Gene transfer of integration defective anti-HSV-1 meganuclease to human corneas ex vivo.

Corneal graft rejection is a major problem in chronic herpetic keratitis (HK) patients with latent infection. A new class of antiviral agents targeting latent and active forms of herpes simplex virus type 1 (HSV-1) is importantly required. Meganucleases are sequence-specific homing endonucleases capable of inducing DNA double-strand breaks. A proof-of-concept experiment has shown that tailor-made meganucleases are efficient against HSV-1 in vitro. To take this work a step forward, we hypothesized that the pre-treatment of human corneas in eye banks using meganuclease-encoding vectors will allow HK patients to receive a medicated cornea to resist the recurrence of the infection and the common graft rejection problem. However, this strategy requires efficient gene delivery to human corneal endothelium. Using recombinant adeno-associated virus, serotype 2/1 (rAAV2/1), efficient gene delivery of a reporter gene was demonstrated in human corneas ex vivo. The optimum viral dose was 3.7 × 10(11) VG with an exposure time of 1 day, followed by 6 days incubation in de-swelling medium. In addition, 12 days incubation can result in transgene expression in excess of 70%. Using similar transduction conditions, meganuclease transgene expression was detected in 39.4% of the endothelial cells after 2 weeks in culture. Reduction of the total viral load in the media and the endothelial cells of corneas infected with HSV-1 was shown. Collectively, this work provides information about the optimum conditions to deliver genetic material to the cornea, and demonstrates for the first time the expression of meganuclease in human corneas ex vivo and its antiviral activity. In conclusion, we demonstrate that the treatment of human corneas in eye banks before transplantation is a new approach to address the unmet clinical needs in corneal diseases.

Different distribution of phenotypes and glucose tolerance categories associated with two alternative proposed cutoffs of insulin resistance.

We investigated whether two alternative HOMA-IR thresholds recently proposed identify similar phenotype and have the same impact on gluco-metabolic risk. The two IR cutoffs, IR1 and IR2 (IR1: HOMA-IR >5.9 and IR2: HOMA-IR between 2.8 and 5.9 with HDL-C <51 mg/dl), were applied to a database of 2,360 outpatients, and their association with phenotypes, glucose tolerance, lipids and metabolic syndrome (MetS) was examined. IR1 group showed 5.5% of overweight versus 27.8% of IR2 subjects, and obesity was present in 92.3 versus 68.4%, respectively. We observed the major prevalence of pathological waist in IR1 compared to IR2 subjects: 96.0 versus 80.5% (p < 0.001). After OGTT, IR1 patients presented higher prevalence of impaired glucose tolerance (IGT: 25.8 vs. 20.2%, p < 0.001) and DM2 was diagnosed in 39.7% of IR1 versus 11.3% of IR2 patients (p < 0.001) with odds ratio (OR) 8.3 (95% CI 6.1-11.6) versus 0.8 (0.6-1.2), respectively. IR1 versus IR2 cutpoint showed higher significant (mean ± SEM) total cholesterol (224.8 ± 2.6 vs. 213.1 ± 1.7 mg/dl, p < 0.001) and triglyceride (208.1 ± 12.3 vs. 177.4 ± 4.8 mg/dl, p < 0.001) levels. MetS prevalence was significantly higher in IR1 than IR2 (89.0 vs. 78.3%, p < 0.001). The IR1 cutpoint was associated with a higher OR of MetS 7.3 (5.3-10.2) versus 5.2 (2.8-9.5) of IR2. In summary, the two alternative HOMA-IR cutoffs identify subjects with different distribution of phenotypes and gluco-metabolic risk. The IR1 patients are characterized by higher prevalence of obesity, pathological waist, MetS, dyslipidemia and IGT/DM2.

Beat to beat analysis of mechanical heart valves by means of return map.

Three mechanical heart valves (two bileaflet prostheses and a tilting one) were investigated in a basic hardware setup in order to evaluate with a hydrophone their opening and closing action in time and in amplitude of each beat. The recorded signal was then segmented into the series of cycles xi(t) having a temporal duration equal to the working period imposed on the valve. Two return maps were defined, in order to evaluate the degree of dispersion of the resulting scatter plot: (i) the amplitude map xi(t) versus xi+1(t); (ii) the delay map for the closure of the valve within each beat versus the successive ones. To evaluate the results obtained, two indices were proposed based on both the degree of dispersion and the deviation of the regression line of the resulting scatter plot with respect to the bisector of the map plane. The tilting disc valve showed a lower degree of dispersion, both in the amplitude signal and in the closure time delays, with respect to the other two bileaflet heart valves. The methodology proposed here could be regarded as an alternative non-invasive tool to investigate the dynamic behaviour of prosthetic heart valves, especially in the case of their suspected failure.

Development of a hemicornea from human primary cell cultures for pharmacotoxicology testing.

We report the reconstruction and characterization of a hemicornea (epithelialized stroma), using primary human cells, for use in research and as an alternative to the use of animals in pharmacotoxicology testing. To create a stromal equivalent, keratocytes from human corneas were cultured in collagen-glycosaminoglycan-chitosan foams. Limbal stem cell-derived epithelial cells were seeded on top of these, giving rise to hemi-corneas. The epithelium appeared morphologically similar to its physiological counterpart, as shown by the basal cell expression of p63 isoforms including, in some cases, the stem cell marker p63DeltaNalpha, and the expression of keratin 3 and 14-3-3sigma in the upper cell layers. In addition, the cuboidal basal epithelial cells were anchored to a basement membrane containing collagen IV, laminin 5, and hemidesmosomes. In the stromal part, the keratocytes colonized the porous scaffold, formed a network of interconnecting cells, and synthesized an ultrastructurally organized extracellular matrix (ECM) containing collagen types I, V, and VI. Electron microscopy showed the newly synthesized collagen fibrils to have characteristic periodic striations, with diameters and interfibril spacings similar to those found in natural corneas. Compared to existing models for corneal pharmacotoxicology testing, this new model more closely approaches physiological conditions by including the inducing effects of mesenchyme and cell-matrix interactions on epithelial cell morphogenesis.

Morphological analysis of in vivo velocity field in the alteration of the vasomotor tone.

Vessel wall remodeling is involved in atherogenesis and in several important vascular diseases affecting mainly aged and prosthetic implanted patients. This adaptive response to pathological states in arterial hemodynamics strongly suggests that flow-derived stresses act as mechanical stimuli to the release of endothelium-derived vasoactive factors, leading to vascular alterations. As the correlation of intimal hyperplasia (IH) with blood flow alterations in arteries has been shown to be significant, and as it is well-known that clinical procedures carry a substantial risk of development of vascular disease, the relevance of local hemodynamics must be investigated to describe changes in compliance matching in prosthetic applications. The aim of our research is to investigate the use of principal components analysis, together with varimax rotation, in the individuation process of morphological characteristics of real time ultrasound in in vivo recordings of blood flow velocities, as provided by two different carotid perivascular manipulations. This would be of use in the clinical assessment of atherogenesis, hypertension, prosthetic replacement or more in general in all applications in which vascular tone may be impaired. Data recordings refer to previous animal experiments where the Moncada model was investigated by means of an ultrasound profilometer. The present study confirms the feasibility of the proposed analysis to follow vascular pathology evolution, distiguishing between an in progress and a static situation.

Proposal for a quantitative description of blood spiral flow in medical devices.

The association between specific blood flow patterns and blood behaviour through medical devices suggests that a Lagrangian study may be a useful instrument for the evaluation of the thrombogenic and/or hemolytic potential of certain devices' geometries and biomaterials. In this study a description of blood particle trajectories in terms of their spiral contents is proposed; such a mathematical description for blood spiral flow, computed along several pathlines, is tested for a quantitative determination of the spiralled motion of blood flow into two three-dimensional numerical models, having different design characteristics, of venous cannula inserted in a vessel. As the influence of vortical flow conditions have been observed to have both beneficial and detrimental influence on blood behaviour in terms of blood-device interaction, of the degradation of its components, and of the efficiency of mass-exchange (in red cells oxygenation and plasma filtration, for example), the herein proposed method for the description of spiral laminar motion may be a helpful instrument to build up a tool to investigate, for example, the existence of correlations between level of spiral flow and geometry (as in the present investigated test case), rather than the effects of blood-surface contact. The results obtained in this test case investigation, confirm the effectiveness of the proposed function for a quantitative analysis of spiral flow in medical devices.

Effects of subthreshold shocks on wavelet propagation during atrial fibrillation in humans.

OBJECTIVES: Our objectives are: first to investigate the effects of internal cardioversion energies on the wave fronts propagation in the right atrium immediately after the energy delivery; second, to track the time course of these effects. METHODS: The study is based on a measure of organization of the endoatrial electrograms obtained by a multipolar basket catheter inserted in the right atrium. We estimated the level of organization by computing the percentage of points laying on the signal baseline (i.e., number of occurrences, NO). NO values were computed on two-second long windows. Six non-overlapped windows were selected, one just before and five just after the last unsuccessful shock. RESULTS: Immediately after the shock most of the patients exhibited an increase in the organization patterns. This increase was more evident in those patients with rather disorganized patterns and higher energy threshold. This effect fades within a few seconds after the shock delivery. CONCLUSIONS: Our data confirm the idea that the electrical shock causes a widespread extinction of electrical wavefronts, which regenerates after the shock. Since an increase of organization may lead to a reduction of energy threshold, a potential application of these findings might consist in the delivery of multiple subthreshold shocks instead of a single one.

Endovascular stents: market vigilance and risk factors.

With the aim of enhancing the safety and reliability level of coronary stents, we analyzed data collected from accident reports drawn from the MAUDE database (Manufacturer and User Facility Device Experience Database) of the FDA from 1996 to 2000. This analysis allowed us to highlight problems related to the use of coronary stents by means of the analysis of these reports at different levels, beginning from the causes that can lead to a certain type of accident up to the possible complication related to that event. Moreover we analyzed the procedure outcomes in terms of stent position inside the patient's body and the possible therapies adopted to solve the problems. The results showed that the most probable event that can lead to an accident is the stent separation from the balloon which, alone, turns up in a number of cases equal to the sum of all the others. This result highlights the importance of the technical skill of the operators accomplished by special training and of the importance of clarity and completeness in the instructions for the use of the device. Another critical point is the reliability of the device which must guarantee an adequate safety level when it is used according to the instructions.

Electromagnetic interference to infusion pumps from GSM mobile phones.

Electromagnetic interference (EMI) to critical care medical devices has been reported by various groups. Previuos studies have demonstrated that infusion and syringe pumps are susceptible of false alarm buzzing and block, when exposed to various EMI sources. Whether these events may have clinical relevance is still debated. The risk of EMI depends on several factors such as phone emitted power, distance and carrier frequency. We investigated the EMI on infusion and siringe pumps from GSM phones at various distances and emitted powers. Malfunctions were observed in 4/7 infusion pumps and 1/4 syringe pumps exposed to mobiles at their maximum output, for distances as long as 30 cm. The maximum power not inducing any malfunction even at 0 cm distance was also determined. The selection of a proper maximum power class reduces significantly the risk of EMI. Such a function is already built in the GSM standard and thus represents one of the feasible solutions to the EMI problem in hospitals.

Heart rate and blood pressure variability in patients implanted with rate-responsive pacemaker.

Rate-responsive pacemakers (PMs) aim at having pacing rates as similar to physiological cardiac rhythms as possible. The pacemaker INOS(2+)-CLS (Biotronik, Germany) implements a closed loop strategy (CLS) based on indirect measures of right ventricle contractility using intracardiac impedance signal. The contractility is, in turn, related to the autonomic nervous system control to the heart. Aim of this study was to evaluate the 24h beat-to-beat heart rate and blood pressure profiles in patients implanted with CLS rate adaptive PM. 24h ECG and arterial pressure waveform acquisition were performed by a digital Holter system by the Portapres equipment, respectively. A proper-designed algorithm was developed to classify PM pacing modalities. For each beat we estimated the heart rate (HR), and the systolic and diastolic pressure values (SP, DP). So far, 6 patients have been studied: 4 patients have been analyzed both with and without rate responsive modalities (DDD-R and DDD, respectively); 2 patients have been studied only with rate-responsive modality. Results obtained in 6 patients show that this rate adaptive PM accurately preserve the heart rate and blood pressure variability throughout the 24h. In particular, the rate adaptation of PM based on impedance measurements succeeds in maintaining the spontaneous HR, SP and DP on a beat-to-beat basis.

Nonlinear coupling among heart rate, blood pressure, and respiration in patients susceptible to neuromediated syncope.

The aim of this study is to evaluate the degree of coupling between the cardiovascular variability series and the respiration in subjects susceptible to neurally mediated syncope. Twenty-one informed patients susceptible to syncope and ten sex- and age-matched control subjects were enrolled in the study. ECG, respiration activity, and arterial blood pressure were simultaneously recorded at rest (controlled and free breathing) and during the 70 degrees head-up TILT test (free breathing). The degree of nonlinear coupling among heart rate variability (HRV), blood pressure variability (BPV), and respiration was quantified by means of two indices according to a multivariate embedding-based approach. Eleven patients developed syncope during the TILT test. We found that during the late TILT phase, the TILT-positive group experienced a significant increase in nonlinear coupling respect to the mid TILT phase (p < 0.01, Wilcoxon nonparametric test for pair data) while the TILT-negative group did not (p < 0.01, Mann-Whitney U-test). If the proposed nonlinear coupling indexes can be considered expression of the coupling mechanisms involved in the vagal regulation of the cardiovascular system, an increase in vagal tone accompanied by a decrease in sympathetic activity seem to occur before a vasovagal event.

A novel heart/trunk simulator for the study of electromagnetic interference with active implantable devices.

This paper describes a portable heart simulator for the study of electromagnetic interference with active implantable devices. The simulator consists of plexiglas box divided into three chambers simulating the left atrium and the ventricles, plus a lateral compartment for the implantable device. The box is linked to a laptop computer by an analogue-to-digital convertor board, and the three chambers are monitored and driven by dedicated hardware and software interfaces. Synthetic endocardial atrial and ventricle signals for 13 cardiac rhythms are stored in the computer. They are applied to the cardiac chambers by AgCl plates. Sensing electrodes are in the form of AgCl needles inserted in saline. The simulator was able to demonstrate the behaviour of three pacemakers tested in the absence and presence of electromagnetic interference, generated by mobile phones (European GSM 900 and 1800 MHz) that emitted up to 2W (1 W at 1800 MHz). Pacemakers can be programmed with sensitivity from 0.1 mV to 5 mV, pulse width from 0.1 ms to 1.5 ms and pulse amplitude from 0.5 V to 5 V. The structural separation in three cardiac chambers (plus the one for the device) allowed a fast analysis procedure for dual- and tri-chamber implantable devices.

On the mechanisms of interference between mobile phones and pacemakers: parasitic demodulation of GSM signal by the sensing amplifier.

The aim of this study was to investigate the mechanisms by which the radiated radiofrequency (RF) GSM (global system for mobile communication) signal may affect pacemaker (PM) function. We measured the signal at the output of the sensing amplifier of PMs with various configurations of low-pass filters. We used three versions of the same PM model: one with a block capacitor which short circuits high-frequency signals; one with a ceramic feedthrough capacitor, a hermetically sealed mechanism connecting the internal electronics to the external connection block, and one with both. The PMs had been modified to have an electrical shielded connection to the output of the sensing amplifier. For each PM, the output of the sensing amplifier was monitored under exposure to modulated and non-modulated RF signals, and to GSM signals (900 and 1800 MHz). Non-modulated RF signals did not alter the response of the PM sensing amplifier. Modulated RF signals showed that the block capacitor did not succeed in short circuiting the RF signal, which is somehow demodulated by the PM internal non-linear circuit elements. Such a demodulation phenomenon poses a critical problem because digital cellular phones use extremely low-frequency modulation (as low as 2 Hz). which can be mistaken for normal heartbeat.

Pathological patient in protocol definition for bench testing of mechanical cardiac support system.

Clinical techniques for the restoration of a failing heart are mainly based on the use of mechanical assist devices. In recent years, with the growing need for mechanical circulatory support, these devices have been shown to be a useful therapeutic tool, thanks to their intrinsic capability to unload the failing ventricle, allowing the heart to recover. Mechanical circulatory support systems (MCSS) require an accurate biomechanical characterization of the complex interaction that occurs between the patient and the mechanical support. A protocol for MCSS testing is proposed which takes into account several working conditions, in a modified test mock loop apparatus able to mimic various pathological conditions. Both physiological and pathological conditions can be replicated to show the actual efficacy of a MCSS device in correctly supporting a wide spectrum of ventricular conditions. The test bench is able to simulate the recovery of the pathological condition quite accurately, showing, at the same time, that this set up can be a reliable choice to characterize cardiac support devices. Thus the results of this experimentation can be useful to clinicians in forecasting the response of the heart affected by a cardiac disease and to set appropriate parameters for suitable assistance.

Numerical simulation of a realistic total cavo-pulmonary connection: effect of unbalanced pulmonary resistances on hydrodynamic performance.

Total cavo pulmonary connection (TCPC) is one of the surgical techniques adopted to compensate the failure of the right heart in pediatric patients. The main goal of this procedure is the realization of a configuration for the caval veins and for the pulmonary arteries that can guarantee as low as possible pressure losses and appropriate lung perfusion. Starting from this point of view, a realistic TCPC with extracardiac conduit (TECPC) is investigated by means of Computational Fluid Dynamics (CFD) to evaluate the pressure loss under different pressure conditions, simulating different vessel resistances, on the pulmonary arteries. A total flow of 3 L/min, with a distribution between the inferior vena cava (IVC) and the superior vena cava (SVC) equal to 6/4, was investigated; three different boundary conditions for the pressure were imposed, resulting in three simulations in steady-state conditions, to the right pulmonary artery (RPA) and to the left pulmonary artery (LPA), simulating a balanced (deltaP(LPA-RPA) = 0 mmHg) and two unbalanced pulmonary resistances to blood flow (a pressure difference deltaP(LPA-RPA) = +/- 2 mmHg, respectively). The geometry for the TECPC was realized according to MRI derived physiological values for the vessels and for the configuration adopted for the anastomosis (the extra-cardiac conduit was inclined 22 degrees towards the left pulmonary artery with respect to the IVC axis). The computed power losses agree with previous in vitro Particle Image Velocimetry investigations. The results show that a higher resistance on the LPA causes the greater pressure loss for the TECPC under study, while the minimum pressure loss can be achieved balancing the pulmonary resistances, subsequently obtaining a balanced flow repartition towards the lungs.

Computational model of the fluid dynamics of a cannula inserted in a vessel: incidence of the presence of side holes in blood flow.

Vascular access methods, performed by the insertion of cannulae into vessels, may disturb the physiological flow of blood, giving rise to non-physiological pressure variations and shear stresses. To date, the hydrodynamic behaviour of the cannulae has been evaluated comparing their pressure loss-flow rate relationships, as obtained from in vitro experiments using a monodimensional approach; this methodology neither furnish information about the local fluid dynamics nor the established flow field in specific clinical work conditions. Since the shear stress is a critical factor in the design of artificial circulatory devices, more knowledge should be necessary about the local values assumed by the haemodynamic parameters during cannulation. An alternative way to investigate the fluid dynamic as accurately as possible is given by numeric studies. A 3D model of cannula concentrically placed in a rigid wall vessel is presented, with the finite element methodology used to numerically simulate the steady-state flow field in two different venous cannulation case studies, with two cannulae having a central hole and two or four side holes, respectively, with the same boundary conditions. Lower velocity and shear stress peak values have been computed for the model with four side holes upstream of the central hole, in the region of the cannula where the inlet flows meet and towards cannula's outlet, due to the increased flow symmetry and inlet area with respect to the model with two side holes. Starting from the investigation of different cannula designs, numerically assessing the local fluid dynamics, indications can be drawn to support both the design phase and the device optimal clinical use, in order to limit risks of biomechanical origin. Thus the presence of four side holes implied, as a consequence of the greater inlet area and of the increased symmetry, a less disturbed blood flow, together with reduced shear stress values. Furthermore, results show that the numerical simulations furnished useful informations on the interaction between vessel and cannula, e.g. on the fluid dynamics establishing in the free luminal space left, in the vessel, by the inserted cannula.

Potential mechanical blood trauma in vascular access devices: a comparison of case studies.

Since vascular access devices may cause disturbances in blood flow, possibly damaging red blood cells (RBCs), the correlated risk of lysis must be assessed. The monodimensional approach for the evaluation of cannulae hydrodynamic behaviour (in vitro measured flow curves) does not furnish information on the local flow field occurring in specific clinical conditions. Researchers consider the prediction of blood trauma, induced by mechanical loading, to optimize the design phase, and to furnish indications on their optimal clinical use. In this study, a model of cannula inserted in a non compliant wall vessel was used as a test bench in a Computational Fluid Dynamics (CFD) problem. By means of CFD the flow field was 3D analysed to achieve information on velocity and shear stress local values, when cannula is used for inflow and outflow cannulation. A prediction of potential blood corpuscle damage, based on a power law, quantified the potential blood damage. Several numerical simulations, with different cannula/vessel flow rate ratios were provided, to investigate the incidence of local sites in the design on blood damaging potential during cannulation. Several regions appeared to be sensitive to the flow rate not only inside the cannula but also in the space between cannula and vessel, suggesting new indications for the assessment of a quality factor based on the evaluation of induced blood cells injury.

Hydraulic functional characterisation of aortic mechanical heart valve prostheses through lumped-parameter modelling.

Lumped-parameter modelling techniques are proposed as a method for studying the hydraulic characteristics of mechanical prosthetic heart valves (PHVs). The global hydraulic behaviour of PHVs in the open position was modelled by taking into account the (nonlinear) resistive and (linear) inertial factors governing the time-dependent relationship between transvalvular pressure drop and fluid flow rate, and neglecting the leaflets' opening and closure transient phenomena. Statistically defined indices associated to the parameters' values attest how properly the model describes PHV hydraulic behaviour. Local fluid dynamics is not modelled with this approach. The proposed method was implemented in a software program and applied to the characterisation of the aortic StJude Medical, StJude Medical Hemodynamic Plus and CarboMedics PHVs, basing on steady- and pulsatile-flow hydraulic-bench experimental data. The results showed that reliable parameters expressing hydraulic resistance can be derived from steady-flow data (R(2)>0.995). Inertance parameters derived from pulsatile-flow experiments are liable to a degree of uncertainty (confidence intervals up to 17%), however, comparing the reconstructed vs. measured pressure drop during systolic time demonstrates that this deficiency is mostly due to the missing description of initial, transient oscillations presumably related to the leaflets' opening (not modelled).

Measure of synchronisation of right atrial depolarisation wavefronts during atrial fibrillation.

A new index of synchronisation (IS) between the electrical activity of pairs of close atrial sites during atrial fibrillation (AF) is introduced. The index assesses the probability of finding synchronous activations in intra-atrial bipolar electrograms and is based on the assumption that two activations closely spaced in time are likely to belong to the same depolarisation wavefront. A dedicated statistical treatment to test this hypothesis is also illustrated. Experimental data were obtained using a multipolar basket catheter in the right atrium in 20 patients during normal sinus rhythm (NSR), atrial flutter (AFL, one patient), high-frequency pacing (HFP, two patients) and chronic AF (17 patients), and 30 segments were obtained from each. From the 24 pairs of bipoles, a single averaged IS and its standard deviation were extracted. The IS was 1 in NSR and HFP and 0.95 +/- 0.02 during AFL. During AF, the IS provided a quantitative measure of the degree of coupling of various atrial sites. The IS varied significantly among the recording sites (range 0.38-0.96), showing a patient-dependent pattern, and decreased as the arrhythmia complexity increases. No temporal trends were observed for the IS values in any chronic AF patient. On average, in each site, the dispersion of the IS over time was lower than 32% of the mean, for all patients. Additional relevant features of the proposed index are its high temporal resolution (2s) and robustness to activation time estimation error, to missing or false detections and to the ever-changing pattern of propagation. The index of synchronisation is a descriptor of the electrophysiological properties of atrial tissues.

Non-linear coupling of atrial activation processes during atrial fibrillation in humans.

The activation patterns underlying the electrical activity of the heart during atrial fibrillation (AF) are not entirely random. The aim of this study was to assess the local organization of the activation processes during AF by estimating the non-linear coupling between activation sequences (ASs) in two atrial sites. To quantitatively estimate the degree of non-linear coupling we extracted two indices based on a multivariate embedding procedure and on the estimation of the correlation dimension (CD) and correlation entropy (CE), termed independence of complexity and of independence of predictability, respectively. We analysed AS in two atrial sites in 30 informed subjects during chronic AF of type I, II and III (Wells' classification), ten 6-s-long episodes of each type. Surrogates were used to reject the hypothesis that the time series were generated by linear stochastic dynamics. We estimated CD and CE according to the coarse-grained approach, which leads to a fixed high value for the embedding dimension in all the analysed ASs, and a typical value for the distance between the two ASs in the phase space. Various degrees of organization, ranging from completely synchronized to fully de-coupled signals, were observed: significant degrees of non-linear coupling were found in segments belonging in types I and II AF, whereas type III electrograms always turned out to be weakly coupled. This finding links the morphology of single electrograms to the synchronization between pairs of closely spaced electrograms. Our bivariate approach suggests that the measurement of organization during AF should be based on the estimation of the non-linear coupling between two sites. This approach appears to be more reliable and sensitive than non-linear analysis of single electrograms or linear analysis of their coupling.