Assessing the strength of cardiac and sympathetic baroreflex controls via transfer entropy during orthostatic challenge

Vasoconstriction during non-hypotensive hypovolemia is not associated with activation of baroreflex: A causality-based approach

Non-hypotensive hypovolemia simulated with oscillatory lower body negative pressure in the range of -10 to -20 mmHg is associated with vasoconstriction {increase in total peripheral vascular resistance (TPVR)}. Due to the mechanical stiffening of vessels, there is a disjuncture of mechano-neural coupling at the level of arterial baroreceptors which has not been investigated. The study was designed to quantify both the cardiac and vascular arms of the baroreflex using an approach based on Wiener-Granger causality (WGC) - partial directed coherence (PDC). Thirty-three healthy human volunteers were recruited and continuous heart rate and blood pressure {systolic (SBP), diastolic (DBP), and mean (MBP)} were recorded. The measurements were taken in resting state, at -10 mmHg (level 1) and -15 mmHg (level 2). Spectral causality - PDC was estimated from the MVAR model in the low-frequency band using the GMAC MatLab toolbox. PDC from SBP and MBP to RR interval and TPVR was calculated. The PDC from MBP to RR interval showed no significant change at -10 mmHg and -15 mmHg. No significant change in PDC from MBP to TPVR at -10 mmHg and -15 mmHg was observed. Similar results were obtained for PDC estimation using SBP as input. However, a significant increase in TPVR from baseline at both levels of oscillatory LBNP (p-value <0.001). No statistically significant change in PDC from blood pressure to RR interval and blood pressure to TPVR implies that vasoconstriction is not associated with activation of the arterial baroreflex in ≤-15 mmHg LBNP. Thereby, indicating the role of cardiopulmonary reflexes during the low level of LBNP simulated non-hypotensive hypovolemia.

Assessing Correlation between Heart Rate Variability Markers Based on Laguerre Expansion and Direct Measures of Sympathetic Activity during Incremental Head-up Tilt

Traditional frequency domain analysis of heart period (HP) variability allows the estimation of the parasympathetic modulation directed to the heart but the sympathetic one remains largely unknown. Recently, sympathetic and parasympathetic activity indexes (SAI and PAI) have been proposed to address this issue. SAI and PAI were derived from HP variability via the application of an orthonormal Laguerre expansion allowing the separation of HP variations driven by sympathetic and parasympathetic outflows. In this study, SAI and PAI were validated against tonic and variability measures of muscle sympathetic nerve activity (MSNA) and more traditional markers derived from HP variability. Indexes were calculated in 12 healthy subjects (9 females, age from 20 to 36 years, median 22.5 years) undergoing incremental head-up tilt. Results showed that traditional HP and MSNA variability markers as well as SAI and PAI were modified in proportion to the magnitude of the postural challenge. However, SAI was not correlated with any MSNA markers and PAI was not linked to respiratory sinus arrhythmia. SAI and PAI can capture modifications of cardiac control induced by the orthostatic challenge but they might be weak surrogates of vagal and sympathetic activities and/or modulations.Clinical Relevance- SAI and PAI markers are useful to characterize cardiac control but poorly linked with autonomic nervous system state.

The cardiac, vasomotor, and myocardial branches of the baroreflex in fibromyalgia: Associations with pain, affective impairments, sleep problems, and fatigue

This study investigated the cardiac, vasomotor, and myocardial branches of the baroreflex in fibromyalgia using the spontaneous sequence method. Systolic blood pressure (SBP), interbeat interval (IBI), stroke volume (SV), pre-ejection period (PEP), and total peripheral resistance (TPR) were continuously recorded in 40 fibromyalgia patients and 30 healthy individuals during a cold pressor test and a mental arithmetic task. Sequences of covariation between SBP and IBI (cardiac branch), SV and PEP (myocardial branch), and TPR (vasomotor branch) were identified. Baroreflex sensitivity (BRS) was represented by the slope of the regression line between values in the sequences; baroreflex effectiveness (BEI) was indexed by the proportion of progressive SBP changes that elicited reflex responses. Patients exhibited lower BRS in the three branches, lower BEI in the cardiac and vasomotor branches, and reduced reactivity in cardiac BRS and BEI, SBP, IBI, SV, and PEP. Moreover, BRS and BEI were inversely related to clinical pain, cold pressor pain, depression, trait anxiety, sleep problems, and fatigue. Reduced function of the three baroreflex branches implies diminished resources for autonomic inotropic, chronotropic, and vascular regulation in fibromyalgia. Blunted stress reactivity indicates a limited capacity for autonomic cardiovascular adjustment to situational requirements. The associations of BRS and BEI with pain perception may reflect the antinociceptive effects arising from baroreceptor afferents, where reduced baroreflex function may contribute to the hyperalgesia characterizing fibromyalgia. The associations with affective impairments, sleep problems, and fatigue suggest that baroreflex dysfunctions are also involved in the secondary symptoms of the disorder.

Vascular resistance arm of the baroreflex: methodology and comparison with the cardiac chronotropic arm

Baroreflex response consists of cardiac chronotropic (effect on heart rate), cardiac inotropic (on contractility), venous (on venous return) and vascular (on vascular resistance) arms. Because of the simplicity of its measurement, the cardiac chronotropic arm is most often analyzed. The aim was to introduce a method to assess the vascular baroreflex arm and to characterize its changes during stress. We evaluated the effect of orthostasis and mental arithmetics (MA) in 39 (22 women, 17 men; median age: 18.7 yr) and 36 (21 women, 15 men; 19.2 yr) healthy volunteers, respectively. We recorded systolic (SBP) and mean (MBP) blood pressure by volume-clamp method and R-R interval (RR) by ECG. Cardiac output (CO) was recorded by impedance cardiography. From MBP and CO, peripheral vascular resistance (PVR) was calculated. The directional spectral coupling and gain of cardiac chronotropic (SBP to RR) and vascular (SBP to PVR) arms were quantified. The strength of the causal coupling from SBP to PVR was significantly higher than that of SBP to RR coupling over the whole protocol (P < 0.001). Along both arms, the coupling was higher during orthostasis compared with the supine position (P < 0.001 and P = 0.006); no MA effect was observed. No significant changes in the spectral gain (ratio of RR or PVR change to a unit SBP change) across all phases were found (0.111 ≤ P ≤ 0.907). We conclude that changes in PVR are tightly coupled with SBP oscillations via the baroreflex, providing an approach for baroreflex vascular arm analysis with the potential to reveal new aspects of blood pressure dysregulation.NEW & NOTEWORTHY Baroreflex response consists of several arms, but the cardiac chronotropic arm (blood pressure changes evoking heart rate response) is usually analyzed. This study introduces a method to assess the vascular baroreflex arm with the continuous noninvasive measurement of peripheral vascular resistance as an output considering causality in the interaction between oscillations and slower dynamics of vascular tone changes. We conclude that although vascular baroreflex arm involvement becomes dominant during orthostasis, gain of this interaction is relatively stable.

Transfer Entropy in Artificial and Cardiovascular Environment in Stress

The paper examines the influence of acute and chronic stress on the relationship between systolic blood pressure (SBP) and pulse interval (PI) recorded from laboratory rats with different genetic predispositions for the development of the hypertensive disease. Transfer entropy (TE) was used to examine the direction of information flow between SBP and PI, spontaneous baroreflex sensitivity (BRS) was used to evaluate the ability of adaptation of PI time series to changes in SBP, and the cross-approximate entropy (XApEn) to quantify the SBP-PI synchronization. The effects of the time series length on TE estimation was also investigated in an artificial environment for the time series without a strong causal relation. The consistency of the TE estimation was achieved only for extremely long time series. The results showed that chronic stress influence on the increase in information transmission between SBP and PI (TE) while changes of (BRS) and XApEn were not noticed.

Information-domain method for the quantification of the complexity of the sympathetic baroreflex regulation in healthy subjects and amyotrophic lateral sclerosis patients

BACKGROUND

The sympathetic baroreflex (sBR) adjusts muscle sympathetic nerve activity (MSNA) in response to arterial pressure changes but the relevance of assessing sBR control complexity is unclear.

OBJECTIVE

We propose a method for the evaluation of sBR control complexity.

APPROACH

The approach comprises the quantification of complexity of the sBR latency regulation and the assessment of complexity of the relationship linking MSNA burst to R-wave peak regardless of the variability of the sBR latency. The Shannon entropy (SE) of the sBR latency distribution is taken as an estimate of complexity of the sBR latency regulation. The conditional entropy (CE) of the beat-to-beat binary series obtained by coding the presence/absence of the MSNA burst after an R-wave peak is taken as an estimate of complexity of the sBR control regardless of the sBR latency variability. Surrogate analysis was utilized to set the level of inactive or impaired sBR. The approach was applied to 10 young healthy subjects undergoing head-up tilt (HUT) followed by lower body negative pressure to evoke presyncope (preSYNC) before and after 21 d head-down bed rest (HDBR), and to five amyotrophic lateral sclerosis (ALS) patients undergoing HUT.

MAIN RESULTS

In healthy subjects the surrogate analysis suggested that HUT and preSYNC significantly activated the sBR control but its response was weakened after 21 d HDBR. During preSYNC sBR latency increased significantly only after 21 d HDBR. In ALS patients the complexity of the sBR latency regulation was close to the level set by surrogate analysis and HUT did not trigger any sBR control response.

SIGNIFICANCE

The proposed method for sBR control complexity quantification was useful in detecting the impairment of the sBR control after 21 d HDBR in healthy subjects and the dysfunction of the sBR regulation in ALS patients.

Characterization of the Asymmetry of the Cardiac and Sympathetic Arms of the Baroreflex From Spontaneous Variability During Incremental Head-Up Tilt

Hysteresis of the baroreflex (BR) is the result of the different BR sensitivity (BRS) when arterial pressure (AP) rises or falls. This phenomenon has been poorly studied and almost exclusively examined by applying pharmacological challenges and static approaches disregarding causal relations. This study inspects the asymmetry of the cardiac BR (cBR) and vascular sympathetic BR (sBR) in physiological closed loop conditions from spontaneous fluctuations of physiological variables, namely heart period (HP) and systolic AP (SAP) leading to the estimation of cardiac BRS (cBRS) and muscle sympathetic nerve activity (MSNA) and diastolic AP (DAP) leading to the estimation of vascular sympathetic BRS (sBRS). The assessment was carried out in 12 young healthy subjects undergoing incremental head-up tilt with table inclination gradually increased from 0 to 60°. Two analytical methods were exploited and compared, namely the sequence (SEQ) and phase-rectified signal averaging (PRSA) methods. SEQ analysis is based on the detection of joint causal schemes representing the HP and MSNA burst rate delayed responses to spontaneous SAP and DAP modifications, respectively. PRSA analysis averages HP and MSNA burst rate patterns after aligning them according to the direction of SAP and DAP changes, respectively. Since cBRSs were similar when SAP went up or down, hysteresis of cBR was not detected. Conversely, hysteresis of sBR was evident with sBRS more negative when DAP was falling than rising. sBR hysteresis was no longer visible during sympathetic activation induced by the orthostatic challenge. These results were obtained via the SEQ method, while the PRSA technique appeared to be less powerful in describing the BR asymmetry due to the strong association between BRS estimates computed over positive and negative AP variations. This study suggests that cBR and sBR provide different information about the BR control, sBR exhibits more relevant non-linear features that are evident even during physiological changes of AP, and the SEQ method can be fruitfully exploited to characterize the BR hysteresis with promising applications to BR branches different from cBR and sBR.

Transfer Information Assessment in Diagnosis of Vasovagal Syncope Using Transfer Entropy

The paper presents an application of Transfer Entropy (TE) to the analysis of information transfer between biosignals (heart rate expressed as R-R intervals (RRI), blood pressure (sBP, dBP) and stroke volume (SV)) measured during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised of 80 patients who were divided into two groups: the HUTT(+) group consisting of 57 patients who developed syncope during the passive phase of the test and HUTT(-) group consisting of 23 patients who had a negative result of the passive phase and experienced syncope after provocation with nitroglycerin. In both groups the information transfer depends on the phase of the tilt test. In supine position the highest transfer occurred between driver RRI and other components. In upright position it is the driver sBP that plays the crucial role. The pre-syncope phase features the highest information transfer from driver SV to blood pressure components. In each group the comparisons of TE between different phases of HUT test showed significant differences for RRI and SV as drivers.

The Interaction Analysis between the Sympathetic and Parasympathetic Systems in CHF by Using Transfer Entropy Method

Congestive heart failure (CHF) is a cardiovascular disease associated with autonomic dysfunction, where sympathovagal imbalance was reported in many studies using heart rate variability (HRV). To learn more about the dynamic interaction in the autonomic nervous system (ANS), we explored the directed interaction between the sympathetic nervous system (SNS) and the parasympathetic nervous system (PNS) with the help of transfer entropy (TE). This article included 24-h RR interval signals of 54 healthy subjects (31 males and 23 females, 61.38 ± 11.63 years old) and 44 CHF subjects (8 males and 2 females, 19 subjects' gender were unknown, 55.51 ± 11.44 years old, 4 in class I, 8 in class II and 32 in class III~IV, according to the New York Heart Association Function Classification), obtained from the PhysioNet database and then segmented into 5-min non-overlapping epochs using cubic spline interpolation. For each segment in the normal group and CHF group, frequency-domain features included low-frequency (LF) power, high-frequency (HF) power and LF/HF ratio were extracted as classical estimators of autonomic activity. In the nonlinear domain, TE between LF and HF were calculated to quantify the information exchanging between SNS and PNS. Compared with the normal group, an extreme decrease in LF/HF ratio (p = 0.000) and extreme increases in both TE(LF→HF) (p = 0.000) and TE(HF→LF) (p = 0.000) in the CHF group were observed. Moreover, both in normal and CHF groups, TE(LF→HF) was a lot greater than TE(HF→LF) (p = 0.000), revealing that TE was able to distinguish the difference in the amount of directed information transfer among ANS. Extracted features were further applied in discriminating CHF using IBM SPSS Statistics discriminant analysis. The combination of the LF/HF ratio, TE(LF→HF) and TE(HF→LF) reached the highest screening accuracy (83.7%). Our results suggested that TE could serve as a complement to traditional index LF/HF in CHF screening.

Peripheral Resistance Baroreflex During Incremental Bicycle Ergometer Exercise: Characterization and Correlation With Cardiac Baroreflex

The arm of the baroreflex (BR) controlling peripheral resistances (PR), labeled as BR of PR (prBR), was characterized through an extension of the cardiac BR (cBR) sequence analysis. The method exploits recordings of skin blood flow (SBF) from the palm of the non-dominant hand via a laser Doppler flowmeter and of arterial pressure (AP) from the middle finger of the same hand via a plethysmographic device. PR was estimated beat-by-beat as the ratio of mean AP to mean SBF computed over the same heart period (HP). Peripheral resistances-diastolic arterial pressure (PR-DAP) sequences featuring simultaneous increases of PR and decreases of diastolic AP (DAP) or vice versa were identified and the slope of the regression line in the (DAP, PR) plane was taken as an estimate of prBR sensitivity (BRS_prBR). The percentage of prBR sequences (SEQ%_prBR) was taken as a measure of prBR involvement and the prBR effectiveness index (EI_prBR) was computed as the fraction of DAP sequences capable to drive antiparallel PR variations. Analogous markers were computed over cBR from HP and systolic AP (SAP) variability [i.e., cBR sensitivity (BRS_cBR), percentage of cBR sequences (SEQ%_cBR)_, and effectiveness index of the cBR (EI_cBR)]. prBR and cBR were typified during incremental light-to-moderate bicycle ergometer exercise at 10, 20, and 30% of the maximum effort in 16 healthy subjects (aged from 22 to 58 years, six males). We found that: (i) BRS_cBR decreased gradually with the challenge, while BRS_prBR declined only at the heaviest workload; (ii) SEQ%_cBR decreased solely at the lightest workload, while the decline of SEQ%_prBR was significant regardless of the intensity of the challenge; (iii) EI_prBR and EI_cBR were not affected by exercise; (iv) after pooling together all the data regardless of the experimental conditions, BRS_prBR and BRS_cBR were uncorrelated, while SEQ%_cBR and SEQ%_prBR as well as EI_cBR and EI_prBR, were significantly and positively correlated; (v) when the correlation between SEQ%_cBR and SEQ%_prBR and between EI_cBR and EI_prBR was assessed separately in each experimental condition, it was not systematically detected. This study suggests that prBR characterization provides information complementary to cBR that might be fruitfully exploited to improve patients' risk stratification.

Role of respiration in the cardiovascular response to orthostatic and mental stress

The objective of this study was to determine the response of heart rate and blood pressure variability (respiratory sinus arrhythmia, baroreflex sensitivity) to orthostatic and mental stress, focusing on causality and the mediating effect of respiration. Seventy-seven healthy young volunteers (46 women, 31 men) aged 18.4 ± 2.7 yr underwent an experimental protocol comprising supine rest, 45° head-up tilt, recovery, and a mental arithmetic task. Heart rate variability and blood pressure variability were analyzed in the time and frequency domain and modeled as a multivariate autoregressive process where the respiratory volume signal acted as an external driver. During head-up tilt, tidal volume increased while respiratory rate decreased. During mental stress, breathing rate increased and tidal volume was elevated slightly. Respiratory sinus arrhythmia decreased during both interventions. Baroreflex function was preserved during orthostasis but was decreased during mental stress. While sex differences were not observed during baseline conditions, cardiovascular response to orthostatic stress and respiratory response to mental stress was more prominent in men compared with women. The respiratory response to the mental arithmetic tasks was more prominent in men despite a significantly higher subjectively perceived stress level in women. In conclusion, respiration shows a distinct response to orthostatic versus mental stress, mediating cardiovascular variability; it needs to be considered for correct interpretation of heart rate and blood pressure phenomena.

Non-linear Heart Rate and Blood Pressure Interaction in Response to Lower-Body Negative Pressure

Early detection of hemorrhage remains an open problem. In this regard, blood pressure has been an ineffective measure of blood loss due to numerous compensatory mechanisms sustaining arterial blood pressure homeostasis. Here, we investigate the feasibility of causality detection in the heart rate and blood pressure interaction, a closed-loop control system, for early detection of hemorrhage. The hemorrhage was simulated via graded lower-body negative pressure (LBNP) from 0 to -40 mmHg. The research hypothesis was that a significant elevation of causal control in the direction of blood pressure to heart rate (i.e., baroreflex response) is an early indicator of central hypovolemia. Five minutes of continuous blood pressure and electrocardiogram (ECG) signals were acquired simultaneously from young, healthy participants (27 ± 1 years, N = 27) during each LBNP stage, from which heart rate (represented by RR interval), systolic blood pressure (SBP), diastolic blood pressure (DBP), and mean arterial pressure (MAP) were derived. The heart rate and blood pressure causal interaction (RR↔SBP and RR↔MAP) was studied during the last 3 min of each LBNP stage. At supine rest, the non-baroreflex arm (RR→SBP and RR→MAP) showed a significantly (p < 0.001) higher causal drive toward blood pressure regulation compared to the baroreflex arm (SBP→RR and MAP→RR). In response to moderate category hemorrhage (-30 mmHg LBNP), no change was observed in the traditional marker of blood loss i.e., pulse pressure (p = 0.10) along with the RR→SBP (p = 0.76), RR→MAP (p = 0.60), and SBP→RR (p = 0.07) causality compared to the resting stage. Contrarily, a significant elevation in the MAP→RR (p = 0.004) causality was observed. In accordance with our hypothesis, the outcomes of the research underscored the potential of compensatory baroreflex arm (MAP→RR) of the heart rate and blood pressure interaction toward differentiating a simulated moderate category hemorrhage from the resting stage. Therefore, monitoring baroreflex causality can have a clinical utility in making triage decisions to impede hemorrhage progression.

Mathematical methods in medicine: neuroscience, cardiology and pathology

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.