Application of L1-Norm Regularization to Epicardial Potential Solution of the Inverse Electrocardiography Problem

The electrocardiographic inverse problem of computing epicardial potentials from multi-electrode body-surface ECG measurements, is an ill-posed problem. Tikhonov regularization is commonly employed, which imposes penalty on the L2-norm of the potentials (zero-order) or their derivatives. Previous work has indicated superior results using L2-norm of the normal derivative of the solution (a first order regularization). However, L2-norm penalty function can cause considerable smoothing of the solution. Here, we use the L1-norm of the normal derivative of the potential as a penalty function. L1-norm solutions were compared to zero-order and first-order L2-norm Tikhonov solutions and to measured ‘gold standards’ in previous experiments with isolated canine hearts. Solutions with L1-norm penalty function (average relative error [RE] = 0.36) were more accurate than L2-norm (average RE = 0.62). In addition, the L1-norm method localized epicardial pacing sites with better accuracy (3.8 ± 1.5 mm) compared to L2-norm (9.2 ± 2.6 mm) during pacing in five pediatric patients with congenital heart disease. In a pediatric patient with Wolff–Parkinson–White syndrome, the L1-norm method also detected and localized two distinct areas of early activation around the mitral valve annulus, indicating the presence of two left-sided pathways which were not distinguished using L2 regularization.     

Noninvasive Electrocardiographic Imaging (ECGI): Application of the Generalized Minimal Residual (GMRes) Method

Electrocardiographic imaging (ECGI) is a developing imaging modality for cardiac electrophysiology and arrhythmias. It reconstructs epicardial potentials, electrograms, and isochrones from electrocardiographic body-surface potentials noninvasively. Current ECGI methodology employs Tikhonov regularization, which imposes constraints on the reconstructed potentials or their derivatives. This approach can sometimes reduce spatial resolution by smoothing the solution. Accuracy depends on a priori knowledge of solution characteristics and determination of an optimal regularization parameter. These properties led us to implement an independent, iterative approach for ECGI—the generalized minimal residual (GMRes) method—which does not apply constraints. GMRes was applied to experimental data during activation/repolarization of normal and infarcted hearts. GMRes reconstructions were compared to Tikhonov reconstructions and to measured gold standards in isolated hearts. Overall, the accuracy of GMRes solutions was similar to Tikhonov regularization. However, in certain cases GMRes recovered localized potential features (e.g., multiple potential minima), which were lost in the Tikhonov solution. Simultaneous use of these two complementary methods in clinical ECGI will ensure reliability and maximal extraction of diagnostic information in the absence of a priori information about a patient's condition.© 2003 Biomedical Engineering Society. PAC2003: 8719Hh, 8757Gg     

Computational imaging of the cardiac activities using magnetocardiography

Abstract

The electrical impulses of the heart will generate a tiny magnetic field outside the thorax that is measured as Magnetocardiographic signals. The challenging study is to estimate the cardiac activities in terms of depolarisation and repolarization maps from the measured signals called as inverse problem. This is computed only if one has solved generic or subject- specific prior models using the anatomical structures of the myocardium, the torso and the detectors called as forward problem. In this study, the Discretised heart is priorily assumed as the dipolar sources forming a double layer. The thorax structure modelled with finite element meshes is considered in the forward study. The magnetocardiographic data are simulated using uniform double layer model representing transmembrane distribution on the epicardium and endocardium. Using this data, the activation maps are non-invasively imaged on the heart surface using Tikhonov’s regularisation technique. The inverse study is extended to reconstruct the depolarisation sequences of the abnormal cases.     

L-曲线估计正则化参数对高刺激率听觉诱发电位重建的影响

探讨在暂态的听觉诱发电位（AEP）重建问题中,当一些L-曲线中出现多个拐点,给正则化参数的确定带来困难时,如何确立最优的正则化参数。本研究提出把高刺激率下AEP去卷积问题转化为一个线性系统逆问题处理,并且引入正则化技术修正目标函数,以解决由于变换矩阵的病态条件带来的无效解;同时采用一个十分典型的正则化参数估计常用方法（L-曲线法）估计正则化参数;针对L 曲线方法存在欠估计的情况,提出在参数选择过程中结合AEP的先验知识,选择L-曲线曲率图中其他曲率极大值点所对应的正则化参数。结果表明,L-曲线方法在大多数情况下,能较好的估计正则化参数,在存在欠估计问题时,则要重新正确选择正则化参数。再重建的暂态AEP与常规AEP的相关系数分别提高了0.14和0.21,相对误差分别下降了0.30和3.25,从而实现暂态AEP信号较好重建。正则化参数控制着目标函数中正则化的程度,对暂态AEP的重建性能影响很大,对于存在复杂曲率结构的L-曲线,根据AEP自身范数的取值范围能够方便地确定出合理的正则化参数,从而改善了AEP重建性能。     

Increased chemokinetic and chemotactic responses of eosinophils in asthmatic patients

The aim of the present study was to investigate the migratory responses of eosinophil and neutrophil granulocytes from asthmatic patients compared with granulocytes from healthy individuals. Twenty-three patients with unstable and severe asthma and blood eosinophilia (greater than 400 x 10(6) cells/l) were selected for the study. Eosinophil and neutrophil chemotactic and chemokinetic responses were tested twice, at the beginning and end of a 5 week treatment period. Lung function was followed by daily measurements of PEF. The eosinophils of the asthmatics demonstrated increased chemokinetic responses to albumin, autologous serum, and normal human serum (NHS), and an increased chemotactic response to NHS at the beginning of the treatment period compared with eosinophils from the references. At the end of the period the eosinophil chemokinetic responses to albumin, autologous serum and NHS were still increased and so was the chemotactic response to zymosan-activated serum (ZAS). The neutrophil migratory responses were not increased compared with those of the references, except for the chemokinetic response to autologous serum, which was increased both at the beginning and end of the treatment period. Patients in whom the eosinophil migratory responses, to most of the agents used, decreased over the treatment period, demonstrated a significantly greater improvement of their lung function at the end of the period compared with patients in whom the eosinophil migratory responses increased. However, no direct relationship between eosinophil migratory responses and lung function of the patients was found. In conclusion, the present investigation demonstrated increased migratory responses of eosinophils from asthmatic patients. This enhanced responsiveness is proposed to be due to priming of the eosinophils in vivo, and might be one mechanism behind the selective recruitment of eosinophils to the lungs of asthmatics.     

Identification of IL-16 as the lymphocyte chemotactic activity in the bronchoalveolar lavage fluid of histamine-challenged asthmatic patients

Objective: We have previously demonstrated that the earliest lymphocyte chemotactic factors present in bronchoalveolar lavage fluid (BALF) of subjects with atopic asthma after subsegmental antigen challenge are IL-16 and MIP-1α, of which IL-16 appears to contribute a majority of the chemotactic activity. Because IL-16 is released in vitro after histamine stimulation of CD8⁺ T cells and epithelial cells, we evaluated the potential role of histamine in the release of IL-16 into the airways of allergic asthmatics in vivo. Methods: Eight allergic asthmatic subjects, six normal subjects, and six atopic nonasthmatic subjects were challenged with saline in the lingula and with serial concentrations of histamine (1 × 10^-7 to 5 × 10^-5 mol/L) in the right middle lobe followed by bronchoalveolar lavage (BAL) 15 minutes and 6 hours later. Results: The BALF from saline- and histamine-challenged lobes of normal subjects and atopic nonasthmatic subjects contained no significant lymphocyte chemoattractant activity. In six of the eight atopic asthmatic subjects, the histamine-challenged but not saline-challenged segment contained IL-16 chemotactic activity but no other identifiable lymphocyte chemoattractant activities at 6 hours. Conclusions: IL-16 appears in the airways after histamine challenge and therefore could contribute to the earliest infiltration of CD4⁺T cells and eosinophils observed after antigen challenge due to histamine release from mast cells. (J Allergy Clin Immunol 1998;101:786-792.)     

电阻抗成像技术

介绍了一种新的医学图像重建技术--电阻抗成像技术(EIT).EIT依据生物组织不同部位的导电参数(电阻率、介电常数/电容率)以及同一部位在正常和病变时导电参数的变化来判断疾病的源.EIT设备通过对体组织表面电流、电压的施加及测量来获知体组织内部导电参数的分布,并重建出反映体组织内部的图像.详细分析了EIT成像中遇到的关键问题以及现有的主要应对方法,列举了EIT技术在临床医学上的应用现状,同时对EIT在技术和临床上的发展趋势进行了展望.     

Effect of a 4-week treatment with theophylline on sputum eosinophilia and sputum eosinophil chemotactic activity in steroid-naive asthmatics

BACKGROUND: The precise mechanism of action of theophylline in asthma is not fully understood but recent data have drawn attention to its potential anti-inflammatory effect. OBJECTIVE: The purpose of this study was to assess the effect of theophylline on sputum eosinophilia and sputum eosinophil chemotactic activity in steroid-naive asthmatics. METHOD: We performed a 4-week randomized double-blind, placebo-controlled, parallel group study in 21 mild to moderate steroid-naive asthmatics whose sputum eosinophilia was found twice > 5% during the run in period. Eleven subjects received 600 mg/24 h theophylline for the first 2 weeks and 900 mg/24 h for the last 2 weeks while 10 subjects took a placebo for 4 weeks. Sputum was induced after 2 and 4 weeks of treatment and 1 week after stopping the treatment. The sputum samples were compared for their cell counts, eosinophil cationic protein (ECP) levels and eosinophil chemotactic activity using micro-Boyden chambers. RESULTS: Serum theophylline concentrations reached 7 and 11 microg/mL at V3 and V4, respectively. Intragroup comparisons showed that theophylline, but not placebo, caused a significant reduction in sputum eosinophil counts at V3 (62 +/- 10% from baseline, P < 0.01) and a strong trend at V4 (67 +/- 16% from baseline, P = 0.07) when compared to baseline. The intergroup difference obtained after comparing the area under the curve over the 4 week treatment period only approached the statistical significance (P = 0.08). At baseline the fluid phase of the sputum contained a significant eosinophil chemotactic activity which was inhibited after a 4-week treatment by theophylline (P < 0. 01) but not by placebo. The mean sputum theophylline levels after 4 weeks of treament (1.7 microg/mL) was lower than that required to cause significant inhibition of eosinophil chemotaxis in vitro. CONCLUSION: Theophylline decreases the natural sputum eosinophil chemotactic activity present in asthmatics. However, when using a small sample size, the 35% reduction in sputum eosinophilia achieved by theophylline failed to reach statistical significance when compared to that seen after placebo.     

A Minimal Product Method and Its Application to Cortical Imaging

In order to reduce the spatial blurring effect due to the head volume conductor, cortical imaging technique (CIT) can be used to reconstruct the cortical potential distribution from the scalp potential measurement with enhanced spatial resolution. To overcome the ill-posed nature of the inverse problem, Tikhonov regularization (TIK) and truncated Singular Value Decomposition (TSVD) are commonly used by choosing the appropriate regularization parameter and truncation parameter, respectively. We have developed a minimal product method (MINP) to determine the regularization and truncation parameters. The present computer simulation and experimental results indicate that the MINP can be easily implemented in both TIK and TSVD with satisfactory performance, and suggest the potential applications of the MINP method in determining the corner of the L-curve.     

Impaired chemotactic responses of bronchoalveolar leukocytes in experimental pneumoconiosis

Rats were exposed to clouds of the following pneumoconiotic dusts: quartz, coal-mine dust, and chrysotile asbestos at 10 or 50 mg/m3 for 8, 32, and 75 days; for comparison, rats were also exposed to the non-pathogenic dust titanium dioxide (TiO2). The bronchoalveolar leukocytes (macrophages and neutrophils) from dust-exposed and control rats were obtained by lavage and tested for their ability to migrate toward zymosan-activated serum. Varying amounts of neutrophils were present depending on the ability of the dust to cause inflammation and the length of exposure. There was a marked loss of chemotactic ability in leukocytes from rats inhaling the pneumoconiotic dusts compared with controls; TiO2-exposed leukocytes had some impairment of chemotaxis, but this was substantially less than that found with the pneumoconiotic dusts. The loss of chemotactic activity did not correlate with the percentage of neutrophils in the lavage cells except when there were very high levels of neutrophils, and there was substantial impairment of chemotaxis with negligible numbers of neutrophils, showing that macrophage chemotaxis was impaired. A phagocytic burden within the leucocytes was not sufficient alone to inhibit chemotaxis, nor was the loss of chemotactic activity due to occupied receptors, since incubation failed to restore chemotaxis. Loss to chemotactic activity by leukocytes from pneumoconiotic dust-exposed lung could be an important factor in the development of pneumoconiosis.     

The functional heterogeneity of murine-resident macrophages to a chemotactic signal and induction of C3b-receptor-mediated ingestion

Peritoneal macrophages (MØ) were derived from unstimulated Balb/c mice and separated into distinct subpopulations based on their buoyant densities on discontinuous gradients of Percoll. They were assayed for their relative capacities to migrate toward a chemotactic stimulant and to be induced, in vitro, to express C3b-receptor-mediated ingestion. Functional heterogeneity was demonstrated in both chemotactic responsiveness and in the induction of ingestion activity; two subpopulations representative of approximately 50% of the peritoneal MØ were both quantitatively more responsive to a chemotactic stimulus and to the induction of ingestion activity. Upon cultivation of the MØ for up to 4 days an initially unresponsive subpopulation (i.e. to the induction signal for ingestion) acquired the capacity to respond to the signal for the induction of C3b-coated erythrocytes, whereas a fourth subpopulation remained unresponsive. These findings suggest that among a population of unstimulated MØ there may exist subpopulations in different states of differentiation.     

A quantitative microassay for leukocyte chemotaxis,using a microscopic slide system with complement-activating yeast particles as gradient source

A simple quantitative microassay was developed for studying polymorphonuclear leukocyte (PMNL) chemotaxis under conditions where the number of available cells is a limiting factor, e.g., pustules, neutropenia, small children and cerebrospinal fluid.PMNL suspensions are placed on glass slides to which fluorescein-labeled yeast particles have been fixed. After adherence, normal human serum is added to the slides. Owing to complement activation, a chemotactic gradient which attracts the adherent PMNL is formed around the yeast particles. The number of PMNL-associated yeast particles in the presence of normal serum is scored, and compared with cells migrating in the presence of inactivated serum or in the absence of serum. A locomotory index is calculated as the number of yeast particles associated with PMNL divided by the total number of yeast particles.     

Apolipoprotein(a) is a human vascular endothelial cell agonist: studies on the induction in endothelial cells of monocyte chemotactic factor activity

Elevated levels of lipoprotein(a), Lp(a), are associated with premature atherosclerosis; however, the mechanisms of its atherogenicity are not known. Recruitment of monocytes to the blood vessel wall is an early event in atherogenesis. Since Lp(a) is associated with macrophages in the plaque, we have examined the effect of Lp(a) on inducing monocyte chemotactic activity (MCA) in vascular endothelial cells. We report that Lp(a) and apo(a) induced human umbilical vein (HUVEC) and coronary artery endothelial cells to secrete monocyte chemotactic activity as early as 30 min of incubation. In the absence of cells, Lp(a) had no direct monocyte chemotactic activity. Actinomycin D and cycloheximide inhibited the HUVEC response, indicating that protein and RNA synthesis were required. Endotoxin was shown not to be responsible for the induction of monocyte chemotactic activity. Granulocyte monocyte-colony stimulating factor antigen was not detected in the Lp(a)-conditioned medium, nor was monocyte chemoattractant protein-1 mRNA induced by Lp(a). These results suggest that Lp(a) may be involved in the recruitment of monocytes to the vessel wall, thus providing a novel mechanism for the participation of Lp(a) in the atherogenic process.     

A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor

Present address: Program in Scientific Computing and Computational Mathematics, Division of Applied Mechanics, Durand 252, Stanford University, California 94305, USA. In order to accomplish the transition from avascular to vasculargrowth, solid tumours secrete a diffusible substance known astumour angiogenesis factor (TAF) into the surrounding tissue.Endothelial cells which form the lining of neighbouring bloodvessels respond to this chemotactic stimulus in a well-orderedsequence of events consisting, at minimum, of a degradationof their basement membrane, migration, and proliferation. Amodel mechanism is presented which includes the diffusion ofthe TAF into the surrounding host tissue and the response ofthe endothelial cells to the chemotactic stimulus. The modelaccounts for the main observed events associated with the endothelialcells during the process of angiogenesis (i.e. cell migrationand proliferation); the numerical results compare very wellwith experimental observations. The situation where the tumour(i.e. the source of TAF) is removed and the vessels recede isalso considered.     

The role of an adherent cell in the production of monocyte chemotactic factor

The functional role of an adherent cell in assisting a variety of in vitro immune responses is well established. An assay for human monocyte chemotaxis in vitro was utilized as a means of investigating the role of adherent cells in the production of the monocyte chemotactic factor that is produced by peripheral blood lymphocytes upon stimulation with Concanavalin A. Depletion of a population of adherent cells by passage of peripheral blood mononuclear cells through a Sephadex G-10 column rendered the latter incapable of producing monocyte chemotactic factor. The requirement for adherent cells in the production of a ‘lymphokine’ is in agreement with many previous works of a similar nature performed in other experimental systems.     

Direct Inference of the Spectra of Pericardial Potentials Using the Boundary-Element Method

New methods, based on Tikhonov regularization, were developed to infer the magnitude and phase of pericardial potentials directly. These methods were tested in an adult-male torso model using measured human epicardial potentials. With 1% noise added to body-surface potentials, regularization with an optimal parameter at each frequency from 1 to 100 Hz gave an average relative error (RE) in inferred spectral magnitudes of 0.44. Regularization with the composite–residual–smoothing–operator (CRESO) parameter increased the RE slightly to 0.47. With 10% additive noise, 10 mm overestimation of heart radius, and a 10 mm error in heart position, the average CRESO parameter from 1 to 100 Hz gave an average RE of 0.71. Performance was frequency dependent. The smallest REs occurred at low frequencies. With 1% noise, optimal regularization gave average REs of 0.20, 0.40, and 0.53 in the 1–15, 15–46, and 46–100 Hz bands, respectively. Direct inference of spectral magnitudes was more accurate than Fourier transformation of inferred time-domain waveforms. Results suggest that when heart size and location are not known, minimum REs in spectral estimates are found using an overestimated heart size and a regularization parameter which is the average value over the frequency band of interest. © 1999 Biomedical Engineering Society. PAC99: 8719Hh, 8719Nn, 0260Lj     

脑磁源成像技术的研究进展

基于分布源模型的脑磁源成像 (neuromagnetic source im aging)技术构架在图像重建基础上重建脑内神经活动的电流源分布图像 ,是 MEG逆问题中一个非常活跃和开放的研究方向。本文较为系统地论述了磁源成像的发展过程 ,并对目前一些常用的具体重建方法进行了介绍和分析。由于脑磁逆问题的不定性 ,必须引人正则方法来转化为适定问题 ,文中从确定性和随机性两大正则理论框架的角度来阐述各种重建方法。最后探讨了脑磁源成像技术的发展动向     

Adhesion molecule expression and response to chemotactic agents of human monocyte-derived macrophages

Human monocyte-derived macrophages have been proposed as agents of anti-tumour immunotherapy. The aim of the present study was to investigate in vitro the properties of these cells likely to control their recruitment to the sites of inflammation and tumours. The expression of adhesion molecules involved in the binding of monocytes to endothelial cells was modified during monocyte-macrophage differentiation, with a significant increase in CD11c, CD14 and intercellular adhesion molecule-1 (ICAM-1). Monocyte-derived macrophages were sensitive to chemoattractants, in particular to the monocyte-specific chemokine monocyte chemotactic protein-1 (MCP-1). They responded by an increased expression of adhesion molecules and were attracted by the cytokine in an under-agarose migration assay. The migration response, however, decreased after days 4–5 of monocyte differentiation into macrophage. In conclusion, human monocyte-derived macrophages show alterations of surface structures involved in the recognition of inflammatory endothelium. This may explain why the cells are poorly recruited to the sites of inflammation and tumours when introduced into the circulation.     

基于GMRES和Tikhonov正则化的生物电阻抗图像重建算法

电阻抗层析成像(Electrical impedance tomography,EIT)是利用被测物体场内部电导率分布不均匀性,通过边界注入电流,测量边界电压变化,重构被测场内电导率分布图像。由于EIT测量数据有限,场域存在严重的非线性,导致问题的欠定性。我们介绍了一种新的组合算法,利用GMRES算法生成Krylov子空间,并结合Tik-honov正则化方法进行图像重建。该算法不仅改善了实时性,而且提高了成像质量及鲁棒性。