Physiology in fractal dimensions: Error tolerance

The natural variability in physiological form and function is herein related to the geometric concept of a fractal. The average dimensions of the branches in the tracheobronchial tree, long thought to be exponential, are shown to be an inverse power law of the generation number modulated by a harmonic variation. A similar functional form is found for the power spectrum of the QRS-complex of the healthy human heart. These results follow from the assumption that the bronchial tree and the cardiac conduction system are fractal forms. The fractal concept provides a mechanism for the morphogenesis of complex structures which are more stable than those generated by classical scaling (i.e., they are more error tolerant).     

Haemostatic investigations: The impact of new technologies

Blood loss following trauma is controlled by a complex series of interactions involving the vascular surface, blood platelets and ‘activated’ coagulation factors. Activation of the coagulation cascade involves a series of zymogen to enzyme transformations with each enzyme associating with a co-factor on a ‘surface’ such as negatively charged platelet membrane phospholipid to form reaction complexes. In physiological terms it is possible that this system is continuously switched on producing low levels of activated serine proteases which are continuously being neutralised by protease inhibitors and co-factor neutralising reactions which down-regulate blood clotting processes, thus maintaining patency of the vascular tree. It is in this context that the concept of identifying molecular markers of haemostatic activation is well recognised. The haemostatic investigations now include biochemical and immunological investigations in order to detect small concentrations of products from intravascular thrombin generation, platelet-specific proteins released as a consequence of platelet release reaction, circulating activated clotting factors, activation peptides and ‘activated clotting factor-inhibitor’ complexes. This review will concentrate on new markers of haemostasis which are currently being used in the investigation of thrombosis.     

QRS wave detection

A QRS complex detector based on optimum predetection with a matched filter is described. In order to improve the accuracy of the QRS complex recognition under conditions of Gaussian noise and variable QRS amplitude, the first derivative of the e.c.g. was used with zero threshold detection. In addition, two nonlinear circuits cut off low amplitude noise and all spikes which appear for a fixed time after QRS detection. Calculation of errors shows that differentiation reduces Gaussian error by √6 and errors caused by variable QRS amplitudes are close to zero. This detector is especially useful with biotelemetry systems since it reduces many interferences due to patient movement and communication channel distortion.     

基于子波多尺度分辨的心电QRS波分类方法的研究

本文分析了心电QRS波的子波多尺度分辨特征,探讨了曲线非线性分开维数的计算方法,提出了一种新的QRS波的分类方法：对心电QRS复合波进行子波多尺度分解,在尺度为4的情况下,根据局部正负极大值对检测出它们前后两个零点Zp1,Zp2,计算出局部正负极大值对位于┃Zp1,Zp┃之间的曲线段的分形维数。根据局部正负极大值对的幅度和分开维数能很好地检出正常心电信号的QRS波及早搏信号;该方法具有很强的抗噪能力,提高了QRS波的正确检出率。     

Delineation of the QRS complex using the envelope of the e.c.g.

A new algorithm for QRS delineation has been developed. Based on the envelope of the e.c.g. signal a delineation function is defined, which yields a single positive pulse for each complex. From this function the onset and end of the QRS or, alternatively, a fiducial point is determined. To remove low-frequency component such as S-T abnormalities without distortion of the QRS complex, a filter with time-varying characteristics is used. The accuracy of the method has been evaluated in a test set of different QRS complexes obtained from coronary care patients. For QRS onset, the standard deviation of the difference between automated and manual determination was 7 ms in normal beats and 14 ms in ectopic beats. With simulated noise added to each waveform an average dispersion of 7 ms was observed in the recognition of the QRS onset at a signal-to-noise ratio of 15 dB. The corresponding dispersion in the location of a fiducial point was 2 ms. Using simulated e.c.g. data, the stability of the method is demonstrated for transitions between different waveform morphologies. Presented in part at ‘Computers in cardiology’, Florence, 23rd–25th September 1981     

Experimental investigation and computational modeling of hydrodynamics in bifurcating microchannels

Methods involving microfluidics have been used in several chemical, biological and medical applications. In particular, a network of bifurcating microchannels can be used to distribute flow in a large space. In this work, we carried out experiments to determine hydrodynamic characteristics of bifurcating microfluidic networks. We measured pressure drop across bifurcating networks of various complexities for various flow rates. We also measured planar velocity fields in these networks by using particle image velocimetry. We further analyzed hydrodynamics in these networks using mathematical and computational modeling. Our results show that the experimental frictional resistances of complex bifurcating microchannels are 25–30% greater than that predicted by Navier–Stokes equations. Experimentally measured velocity profiles indicate that flow distributes equally at a bifurcation regardless of the complexity of the network. Flow division other than bifurcation such as trifurcation or quadruplication can lead to heterogeneities. These findings were verified by the results from the numerical simulations.     

Revealing the mechanisms underlying embolic stroke using computational modelling

Computational forecasting of arterial blockages in a virtual patient has the potential to provide the next generation of advanced clinical monitoring aids for stroke prevention. As a first step towards a physiologically realistic virtual patient, we have created a computer model investigating the effects of emboli (particles or gas bubbles) as they become lodged in the brain. Our model provides a framework for predicting the severity of microvascular obstruction by simulating fundamental interactions between emboli and the fractal geometry of the arterial tree through which they travel. The model vasculature consisted of a bifurcating fractal tree comprising over a million branches ranging between 1 mm and 12 microm in diameter. Motion of emboli through the tree was investigated using a Monte Carlo simulation to evaluate the effects of the embolus size, clearance time and embolization rate on the number and persistence of blocked arterioles. Our simulations reveal with striking clarity that the relationship between embolus properties and vascular obstruction is nonlinear. We observe a rapid change between free-flowing and severely blocked arteries at specific combinations of the embolus size and embolization rate. The model predicts distinct patterns of cerebral injury for solid and gaseous emboli which are consistent with clinical observations. Solid emboli are predicted to be responsible for focal persistent injuries, while fast-clearing gas emboli produce diffuse transient blockages similar to global hypoperfusion. The impact of solid emboli was found to be dramatically reduced by embolus fragmentation. Computer simulations of embolization provide a novel means of investigating the role of emboli in producing neurological injury and assessing effective strategies for stroke prevention.     

Fast and reliable QRS alignment technique for high-frequency analysis of signal-averaged ECG

The process of QRS alignment as required in signal-averaged ECG can impose serious limitations on the spectral range of the signal output. This effect depends basically on the particular alignment technique being used and on the level and type of noise present in the recorded ECG. In clinical studies where a wide-band (1000 Hz) ECG averager is required, the conventional QRS alignment technique, based on maximum coherence matching (MCM) with a template beat, may not perform consistently well. An alternative QRS alignment technique based on the accurate detection of a single fiducial point (SFP) in the bandpass filtered (3–30 Hz) QRS complex was developed. Using computer simulation methods, a comparative assessment of the frequency bandwidths (3 dB points) offered by both MCM and SFP techniques as a function of noise level (15–100 μ RMS) and type (EMG and 50 Hz interference), was carried out. The results of the comparative assessment indicated a better performance by the SFP technique in all cases of noise. Hence, the SFP technique would perform more reliably for high-frequency analysis of a noisy ECG, especially when 50 Hz interference is high. Furthermore, SFP is considerably faster than MCM (about four times) when implemented digitially, and its analogue realisation is feasible. The SFP technique is suitable for late-potential analysis in the signal-averaged ECG.     

New approach to studies on ECG dynamics: Extraction and analyses of QRS complex irregularity time series

How to extract information intensively from ECGs for the diagnosis of cardiovascular diseases and assessment of heart function is a topical subject. Using a method based on the wavelet transform to calculate the irregularity of the QRS complex, which may relate to inotropy, the QRS complex irregularity time series is successfully extracted from original ECG signals. This provides a new approach to studies of ECG dynamics. With the help of non-linear dynamics theory, the QRS complex irregularity time series of eight subjects, from the MIT/BIH arrhythmia database are studied qualitatively and quantitatively, and the characteristics of ECG dynamics are analysed extensively. The power spectrum, phase portrait, correlation dimension, largest Lyapunov exponent, time-dependent divergence exponent and complexity measure all verify the fact that ECG dynamics are dominated by an underiying 5–6-dimensional non-linear chaotic system, whose complexity measure is about 0.7. The QRS complex irregularity time series contains abundant information about all parts of the heart and the regulation of the autonomic nervous system, and so further analyses are of great potential theoretical and clinical significance to patho-physiology studies and ambulatory monitoring.     

Fractal dynamics of polarized bioelectrodes

This study is concerned with mathematical modelling of the fundamental relationship which exists between the current density and the overpotential across the metalsolution interface in the linear range using methods of system theory enhanced by ‘fractal’ concepts. A primer for both 1/f-type scaling and ‘anomalous’ relaxation/dispersion concepts is provided, followed by a brief review of the research history pertinent to the metal electrode polarization dynamics. Next, the ‘fractal relaxation systems’ approach is introduced to characterize, systems which attenuate with a fractional power-low dependence on frequency through a ‘scaling exponent’. The ‘singularity structure’ which is a scaling, rational system function is proposed to expand fractal systems in terms of basic subsystems individually representing elementary exponential relaxations and collectively exhibiting scaling properties. We stress that the ‘singularity structure’ carries scaling information identical to the conventional ‘distribution of relaxation times’ function. ‘Structure scale’ and ‘view scale’ concepts are presented in the due course to streamline the analysis of scaling phenomena in general and the polarization impedance in particular. System theory-wise, the notable result is that the fractional power function attenuation, or equivalently, the logarithmic nature of the distribution function translates into the ‘self-similar’ pattern replication of the system singularities in the s-plane. The singularity arrangement is governed by a recursive rule solely based on the knowledge of the fractional power factor or the scaling exponent.     

Wavelets as alternative to short-time Fourier transform in signal-averaged electrocardiography

The paper reports experience of using the wavelet transform to build time-frequency distributions of the terminal portion of the QRS-complex. We used wavelets of Morlet at 12 scales, grouped in three sets, to analyse the frequency range 33–404 Hz. On the same patient data we applied the short-time Fourier transform and compared the results. Both representations reflected the time-frequency contents and detected irregular structures in the terminal portion of the QRS complex. The wavelet transform revealed more adequately QRS prolongations characteristic of patients prone to ventricular tachycardia. We may conclude that the wavelet transform can be a flexible alternative to short-time Fourier transform.     

Suppression of the cardiac electric field artifact from the heart action evoked potential

The study of heart action-related brain potentials is strongly disrupted by the presence of an inherent cardiac electric artifact. The hypothesis is presented that most of the electric current coupled to the cardiac field surrounds the skull and flows through the scalp tissue without crossing the cranial cavity. This pseudo two-dimensional conduction model contrasts with the volumetric conduction of the brain electrical activity, and this property is exploited to cancel the cardiac electric artifact. QRS loop vectorcardiographic projections on saggital planes were recorded in 11 healthy subjects in the head and neck areas. Comparative analysis of the projection eccentricittis, estimated by the correlation coefficients of the paired data on each area, supported the hypothesis and allowed the handling of the cardiac electric field at the scalp as if enclosed in a two-dimensional wrapped space. This approach permitted the combination of different heart action-related brain potentials recorded at different electrode positions to cancel the cardiac electric artifact. The cancellation method, applied to the subjects' EEG data, yielded a slow cortical potential with a negligible cardiac electric residue and an amplitude of about 1.5–2 μV, with a maximum around 150 ms and a minimum at 400 ms post-R wave.     

Estimation of the conduction velocity of muscle action potentials using phase and impulse response function techniques

Two new techniques are described for calculating the conduction velocity of action potentials in muscle fibres from surface EMG recordings in human subjects. In the first method the conduction velocity is determined from the impulse response function calculated from the two EMG signals. The peak of this function onsists of a single peak located at the delay between the signals. The velocity probability density distribution is then estimated from this impulse response function. The mode of this distribution occurred at 5 m s⁻¹. The second technique uses the phase part of the frequency response function relating the two EMG signals to determine the conduction velocity. These two new approaches overcome some of the limitations associated with estimating conduction velocity from the maximum absolute value of the cross-correlation function, and provide additional information about the conduction velocity.     

A Cartesian Time–Frequency Approach to Reveal Brain Interaction Dynamics

Summary The study of large-scale interactions from magnetoencephalographic data based on the magnitude of the complex coherence computed at channel level is a widely used method to track the coupling between neural signals. Traditionally, a measure based on the magnitude of the complex coherence estimated by Fourier analysis, has been used under the assumption that the neural signals are stationary. Here, we split the complex coherence in its real and imaginary parts and focus on the latter with the advantage that the imaginary part is insensitive to spurious connectivity resulting from volume conducted “self interaction”. Furthermore, interacting sources alone contribute to a non-vanishing imaginary part of the complex coherence whereas the contribute of non-interacting sources is also mapped from the magnitude of the complex coherence. Since it has been extensively shown that non-stationary stochastic processes contribute to the generation of neural signals, it is fundamental to be able to define interaction measures that are able to follow the temporal variations in the coupling between neural signals. To this purpose time–frequency domain techniques to estimate the magnitude of the complex coherence have been developed in the past decades. Similarly, we extend the analysis of the imaginary part of complex coherence to the time–frequency domain, by using the short-time Fourier transform to analyze the complex coherence as a function of time. In this way, it is possible to get an indication about the dynamic of the underlying source interaction pattern by looking at channel level interactions without the bias introduced by artifactual self-interaction by volume conduction or by the contribute of non-interacting sources. Furthermore, the corresponding imaginary part of the cross-spectrogram can be used to estimate interactions on a source level by localizing pools of sources interacting at a given frequency and by characterizing their dynamics. The method has been applied to magnetoencephalographic data from a cross-modal visual auditory stimulation and provided evidence for the involvement of temporal and occipital areas in the integrated information processing for simultaneous audio-visual stimulation. Furthermore, the source interaction pattern shows a variation in time that reflects a dynamical synchronization of the involved brain sources in the frequency bands of interest.     

心室Purkinje纤维传导系统的自动生成算法

由于Purkinje纤维在心脏心室中的复杂分布，它的仿真成为心电正问题研究中的一个难点。本文利用分形树结构来描述Purkinje纤维传导系统，提出了满足边界条件的分形树生长算法，通过对心内膜擘的球映射，该算法能在心室壁上自动生成Purkinje纤维分形树，不需要人工干预。     

Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images

Fractal analysis is a method of characterizing complex shapes such as the trabecular structure of bone. Numerous algorithms for estimating fractal dimension have been described, but the Fourier power spectrum method is particularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided accurate estimates of fractal dimension for synthesized fractal images. For natural texture images fractality is limited to a range of scales, and the fractal dimension as a function of spatial frequency presents as a fractal signature. We found that the fractal signature was more successful at discriminating between these textures than either the global fractal dimension or other metrics such as the mean width and root-mean-square width of the spectral density plots. Different natural textures were also readily distinguishable using lacunarity plots, which explicitly characterize the average size and spatial organization of structural sub-units within an image. The fractal signatures of small regions of interest (32x32 pixels), computed in the frequency domain after corrections for imaging system noise and MTF, were able to characterize the texture of vertebral trabecular bone in CT images. Even small differences in texture due to acquisition slice thickness resulted in measurably different fractal signatures. These differences were also readily apparent in lacunarity plots, which indicated that a slice thickness of 1 mm or less is necessary if essential architectural information is not to be lost. Since lacunarity measures gap size and is not predicated on fractality, it may be particularly useful for characterizing the texture of trabecular bone.     

Effect of resistive discontinuities on waveshape and velocity in a single cardiac fibre

A computer model of a one-dimensional cardiac fibre of resistively coupled cells is used to investigate the influence of the junction resistance on the nature of conduction. The results of the simulations are presented and indicate that the effect of the junction on both intracellular and extracellular waveshape and on the velocity of propagation depends on the size and frequency of the coupling resistance and the kinetics of the active membrane. Significant changes in these factors are not observed without the generation of prepotentials in the action potential upstroke. The absence of this ‘signature’ in microelectrode recordings of activity in ventricular muscle suggests that under normal conditions cardiac tissue behaves as a functional syncytium.     

兔心电QRS波的三维频谱分析

应用小波转换的三维频谱分析技术,对４０只兔心电ＱＲＳ波进行分析,观察其三维心电频谱的特征。结果显示：正常兔心电ＱＲＳ波的三维频谱形态呈双侧对称的山坡状,频谱宽度约为２４０Ｈｚ,高频成分主要分布在ＱＲＳ波的中部,能幅随频率增加呈下降趋势,其中１００—１０００Ｈｚ与６０—１００Ｈｚ的能量比约为１０,１５０—２５０Ｈｚ与６０—１００Ｈｚ的能量比约为０３５,并证明性别和体重对心电ＱＲＳ波三维频谱各参数不产生严重影响。     

A possible mechanism for the effect of modifiable lateral inhibition in the striatum on the selection of conditioned reflex motor responses

A mechanism is proposed for the effects of striatal dopamine-modifiable lateral inhibition on the selection of conditioned reflex motor responses. According to this mechanism, activation of dopamine D1 (D2) receptors on strionigral (striopallidal) neurons facilitates long-term depression (potentiation) of the inhibitory inputs simultaneously with potentiation (depression) of the excitatory inputs, of sufficient strength to open NMDA channels. For “ weak” excitation, insufficient to open NMDA channels, the modification rules were of the opposite sign. Activation of presynaptic D2 (D1) receptors leads to decreases (increases) in GABA release from strionigral (striopallidal) axon terminals innervating strionigral (striopallidal) cells. As a result, dopamine-modifiable lateral inhibition simultaneously increases both the potentiation (depression) of the excitatory inputs to “strongly” activated strionigral (striopallidal) neurons, increasing (decreasing) their activity, and increases the depression (potentiation) of the excitatory inputs to the “weakly” activated strionigral (striopallidal) neurons, decreasing (increasing) their activity. Subsequent reorganization of neuron activity in the cortex-basal ganglia-thalamus-cortex circuit facilitates selection of conditioned reflex motor responses by further increasing (decreasing) the activity of those motor cortex neurons which were “strongly” (“weakly”) excited by the striatum in conditions of dopamine release in response to the conditioned stimulus. __________ Translated from Zhurnal Vysshei Nervnoi Deyatel’nosti imeni I. P. Pavlova, Vol. 55, No. 4, pp. 444–458, July–August, 2005.