Michele Sorelli

Spatial heterogeneity in the time and frequency properties of skin perfusion

Pathological alterations of the microcirculatory system can be identified by measuring the temporal and spectral properties of laser Doppler flowmetry (LDF) signals acquired on the skin, and their changes following physiological stimulation. A wide range of stimulation protocols and measurement locations is observed in literature. Researchers often use non-invasive stimulation techniques, such as post-occlusive hyperaemia, cold tests, and local heating. As concerns the stimulation/recording sites, the forearm, fingers, and toes are typically selected to conduct microcirculation studies. However, recent clinical investigations showed that different anatomical sites present dissimilar blood flow patterns. Therefore, studies involving the comparison of LDF data, obtained from various anatomical locations, and thus subjected to the intrinsic heterogeneity of the microcirculation, may be methodologically inaccurate. At the moment, no consensus has been reached upon the optimal measurement location, the stimulation pattern, and the physiological parameters of interest. The aim of this study is to quantitatively characterize the heterogeneity of the peripheral perfusion at different anatomical locations: the index finger, the forearm, and the hallux. The skin microvascular system exhibits a complex vasodilatory response in the temporal domain, upon local heating. This physiological reactive hyperaemia comprises two effects: a fast transient response, correlated to neural activation, named axon reflex, followed by a slower hyperaemic plateau, mediated by the release of nitric oxide. In this work, we compare the vasodilatory reaction to heating at the different sites, based on a parametric representation of the perfusion signal. Moreover, skin blood flow is characterized by several components fluctuating at different time scales. Time-frequency decomposition of LDF signals allows to quantitatively evaluate the relative contribution of known physiological mechanisms to the regulation of the peripheral circulation. For this reason, we analyze the wavelet transform coefficients of LDF signals at baseline, to assess potential spatial heterogeneities of the perfusion power spectra among the aforementioned anatomical locations.

Cardiac pulse waves modeling and analysis in laser Doppler perfusion signals of the skin microcirculation

Blood pulse waveform relates to the physical properties of the circulatory system, and carries valuable hemodynamic information for the management of cardiovascular patients. In this paper, we present a modeling technique to reconstruct and characterize the cardiac-related pulse waves, observed in laser Doppler flowmetry signals of the peripheral skin perfusion. We tested the sensitivity of the proposed model to physiological alterations of the vascular system, investigating the effect of ageing on a set of parameters describing the reconstructed pulse waves. Waveform data collected from a set of 56 subjects demonstrate the existence of a significant correlation between ageing and the shape of the peripheral perfusion pulse waves, and indicate a possible relationship with the mechanical properties of the vascular tree.

Particle tracking for the assessment of microcirculatory perfusion

In recent years the development of portable microscopes, which enable the noninvasive bedside evaluation of the sublingual microcirculation in critically ill patients, has expanded the clinical research on this level of the cardiovascular system. Several semi-quantitative scores have been defined in order to provide researchers with a standardized framework for the offline assessment of the microcirculation status. Among those, space-time diagrams (STDs) constitute an established method for obtaining an estimate of the red blood cells (RBCs) flow velocity in capillaries. However, STDs have the drawback of being time-consuming, inherently subjective, and difficult to manage when the flow is not regular. OBJECTIVE In this work we propose an automated method for calculating erythrocyte flow speed, aiming to provide a fast and objective tool for the evaluation of peripheral blood perfusion. APPROACH The proposed method exploits an image segmentation module for estimating the positions of candidate flowing cells. A multi-object tracking algorithm based on Kalman filters analyzes and matches the positions corresponding to specific erythrocytes within consecutive frames. Thus, the output of the filter enables to estimate the displacement of each cell, yielding their instantaneous speed. MAIN RESULTS The method has been validated against the results obtained by the manual analysis of STDs, proving a good agreement for speeds up to 300 μm s-1. At higher speeds, RBC tracking becomes unstable due to the currently limited video acquisition rate (25 Hz) of state-of-the-art devices, that makes the matching between objects appearing in consecutive frames very challenging.

A mathematical model of the effect of metabolic control on joint mobility in youngtype 1 diabetic subjects

Diabetes mellitus is a metabolic disorder representing one of the main problems for the global public health. The impairment of metabolic control can influence periarticular tissue and other major risk factors of limited joint mobility (LJM) also in young type 1 diabetic patients. LJM is a widespread phenomenon in diabetic patients and it is often characterized by ankle stiffness. In particular, a deficit of ankle joint mobility may occur with the onset of the disease; later, this deficit tends to deteriorate in presence of a poor glycemic control. We hypothesized a mathematical model of diabetes mellitus long-term effects, assuming that a reduced metabolic control affects joint mobility according with a Gaussian function: it requires some time for developing a reduction of joint mobility, that persists for a stable period, before fading out with time (in case metabolic control has been recovered). A non-linear optimization estimated the model parameters for obtaining the best fit over a set of patients. Results are in good accordance with empirical estimates: lack of control needs to persist for at least a few months before generating a sensible effect, that persists for up to one year.

Modeling of the Microvascular Pulse for Tracking the Vasoconstriction Response to Deep Inspiratory Gasp

This work demonstrates the suitability of a microvascular pulse decomposition algorithm (PDA) for evaluating the vasoconstriction response to a deep inspiratory gasp (DIG). Synchronous ECG, respiratory, and laser Doppler flowmetry (LDF) signals of 13 healthy subjects (age: 26 \( \pm \) 3 years) were analyzed, and a four-Gaussian PDA was applied to reconstruct the LDF heartbeat pulsations. To assess the tracking of the transient vasoconstriction, the goodness-of-fit achieved during the DIG was compared with the performance at baseline. Moreover, the heart rate (HR) derived from the model’s systolic component was validated against the ECG, comparing the agreement with the one obtained from the wavelet transform analysis (WTA) of the LDF signal. The model’s normalized root-mean-square error and average \( {\text{R}}^{2} \) did not decrease during the DIG (p = 0.249, p = 0.552), and a nearly optimal pulse modeling accuracy was maintained (p = 0.286). Furthermore, the proposed PDA could better reproduce the reference HR than WTA, with a 46.8% reduction of the median root-mean-square error (p < 0.001), which did not worsen during the DIG (p = 0.861). Therefore, this method might find valuable application in the evaluation of neurovascular deterioration.

Multi-gaussian Decomposition of the Microvascular Pulse Detects Alterations in Type 1 Diabetes

Among diabetic patients, microangiopathy represents a relevant cause of morbidity and mortality. Diabetes induces detrimental changes in the biomechanical characteristics of blood microvessels, and fuels the development of a dysfunctional vascularization. Since the structural properties of the circulatory system affect the microvascular pulse, the aim of this study was to detect these vascular alterations through a model-based quantitative analysis of its waveform. Baseline microvascular perfusion was recorded on the hallux with a laser Doppler flowmeter. 54 healthy subjects (age: 34 ± 26 years) and 22 type 1 diabetic (T1D) patients without known cardiovascular complications and smoking history (age: 34 ± 17 years) were compared. A novel multi-Gaussian decomposition algorithm was applied to reconstruct the heartbeat-related oscillations, which were evaluated according to normalized and physiologically-motivated shape descriptors. Eight out of the nine properties assessed significantly differed between the groups (p < 0.001), indicating that the proposed pulse modeling method is sensitive to the effects of T1D on the peripheral perfusion.

Wavelet Phase Coherence Between the Microvascular Pulse Contour and the Respiratory Activity

A wavelet phase coherence (WPC) analysis was conducted in order to evaluate the time-phase relationships between the respiratory activity and the pulse of the peripheral perfusion. The investigation involved a group of 21 young healthy subjects, aged from 20 to 30 years. Cutaneous perfusion was measured by laser Doppler flowmetry, while breathing was simultaneously monitored with a wearable chest band. A multi-Gaussian modeling algorithm was used to decompose the pulse waveform thus enabling the separate characterization of the forward-travelling systolic pulse and the diastolic components arising from vascular impedance mismatch. The WPC between model-derived shape features and the breathing rhythm was assessed, to determine whether their characteristic oscillations were somehow synchronized. In 17 subjects a significant degree of phase coherence was detected in the respiratory frequency band for the area beneath the diastolic phase of the cardiac pulse. This result indicates that the microvascular reflection waves exhibit a marked periodicity linked to the breathing activity.

Glycemic Control Maintained over Time and Joint Stiffness in Young Type 1 Patients: What Is the Mathematical Relationship?

Background: It is widely known that diabetes can induce stiffness and adversely affect joint mobility even in young patients with type 1 diabetes mellitus (T1D). The aim of this study was to identify a mathematical model of diabetes mellitus long-term effects on young T1D patients. Methods: Ankle joint mobility (AJM) was evaluated using an inclinometer in 48 patients and 146 healthy, sex- BMI-, and age-matched controls. Assuming time invariance and linear superposition of the effects of hyperglycemia, the influence of T1D on AJM was formalized as an impulse response putting into relationship past supernormal HbA1c concentrations with the ankle total range of motion. The proposed model was identified by means of a nonlinear evolutionary optimization algorithm. Results: AJM was significantly reduced in young T1D patients (P < .001). AJM in both plantar and dorsiflexion was significantly lower in subjects with diabetes than in controls (P < .001). The identified impulse response indicates that impaired metabolic control requires 3 months to bring out its maximum effect on the reduction of AJM, while the following long-lasting decay phase with the expected AJM recovery times, normally depends on the slow turnover of collagen. HbA1c concentration levels above 7.2% are sufficient to produce a reduction of ankle ROM. Conclusions: In young patients with T1D the lack of glycemic control over time affects AJM. HbA1c levels can serve as a relevant prognostic factor for assessing the progression of LJM in subjects with diabetes.

Evaluation of spatial distribution of skin blood flow using optical imaging

The utilization of optical imaging for the analysis and modeling of microcirculatory flow patterns is raising significant interest. This work focuses on the analysis of the alterations in the spatial distribution of blood flow caused by exposing the skin at a variable temperature. In optical imaging, the measurement of local perfusion at pixel level is not reliable because of the very low signal to noise ratio (SNR) of the resulting signal. To cope with this limitation, a reference signal of pulsatile blood flow is computed by averaging a large region of skin, thus obtaining an improved SNR. Then, for each pixel, we estimate the time shift between the local blood pulse wave and the reference signal, evaluating the peak of the correlation function between the two signals. An image representing the spatial distribution of the time delay is thus created.Textural parameters derived from cooccurrence matrices and from fractal analysis show that both skin heating and cooling produce alterations of the spatial distribution of blood perfusion.