Effect of Age on Complexity and Causality of the Cardiovascular Control: Comparison between Model-Based and Model-Free Approaches

Abstract

The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related modifications of complexity and causality in healthy humans in supine resting (REST) and during standing (STAND). We found that: 1) MF approaches are more efficient than the MB method when nonlinear components are present, while the reverse situation holds in presence of high dimensional embedding spaces; 2) the CE method is the least powerful in detecting age-related trends; 3) the association of HP complexity on age suggests an impairment of cardiac regulation and response to STAND; 4) the relation of SAP complexity on age indicates a gradual increase of sympathetic activity and a reduced responsiveness of vasomotor control to STAND; 5) the association from SAP to HP on age during STAND reveals a progressive inefficiency of baroreflex; 6) the reduced connection from HP to SAP with age might be linked to the progressive exploitation of Frank-Starling mechanism at REST and to the progressive increase of peripheral resistances during STAND; 7) at REST the diminished association from RESP to HP with age suggests a vagal withdrawal and a gradual uncoupling between respiratory activity and heart; 8) the weakened connection from RESP to SAP with age might be related to the progressive increase of left ventricular thickness and vascular stiffness and to the gradual decrease of respiratory sinus arrhythmia.

Cardiovascular control in women with fibromyalgia syndrome: do causal methods provide nonredundant information compared with more traditional approaches?

“…During the active standing, the CG presented a reduction in the BRS gain, which was not observed in FMS patients, since their baroreflex gain was already low in supine posture. The reason to use the ␣ CL and the CR SAP¡HP indices in the present study is due to the fact that they measure different aspects of a relation between variables (18,22). Whereas the CR SAP¡HP estimates the strength of the causal link from SAP to HP, thus quantifying the degree of involvement of the baroreflex (22), ␣ CL estimates the gain of relation from SAP to HP, i.e., the magnitude of the HP variation in response to a unit SAP change.…”

“…The reason to use the ␣ CL and the CR SAP¡HP indices in the present study is due to the fact that they measure different aspects of a relation between variables (18,22). Whereas the CR SAP¡HP estimates the strength of the causal link from SAP to HP, thus quantifying the degree of involvement of the baroreflex (22), ␣ CL estimates the gain of relation from SAP to HP, i.e., the magnitude of the HP variation in response to a unit SAP change. As a general rule, BRS indexes should be considered reliably assessed only when the baroreflex is active, i.e., when the strength of the relation from SAP to HP is significant.…”

“…A Granger causality approach (18,20,22) was utilized to assess, through the calculation of the causality ratio (CR), the strength of the causal relation from SAP to HP (CR SAP¡HP) and from HP to SAP (CRHP¡SAP) variability series in ⍀. In this context, SAP is said to Granger-cause HP if the HP dynamics can be better predicted in ⍀ than in ⍀ ϭ {HP, SAP, RESP} after exclusion of SAP (i.e., ⍀‫گ‬SAPϭ{HP, RESP}) (8).…”

“…However, these approaches to the quantification of BRS have many methodological drawbacks. The most relevant one is the inability to account for causality, thus merging the feedforward pathway from HP to SAP, which is related more to the mechanical properties of the heart and dynamical properties of circulatory system, to the feedback pathway, which is more related to cardiac baroreflex (18,23).In an attempt to overcome this issue, model-based causal closed-loop methods (1, 9, 13, 28), and more recently, a Granger causality approach have been proposed (18,20,22). These methods have been shown to provide complementary information to that obtained by traditional indices about the cardiovascular autonomic regulation.…”

“…In an attempt to overcome this issue, model-based causal closed-loop methods (1, 9, 13, 28), and more recently, a Granger causality approach have been proposed (18,20,22). These methods have been shown to provide complementary information to that obtained by traditional indices about the cardiovascular autonomic regulation.…”