be present within the course of the illness. Presence of agoraphobia and duration of disease were significantly related with higher Panic and Agoraphobia Scale scores in the second assessment, and these relationships were independent from the treatment process. Even if the comorbidity and the severity of panic decrease with treatment, subthreshold panic and comorbid symptoms may still resist in panic disorder.

A dimensionally-heterogeneous closed-loop model for the cardiovascular system and its applications

In the present work a computational model of the entire cardiovascular system is developed using heterogeneous mathematical representations. This model integrates different levels of detail for the blood circulation. The arterial tree is described by a one dimensional model in order to simulate the wave propagation phenomena that take place at the larger arterial vessels. The inflow and outflow locations of this 1D model are coupled with lumped parameter descriptions of the remainder part of the circulatory system, closing the loop. The four cardiac valves are considered using a valve model which allows for stenoses and regurgitation phenomena. In addition, full 3D geometrical models of arterial districts are embedded in this closed-loop circuit to model the local blood flow in specific vessels. This kind of detailed closed-loop network for the cardiovascular system allows hemodynamics analyses of patient-specific arterial district, delivering naturally the appropriate boundary conditions for different cardiovascular scenarios. An example of application involving the effect of aortic insufficiency on the local hemodynamics of a cerebral aneurism is provided as a motivation to reproduce, through numerical simulation, the hemodynamic environment in patients suffering from infective endocarditis and mycotic aneurisms. The need for incorporating homeostatic control mechanisms is also discussed in view of the large sensitivity observed in the results, noting that this kind of integrative modeling allows such incorporation.

A new conceptual paradigm for the haemodynamics of salt-sensitive hypertension: a mathematical modelling approach

A conceptually novel mathematical model of neurogenic angiotensin II-salt hypertension is developed and analysed. The model consists of a lumped parameter circulatory model with two parallel vascular beds; two distinct control mechanisms for both natriuresis and arterial resistances can be implemented, resulting in four versions of the model. In contrast with the classical Guyton-Coleman model (GC model) of hypertension, in the standard version of our new model natriuresis is assumed to be independent of arterial pressure and instead driven solely by sodium intake; arterial resistances are driven by increased sympathetic nervous system activity in response to the elevated plasma angiotensin II and increased salt intake (AngII-salt). We compare the standard version of our new model against a simplified Guyton-Coleman model in which natriuresis is a function of arterial pressure via the pressure-natriuresis mechanism, and arterial resistances are controlled via the whole-body autoregulation mechanism. We show that the simplified GC model and the new model correctly predict haemodynamic and renal excretory responses to induced changes in angiotensin II and sodium inputs. Importantly, the new model reproduces the pressure-natriuresis relationship--the correlation between arterial pressure and sodium excretion--despite the assumption of pressure-independent natriuresis. These results show that our model provides a conceptually new alternative to Guyton's theory without contradicting observed haemodynamic changes or pressure-natriuresis relationships. Furthermore, the new model supports the view that hypertension need not necessarily have a renal aetiology and that long-term arterial pressure could be determined by sympathetic nervous system activity without involving the renal sympathetic nerves.

Effects of pressure-dependent segmental arterial compliance and postural changes on pulse wave transmission in an arterial model of the human upper limb

With increasing interest in the effect of postural changes on arterial blood pressure and vascular properties, it is important to understand effects of pressure-dependent arterial compliance. This study investigates effects of pressure-dependent compliance on pulse wave velocity (PWVar), pressure wave shape, and transmission characteristics in an arterial model of the human arm from heart to radial artery from supine to standing. Estimated central pressure waveform was used as the input for the model, calculated using a validated transfer function (SphygmoCor, AtCor Medical) from recorded radial pulses in 10 healthy male subjects (53.8 ± 7.9 years) during 0, 30, 60 and 90 degree head-up tilt. A 5-segment linear model was optimized using estimated central and recorded radial arterial pulse; each segment represented by an equivalent inductance, resistance and capacitance (compliance (C)) Pressure-dependent compliance (C(P)=a · e(b · P) was added to develop a nonlinear model, and the radial pulse calculated. Comparison of the radial pulse calculated by the linear and nonlinear models showed no statistical difference in systolic, diastolic, mean, and pulse pressure in any position of tilt. However, waveform shape was increasingly divergent at higher angles of tilt (RMS error 2.3 ± 1.2 mmHg supine, 6.5 ± 3.0 mmHg standing) as was PWVar (0% increase from supine to standing in the linear model, 16.7% increase in nonlinear model). Fourier analysis demonstrated peak amplitude of transmission being at higher frequencies and phase delay being lower in the nonlinear model relative to the linear model. Pressure-dependent arterial compliance, whilst having no effect on peak values of pressure, has significant effects on waveform shape and transmission speed, especially with a more upright position.

The CAM-LDPI method: a novel platform for the assessment of drug absorption

OBJECTIVES

This study aimed to explore the use of the chicken chorioallantoic membrane (CAM) with laser doppler perfusion imaging (LDPI) as a platform to assess absorption of vasoactive drugs.

METHODS

The optimal age of the CAM to be employed in the test and the indicator of vasoactivity were first established. Test substances that included common solvents and vasoactive drugs were tested on the CAM surface to determine their irritancy and blood perfusion effects.

KEY FINDINGS

Insignificant changes in blood perfusion were observed with deionized water, 0.9% w/v soldium chloride and 5% w/v glucose monohydrate, as well as theophylline and glucagon. Complex changes in blood perfusion were detected with ethanol, N-methyl-2-pyrrolidone, glycerin and propranolol. Both caffeine and glyceryl trinitrate resulted in a drop in blood perfusion.

CONCLUSIONS

It was concluded that the LDPI offers a rapid and non-invasive method to measure blood perfusion in the CAM. The latter provides a potentially useful platform in formulation studies to evaluate the effects of additives on drug absorption using caffeine or glyceryl trinitrate as model drugs.

Functionality of the baroreceptor nerves in heart rate regulation

Two models describing the afferent baroreceptor firing are analyzed, a basic model predicting firing using a single nonlinear differential equation, and an extended model, coupling K nonlinear responses. Both models respond to the the rate (derivative) and the rate history of the carotid sinus arterial pressure. As a result both the rate and the relative level of the carotid sinus arterial pressure is sensed. Simulations with these models show that responses to step changes in pressure follow from the rate sensitivity as observed in experimental studies. Adaptation and asymmetric responses are a consequence of the memory encapsulated by the models, and the nonlinearity gives rise to sigmoidal response curves. The nonlinear afferent baroreceptor models are coupled with an effector model, and the coupled model has been used to predict baroreceptor feedback regulation of heart rate during postural change from sitting to standing and during head-up tilt. The efferent model couples the afferent nerve paths to the sympathetic and parasympathetic outflow, and subsequently predicts the build up of an action potential at the sinus knot of the heart. In this paper, we analyze the nonlinear afferent model and show that the coupled model is able to predict heart rate regulation using blood pressure data as an input.

The impact of gravity during head-up tilt

The impact of gravity during head-up tilt, a test often used in the clinic to diagnose patients who suffer from dizziness or frequent episodes of syncope, is not well described. This study uses mathematical modeling to analyze experimental blood pressure data measured at the level of the aorta and the carotid sinuses in a healthy volunteer. During head-up tilt the head is lifted above the heart stimulating gravitational pooling of blood in the lower extremities. This shift in volume is followed by an increase in blood pressure in the lower body, while the pressure in the head decreases, while the pressure at the level of the heart is either constant or increases. At the same time, the normal response to head-up tilt is an increase in heart rate. The change in posture, and subsequent change in heart rate, is believed to be mediated via baroreflex inhibition. Traditional understanding of the baroreceptor system is that inhibition is a result of a blood pressure drop. However, only the carotid sinus blood pressure is decreased during head-up tilt, suggesting that the receptors at this location are more prominent than the receptors in the aortic arch. To explore this hypothesis further, we developed a model predicting hydrostatic height between the two locations. Results from this model were compared with measurements. Furthermore, we show, using a differential equations model predicting blood pressure, that it is possible to predict blood pressure measured at the level of the carotid sinuses using heart rate as an input. Finally, we discuss our results in relation to measurements obtained at the two locations.

The complex interaction between ocular perfusion pressure and ocular blood flow - relevance for glaucoma

Glaucoma is an optic neuropathy of unknown origin. The most important risk factor for the disease is an increased intraocular pressure (IOP). Reducing IOP is associated with reduced progression in glaucoma. Several recent large scale trials have indicated that low ocular perfusion pressure (OPP) is a risk factor for the incidence, prevalence and progression of the disease. This is a strong indicator that vascular factors are involved in the pathogenesis of the disease, a hypothesis that was formulated 150 years ago. The relation between OPP and blood flow to the posterior pole of the eye is, however, complex, because of a phenomenon called autoregulation. Autoregulatory processes attempt to keep blood flow constant despite changes in OPP. Although autoregulation has been observed in many experiments in the ocular vasculature the mechanisms underlying the vasodilator and vasoconstrictor responses in face of changes in OPP remain largely unknown. There is, however, recent evidence that the human choroid regulates its blood flow better during changes in blood pressure induced by isometric exercise than during changes in IOP induced by a suction cup. This may have consequences for our understanding of glaucoma, because it indicates that blood flow regulation is strongly dependent not only on OPP, but also on the level of IOP itself. Indeed there is data indicating that reduction of IOP by pharmacological intervention improves optic nerve head blood flow regulation independently of an ocular vasodilator effect.

Electrical properties with relaxation through human blood

The present work aims to study the effects of the blood-microstructure on the electrical conduction from two different but correlated properties: Electrical and mechanical (viscosity), and to derive useful parameters for the evaluation of electrical conduction as a function of the blood viscosity. ac-conductivity and dielectric constant of normal and diabetic blood are measured in the frequency range 10 kHz-1 MHz at the room temperature. An empirical relation relating the resistivity and viscosity of the blood has been presented. The results show that a microfluidic device is a viable and simple solution for determination of electrical and rheological behaviors of blood samples.

Sensitivity analysis and model assessment: mathematical models for arterial blood flow and blood pressure

The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523-1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.

Computational modelling of blood-flow-induced changes in blood electrical conductivity and its contribution to the impedance cardiogram

Studies have shown that blood-flow-induced change in electrical conductivity is of equal importance in assessment of the impedance cardiogram (ICG) as are volumetric changes attributed to the motion of heart, lungs and blood vessels. To better understand the sole effect of time-varying blood conductivity on the spatiotemporal distribution of trans-thoracic electric fields (i.e. ICG), this paper presents a segmented high-resolution (1 mm(3)) thoracic cardiovascular system, in which the time-varying pressures, flows and electrical conductivities of blood in different vessels are evaluated using a set of coupled nonlinear differential equations, red blood cell orientation and cardiac cycle functions. Electric field and voltage simulations are performed using two and four electrode configurations delivering a small alternating electric current to an anatomically realistic and electrically accurate model of modelled human torso. The simulations provide a three-dimensional electric field distribution and show that the time-varying blood conductivity alters the voltage potential difference between the electrodes by a maximum of 0.28% for a cardiac output of about 5 L min(-1). As part of a larger study, it is hoped that this initial model will be useful in providing improved insights into blood-flow-related spatiotemporal electric field variations and assist in the optimal placement of electrodes in impedance cardiography experiments.

Modeling cerebral blood flow and regulation

Cerebral autoregulation is a homeostatic mechanism which maintains blood flow despite changes in blood pressure in order to meet local metabolic demands. Several mechanisms play a role in cerebral autoregulation in order to adjust vascular tone and caliber of the cerebral vessels, but the exact etiology of the dynamics of these mechanism is not well understood. In this study, we discuss two patient specific models predicting cerebral blood flow velocity during postural change from sitting to standing. One model characterises cerebral autoregulation, the other describes the beat-to-beat distribution of blood flow to the major regions of the brain. Both models have been validated against experimental data from a healthy young subject.

Modeling perfusion in the cerebral vasculature

The constant perfusion of a human organ with nutrients and oxygen demands a robust regulatory mechanisms in the face of normal day-to-day pressure variations in the vasculature. The brain, in a similar manner to the heart requires this mechanism to be extremely quick acting, relative to other ways of altering perfusion such as varying systemic blood pressure, since oxygen depravation in the tissues of the brain can be tolerated for only of the order of tens of seconds before significant damage can be done. In recent years computational models, and it must be noted computer architecture have evolved to an extent where mathematicians and engineers can play a large part in discovering how the brain functions physiologically as well as investigating pathological conditions. This review will look at a number of increasingly complex computational models of blood flow to the brain and how variations in arterial geometry can influence the perfusion in the cerebral vasculature. Although these models have provided an insight into complex mechanisms the research area is densely populated with important questions that perhaps only computer models can answer. The review will indicate possible areas of investigation.

Modeling heart rate regulation--part II: parameter identification and analysis

In part I of this study we introduced a 17-parameter model that can predict heart rate regulation during postural change from sitting to standing. In this subsequent study, we focus on the 17 model parameters needed to adequately represent the observed heart rate response. In part I and in previous work (Olufsen et al. 2006), we estimated the 17 model parameters by minimizing the least squares error between computed and measured values of the heart rate using the Nelder-Mead method (a simplex algorithm). In this study, we compare the Nelder-Mead optimization method to two sampling methods: the implicit filtering method and a genetic algorithm. We show that these off-the-shelf optimization methods can work in conjunction with the heart rate model and provide reasonable parameter estimates with little algorithm tuning. In addition, we make use of the thousands of points sampled by the optimizers in the course of the minimization to perform an overall analysis of the model itself. Our findings show that the resulting least-squares problem has multiple local minima and that the non-linear-least squares error can vary over two orders of magnitude due to the complex interaction between the model parameters, even when provided with reasonable bound constraints.

The effects of ageing and passive heating on cardiorespiratory and cerebrovascular responses to orthostatic stress in humans

We tested the hypothesis that older adults, relative to younger adults, would be more prone to critical reductions in cerebral blood flow and oxygenation upon standing during passive heat stress. Six older (70+/-4 years, mean+/-s.d.) and six younger males (29+/-4 years) were heated (oesophageal temperature raised 0.5 degrees C) in a water-perfused suit. Blood flow velocity in the middle cerebral artery (MCAv), cerebral oxygenation, mean arterial pressure (MAP) and end-tidal partial pressure of carbon dioxide (PET,CO2) were measured continuously before and during 3 min standing in each thermal state. At supine normothermic baseline, MCAv was 47% lower in older participants (P<0.001), whilst MAP and cerebral oxygenation were similar between groups (P>0.05). Heating lowered the supine MAP more in younger adults, and elevated heart rate only in this group. Upon initial standing in normothermia, older participants had a greater drop in MCAv (P<0.05 versus young), a lesser drop in MAP (approximately 24 and approximately 42% in older and younger participants, respectively), but slower recovery of MAP (27.3+/-6.8 versus 18.6+/-4.7 s, mean+/-s.d., P=0.004); heating did not exacerbate any postural responses in either age group. During the last minute of standing, MCAv and PET,CO2 were lower in older participants, though age differences were not evident in cerebral oxygenation (normothermic or heated). Thus, independent of heat stress, in addition to lower resting MCAv, there are further age-related reductions in MCAv and slower corrections of MAP following standing. However, these asymptomatic changes seem to represent a physiologically acceptable insult which can be well tolerated in otherwise healthy older participants even during heat stress.

Bilateral transit time assessment of upper and lower limbs as a surrogate ankle brachial index marker

Ankle brachial index is useful in monitoring the pathogenesis of peripheral arterial occlusive diseases. Sphygmomanometer is the standard instrument widely used but frequent prolonged monitoring can be less comfortable for patients. Pulse transit time is known to be inversely correlated with blood pressure and a ratio-based pulse transit time measurement has been proposed as a surrogate ankle brachial index marker. In this study, 17 normotensive adults (9 men; aged 25.4 +/- 3.9 years) were recruited. Two postural change test activities were performed to induce changes in the stiffness of the arterial wall of the moved periphery. Results showed that only readings from the limbs that adopted a new posture registered significant blood pressure and pulse transit time changes (P < .05). Furthermore, there was significant correlation between the ankle brachial index and pulse transit time ratio measure for both test activities (R(2) > or = 0.704). The findings herein suggest that pulse transit time ratio is a surrogate and accommodating ankle brachial index marker.

Timing of caffeine's impact on autonomic and central nervous system measures: clarification of arousal effects

The timing of caffeine effects on arousal levels was examined. From previous work in our laboratory, an increase in skin conductance level (SCL) was used as the marker of arousal increase, and we sought to identify the timing of this and related effects following caffeine ingestion. A single oral dose of caffeine (250 mg) was used in a randomised double-blind placebo-controlled repeated-measures cross-over study. Eyes-closed resting electroencephalogram (EEG) and autonomic data (SCL, heart rate, respiration rate, and systolic and diastolic blood pressure) during 2 min epochs that commenced every 4 min after ingestion, were analysed. The SCL placebo data were used to identify potential arousal measures prior to examining caffeine effects. Caffeine was associated with increased SCL, increased respiratory rate and a global reduction in alpha power. There were no significant cardiovascular effects of caffeine-induced arousal. These caffeine results are consistent with our recent electrodermal and EEG studies of arousal, and confirm the potential use of caffeine as a simple means of experimentally modifying arousal levels without task-related confounds.

A computational approach to predict pulse transit time variations during postural change

The human autonomic nervous system modulates blood pressure (BP) and heart rate in order to maintain homeostasis. Present techniques that monitor BP may cause discomforts to children. Pulse transit time change (DeltaPTT) is known to be inversely correlated to BP change. In this study, a mathematical model using only a few empirical parameters and the measured lower limb vascular path length is introduced to estimate DeltaPTT when a different posture is adopted. To assess the reliability of the model, 23 healthy children aged 8.4 +/- 2.3 years were recruited to adopt the sitting and supine position at discrete intervals. PTT measurements were obtained from their toe with respect to an ECG for both postures. The results showed that there was significant correlation between the model and measured DeltaPTT (P < 0.05; R(2) = 0.813). The findings herein suggest that this simple yet practical model can have the accuracy to estimate the DeltaPTT value. Moreover, it does not require the use of an ECG or pulse oximeter in its computation. Hence, it can provide a rapid prediction before a child adopts a postural change. This may be potentially useful for detection of children with vascular abnormalities at their lower limbs.

Mathematical modeling of gravitational effects on the circulation: importance of the time course of venous pooling and blood volume changes in the lungs

A dip in blood pressure (BP) in response to head-up tilt (HUT) or active standing might be due to rapid pooling in the veins below the heart (preload) or muscle activation-induced drop in systemic vascular resistance (afterload). We hypothesized that, in the cardiovascular response to passive HUT, where, in contrast to active standing, little BP dip is observed, features affecting the preload play a key role. We developed a baroreflex model combined with a lumped-parameter model of the circulation, including viscoelastic stress-relaxation of the systemic veins. Cardiac contraction is modeled using the varying-elastance concept. Gravity affects not only the systemic, but also the pulmonary, circulation. In accordance with the experimental results, model simulations do not show a BP dip on HUT; the tilt-back response is also realistic. If it is assumed that venous capacities are steady-state values, the introduction of stress-relaxation initially reduces venous pooling. The resulting time course of venous pooling is comparable to measured impedance changes. When venous pressure-volume dynamics are neglected, rapid (completed within 30 s) venous pooling leads to a drop in BP. The direct effect of gravity on the pulmonary circulation influences the BP response in the first ∼5 s after HUT and tilt back. In conclusion, the initial BP response to HUT is mainly determined by the response of the venous system. The time course of lower body pooling is essential in understanding the response to passive HUT.

A bond graph model of the cardiovascular system

The study of the autonomic nervous system (ANS) function has shown to provide useful indicators for risk stratification and early detection on a variety of cardiovascular pathologies. However, data gathered during different tests of the ANS are difficult to analyse, mainly due to the complex mechanisms involved in the autonomic regulation of the cardiovascular system (CVS). Although model-based analysis of ANS data has been already proposed as a way to cope with this complexity, only a few models coupling the main elements involved have been presented in the literature. In this paper, a new model of the CVS, representing the ventricles, the circulatory system and the regulation of the CVS activity by the ANS, is presented. The models of the vascular system and the ventricular activity have been developed using the Bond Graph formalism, as it proposes a unified representation for all energetic domains, facilitating the integration of mechanic and hydraulic phenomena. In order to take into account the electro-mechanical behaviour of both ventricles, an electrophysiologic model of the cardiac action potential, represented by a set of ordinary differential equations, has been integrated. The short-term ANS regulation of heart rate, cardiac contractility and peripheral vasoconstriction is represented by means of continuous transfer functions. These models, represented in different continuous formalisms, are coupled by using a multi-formalism simulation library. Results are presented for two different autonomic tests, namely the Tilt Test and the Valsalva Manoeuvre, by comparing real and simulated signals.

Location and variability of epicardiac ganglia in human fetuses

The aim of the study was to determine the morphology of epicardiac ganglia in human fetuses at different stages of their development as these ganglia are considered to be of a pivotal clinical importance. Twenty-one fetal hearts were investigated applying a technique of histochemistry for acetylcholinesterase to visualize the epicardiac neural ganglionated plexus with its subsequent stereoscopic examination on total organs. In all of the examined fetuses, epicardiac neural plexus with numerous ganglia was well recognizable and could be clearly differentiated into seven ganglionated subplexuses, topography and structural organization of which were typical for hearts of adult human. The largest ganglion number comprising 77% of all counted ganglia was identified on the dorsal atrial surface. Fetal epicardiac plexus in gestation period of 15-40 weeks contained 929 +/- 62 ganglia, but ganglion amount did vary substantially from heart to heart. In conclusion, this study implies that the human fetal epicardiac ganglia occupy their definitive location already at gestation period from 15 weeks and their number as well as distribution on heart surface presumably is not age dependent.

Simulation of hemodynamic responses to the valsalva maneuver: an integrative computational model of the cardiovascular system and the autonomic nervous system

The Valsalva maneuver is a frequently used physiological test in evaluating the cardiovascular autonomic functions in human. Although a large pool of experimental data has provided substantial insights into different aspects of the mechanisms underlying the cardiovascular regulations during the Valsalva maneuver, so far a complete comprehension of these mechanisms and the interactions among them is unavailable. In the present study, a computational model of the cardiovascular system (CVS) and its interaction with the autonomic nervous system (ANS) was developed for the purpose of quantifying the individual roles of the CVS and the ANS in the hemodynamic regulations during the Valsalva maneuver. A detailed computational compartmental parameter model of the global CVS, a system of mathematical equations representing the autonomic nervous reflex regulatory functions, and an empirical cerebral autoregulation (CA) model formed the main body of the present model. Based on simulations of the Valsalva maneuvers at several typical postures, it was demonstrated that hemodynamic responses to the maneuver were not only determined by the ANS-mediated cardiovascular regulations, but also significantly affected by the postural-change-induced hemodynamic alterations preceding the maneuver. Moreover, the large-magnitude overshoot in cerebral perfusion immediately after the Valsalva maneuver was found to result from a combined effect of the circulatory autonomic functions, the CA, and the cerebral venous blood pressure.

Modeling baroreflex regulation of heart rate during orthostatic stress

During orthostatic stress, arterial and cardiopulmonary baroreflexes play a key role in maintaining arterial pressure by regulating heart rate. This study presents a mathematical model that can predict the dynamics of heart rate regulation in response to postural change from sitting to standing. The model uses blood pressure measured in the finger as an input to model heart rate dynamics in response to changes in baroreceptor nerve firing rate, sympathetic and parasympathetic responses, vestibulo-sympathetic reflex, and concentrations of norepinephrine and acetylcholine. We formulate an inverse least squares problem for parameter estimation and successfully demonstrate that our mathematical model can accurately predict heart rate dynamics observed in data obtained from healthy young, healthy elderly, and hypertensive elderly subjects. One of our key findings indicates that, to successfully validate our model against clinical data, it is necessary to include the vestibulo-sympathetic reflex. Furthermore, our model reveals that the transfer between the nerve firing and blood pressure is nonlinear and follows a hysteresis curve. In healthy young people, the hysteresis loop is wide, whereas, in healthy and hypertensive elderly people, the hysteresis loop shifts to higher blood pressure values, and its area is diminished. Finally, for hypertensive elderly people, the hysteresis loop is generally not closed, indicating that, during postural change from sitting to standing, baroreflex modulation does not return to steady state during the first minute of standing.

Dual-Channel Photoplethysmography to Monitor Local Changes in Vascular Stiffness

OBJECTIVES

Monitoring arterial distensibility changes is important to understand the cardiovascular status of patient. Pulse transit time (PTT), which is an inverse equivalent of pulse wave velocity (PWV), has shown its potential in such studies. However, its methodological approach in using an electrocardiogram and a peripheral photoplethysmography (PPG) is limited due to the inclusion of pre-ejection period (PEP) in its computation. Previous studies have suggested the using the transit time difference between two peripheral measuring sites (PTT-D) instead. However, it requires two medical instruments and may not be efficient in terms of equipment utility, especially in prolonged clinical studies.

METHODS

Postural changes are known to cause complex haemodynamics adaptation and thereby affecting transit time measurements. A customised dual-channel PPG system based on discrete electronic devices was constructed to evaluate against conventional peripheral-based PTT. 10 healthy adults (7 male; mean age 27.0 yr) were recruited to assess the differences observed in PTT and PTT-D during two postural change test activities.

RESULTS

PTT-D derived from the customised PPG system registered 43.3+/- 5.6 ms and - 31.1+/- 3.8 ms relative changes for the two regulated activities while conventional PTT recorded 43.6+/- 10.3 ms and -31.0+/-m 6.5 ms respectively. The former may have similar results but have significantly lower variance (< 0.05).

CONCLUSIONS

Findings herein suggest that PTT-D derived from the customised PPG system shows potential. It can be used as an alternative to conventional peripheral-based PTT and possibly as a direct assessment of arterial distensibility or PWV variations as it does not include PEP in its time-related computations.

Evaluation of blood pressure changes using vascular transit time

Imbalance of the human haemodynamic system can provide a prognosis of syncope, dizziness or hypertension. This can be assessed by monitoring its responses to postural change. Examining variations in blood pressure (BP) is deemed an effective means to identify symptoms of this associated condition. However, conventional methods do not promote prolonged monitoring due to the discomfort caused to patients. Established correlations between BP and pulse wave transmission have shown its usefulness in clinical applications. In this study, photoplethysmography and phonocardiography were used to estimate BP changes via observed variations in delay transmission or vascular transit time (VTT) at the upper limb. Thirty-one healthy adults (21 male) were recruited to perform three test activities, namely the arm held at heart level, fully raised up and held down. Association of the three BP indices and heart rate variations with transit time changes was then computed. The results showed that observed VTT changes were related to systolic BP (R(2) = 0.820; p < 0.05), diastolic BP (R(2) = 0.517; p < 0.05), mean arterial pressure (R(2) = 0.673; p < 0.05) and heart rate (R(2) = 0.000; p > 0.05). As systolic BP had the strongest correlation, a regression equation was formulated to associate the two parameters. The non-invasive measuring nature of VTT can be more accommodating to patients, especially during continual monitoring. Moreover, it has the added advantage that the pre-ejection period is not included in its time-related derivations.

Pulse transit time changes observed with different limb positions

Pulse transit time (PTT) is a non-invasive measure of arterial compliance. It can be used to assess instantaneous blood pressure (BP) changes in continual cardiovascular measurement such as during overnight respiratory sleep studies. In these studies, periodic changes in limb position can occur randomly. However, little is known about their possible effects on PTT monitored on the various limbs. The objective of this study was to evaluate PTT differences on all four limbs during two positional changes (lowering and raising of a limb). Ten healthy adults (seven male) with a mean age of 27.0 years were recruited in this study. The results showed that the limb that underwent a positional change had significant (p < 0.05) local PTT differences when compared to its nominal baseline value, whereas PTT changes in the other remaining limbs were insignificant (p > 0.05). The mean PTT value measured from a vertically-raised limb increased by 42.7 ms, while it decreased by 28.1 ms with a half-lowered limb. The PTT differences observed during positional change can be contributed to by the complex interactions between hydrostatic pressure changes, autonomic and local autoregulation experienced in these limbs. Hence the findings herein suggest that PTT is able to reflect local circulatory responses despite changes in the position of other limbs. This can be useful in prolonged clinical observations where limb movements are expected.