Michiyoshi Kuwahara

Simple stability criteria for single and composite linear systems with time delays

Easy ways to test the stability of systems involving time delays have been sought. In this paper, several stability conditions with an extremely simple form are provided. First, some criteria for single linear systems with time delays are presented. Then these results are extended to the composite linear systems with time delays which exist in each subsystem and in the interconnections between subsystems. Among these criteria, those which are expressed by scalar inequalities also permit us to assess the transient behaviour of systems.

On an estimate of the decay rate for stable linear delay systems

In this paper it is shown that for a certain class of stable linear delay systems we can obtain an estimate of the decay rate of the solution by a simple computation.

Changes in diastolic properties of the regional myocardium during pacing-induced ischemia in human subjects.

Mechanisms related to alterations in the diastolic properties of the left ventricle during angina were studied in seven patients with coronary artery disease. Single plane left ventriculograms were obtained using a high fidelity micromanometer-tipped catheter in both the resting state and immediately after rapid cardiac pacing. In all patients, typical anginal pain developed with pacing stress. After atrial pacing, the left ventricular end-diastolic pressure increased from 10 +/- 3 to 21 +/- 7 mm Hg (+/- standard deviation) (p less than 0.005) regardless of the changes in the end-diastolic volume. The ejection fraction was reduced from 59 +/- 10 to 48 +/- 13% (p less than 0.05). The diastolic pressure-volume curves shifted upward in post-pacing beats in four patients, while in three the curves shifted more to the right. The regional myocardial function was expressed in quantitative terms by a radial coordinate system with the origin at the center of gravity of the end-diastolic silhouette. Two representative radial grids for normal and ischemic segments were selected. In the normal segment, the end-diastolic length was augmented by 15% (p less than 0.005) and was associated with a 24% increase in stroke excursion with pacing stress (p less than 0.05). The increase in diastolic pressure was accompanied by comparable increases in end-diastolic length, and the diastolic pressure-length relation moved up to the higher portion of the single curve. In the ischemic segment, the end-diastolic length remained unchanged in the post-pacing beat, but segment shortening was significantly reduced.(ABSTRACT TRUNCATED AT 250 WORDS)

Automated method for left ventricular volume measurement by cineventriculography with minimal doses of contrast medium

Cineventriculography is of considerable value in the dimensional analysis of the left ventricular cavity, but conventional methods necessitate injection of large amounts of contrast medium. In this study, small dose left ventriculography, using only 5 ml of dye, was performed in order to minimize the untoward effects of contrast medium. A computer-aided image processing system was also developed to enhance the contrast of the ventricular image by subtracting the reference image to eliminate irrelevant background. The boundary of the left ventricular cavity was automatically determined to calculate the instantaneous volume change throughout the cardiac cycle. With use of this small dose of dye, the elevation of left ventricular end-diastolic pressure that consistently occurred 1 to 3 minutes after injection of conventional large doses could be avoided. (End-diastolic pressure at 1 minute after dye injection averaged 11.8 +/- 4.9 [mean +/- standard deviation] for small dose and 19.1 +/- 6.1 mm Hg for large dose injection.) Values for end-diastolic volume, end-systolic volume and ejection fraction calculated from the two consecutive small and large dose left ventriculograms in 16 patients were similar. Thus, minimal doses of contrast medium permit accurate measurement of left ventricular dimension and function without significant hemodynamic derangement. The optimal projection for regional wall motion analysis can easily be selected by this method with repeated exposure at various degrees of obliquity. With this technique, even noninvasive measurement of left ventricular volume can be provided by intravenous injection of small doses of contrast agent.

Analysis of asynchronous wall motion by regional pressure-length loops in patients with coronary artery disease.

The progression of regional dysfunction during angina pectoris was studied in eight patients with coronary artery disease. Single plane left ventriculograms were obtained using a high fidelity micromanometer-tipped catheter both at rest and immediately after rapid cardiac pacing. Each image of the left ventriculogram was digitized and transferred to a computer. The boundary of the ventricular cavity was automatically determined and sequentially superimposed. Regional shortening was quantified by a radial coordinate system originating at the center of gravity of the end-diastolic silhouette. Thirty-two radial grids were drawn around the center of gravity, and the length of each radial grid was measured to characterize the centripetal motion of a given surface point. Each radial length was then plotted simultaneously and continuously against left ventricular pressure to generate a pressure-length loop. The area of the pressure-length loop provided an index of regional myocardial work. In the ischemic ventricle, the loops exhibited a striking deformity in configuration. Prolonged relaxation of ischemic segments was associated with outward motion of the normal segments. Shortening of the normal segment occurred earlier than that of the ischemic segment associated with its stretch. Thus, the loops of the two areas inclined in opposite directions. Pacing stress increased the magnitude of hypofunction in the potentially ischemic area, the average extent of shortening being reduced by 30% and the segmental work by 25% (p less than 0.005). In the normal area, contrary to the significant increase in segmental shortening (20% above control values [p less than 0.005]), the average segmental work remained at 7% below control values because of an augmented deformation of the loop.(ABSTRACT TRUNCATED AT 250 WORDS)

A stability criterion for linear time-varying systems

In this paper, we derive an algebraic stability criterion of linear time-varying systems employing a specific metric in state-space. Though the used metric includes arbitrary parameters as weights, the criterion itself does not incorporate them. However, if we ask for these parameters, an estimate of the transient state of the systems can be obtained through them. Three examples are illustrated to clarify the character of the obtained criterion.

Upper and lower bounds for the solution to the discrete Lyapunov matrix equation

Both upper and lower bounds for each eigenvalue of the solution to the discrete Lyapunov matrix equation are derived.

Three-dimensional analysis of regional myocardial function in response to nitroglycerin in patients with coronary artery disease

Biplane cineventriculography was performed at rest and after sublingual nitroglycerin in 13 patients with coronary artery disease. In six patients (responders), there was a significant increase in ejection fraction [40 +/- 5 to 52 +/- 4% (p less than 0.001)], while in the other seven (nonresponders), there was no alteration in ejection fraction. To evaluate the extent of regional myocardial response to nitroglycerin, the contractile pattern of the regional myocardium over the entire ventricular surface was analyzed using a computer-generated three-dimensional model. The spatial coordinates that define the elliptic ventricular surface on a given horizontal plane cross section of the chamber were determined by four counter values in the two orthogonal silhouettes. Then, 32 points at equal angles around the center of gravity of the end-diastolic cavity were generated to form the border image. Repetition of this process for 16 successive cross sections allowed for reconstruction of the ventricular surface by the sequence of 32 X 16 (512) points. The regional wall motion was expressed as the percent change of the radial length, drawn from the center of gravity to each surface point. There was significant heterogeneity in regional response to nitroglycerin. In the responders, the normally contracting area was significantly increased (from 16.5 +/- 16.0 to 36.2 +/- 14.9% of the total surface area, p less than 0.001), largely mediated by the greater improvement in segmental shortening of each graded contractile pattern relative to its deterioration. In the nonresponders, a lessening of the severe dysfunction of the given area was associated with significant deterioration of segmental shortening of the other normally contracting area (49.1 +/- 19.7% of the area with a contractile pattern of grade 5 had deteriorated, p less than 0.05). Thus, the ratio of the area with respective graded segmental shortening was virtually unchanged. These differences in response of the ischemic ventricle to nitroglycerin appeared to be related to the development of adequate coronary collateral vessels as well as to an interaction of changes in preload and afterload.

Left ventricular image processing

Left ventricular image processing methods of x-ray cineangiocardiograms and ultrasound echocardiograms are discussed. 3-D reconstruction methods of the left ventricle from ultrasound echocardiograms and magnetic resonance images are also discussed. Boundary detection of the left ventricle and the quantitative analysis of the left ventricular function and wall motion are discussed. To reconstruct 3-D shapes, we need several cross sectional shapes or silhouettes of the left ventricle. Several cross sectional echo images of apical long axis view are taken by changing the angles of rotation of the probe of echo transducer around its axis. Gated multi-phase MRI method is used to obtain each 2 cross sectional images in transverse, coronal and sagittal directions. Some results of 3-D shapes of the left ventricle and myocardium reconstructed are shown and 3-D functional images which give us regional functions of the left ventricular wall on three dimensional shape are shown.

3-D heart image reconstructed from MRI data

An outline of 3-D image reconstruction techniques for the left ventricle and the whole heart from MRI (magnetic resonance imaging) data is discussed. A method is proposed to reconstruct 3-D shapes of each part of the heart, i.e. left ventricle, left atrium, right ventricle, right atrium, aorta and pulmonary artery, in a voxel space using the cross-sectional images obtained by gated MRI of the heart on the transverse, coronal, and sagittal planes. The heart composed by putting together these six parts is superimposed on the original cross-sectional images.<<ETX>>