Quantitative assessment of peripheral arterial obstruction in Raynaud's phenomenon: development of a predictive model of obstructive arterial cross-sectional area and validation with a Doppler blood flow study.

The objective of this study was to develop a method for the analytical assessment of arterial obstruction in conditions of Raynaud's phenomenon capable of providing diagnostic criteria. Numerous attempts have been made to determine and quantify arterial obstruction in terms of Doppler ultrasound measurements of arterial blood velocity. Absent from these methods is a formulation that allows an assessment of arterial obstruction based on the obstructed area as derived from direct measurement. The authors used spectral analysis of velocity signals from a pulsed, range-gated Doppler ultrasonic instrument to make quantitative measurements of arterial blood flow velocity in hands of normal subjects and persons with Raynaud's phenomenon. They measured the peak and mean velocity during the cardiac cycle and the time integral of the velocity signal over the cardiac cycle. These measurements for two distinct hemodynamic states induced by temperature changes allowed them to calculate the fractional change in arterial cross-sectional area produced by the change in temperature through the application of a hydraulic model of digital arterial circulation. They found an equation expressing fractional obstructed area expressed as: dA/A = 2 (dD - taudv - vtau)/(D + vdtau), where D is the time integral of the velocity signal; tau is the blood flow interval, v is the blood velocity; and dD, dtau and dv are the differences in D, tau, and v at two different hemodynamic states produced by two different temperature states. Their findings suggest that over a temperature range of 35 degrees-25 degrees C, normal subjects experience 0.05/ degrees C reduction in cross-sectional area while Raynaud subjects experience a reduction of 5.8%/degrees C. The results, based on findings in 13 subjects, suggest that Doppler ultrasound can differentiate persons with Raynaud's phenomenon from normal subjects. Additionally, the hydraulic model appears to offer the potential of assessing relative stenotic area in other arterial obstructive diseases.

Interpretation of the HJ interval of the normal ballistocardiogram based on the principle of conservation of momentum and aortic ultrasonic Doppler velocity measurements during left ventricular ejection.

The principle of conservation of momentum and the observation that blood acceleration in the ascending aorta is approximately constant during ventricular ejection was applied to develop a new interpretation of the HI and IJ intervals of the normal ballistocardiogram. The results indicate that the acceleration (A), velocity (V), and displacement (D) of the ballistocardiogram in the HI and IJ phases may be expressed by a set of equations which, when evaluated numerically, give theoretical acceleration, velocity, and displacement curves. The theoretical A, V, and D curves corresponded closely to those observed on the normal ballistocardiogram record during the HJ interval.

A transmission line model of the normal aorta and its branches.

A computer model of the aorta and its branches was made based on a simulation of an electrical transmission line using T elements. The model represented the aorta, with branches to the arms and legs and a branch to the head. The values for the capacitance and inductance of each T element could be specified, and a linearly increasing left ventricular pressure was used to drive the model. Transmission line equations were used to select values for the components, and an attempt was made to simulate the results of measurements of blood velocity in the aorta and peripheral arteries of normal subjects. The values obtained with the model showed a close relation to those in experimental studies. The results support the hypothesis that the arterial bed can be well represented by a "lossless" branched transmission line, with impedances matched at each branch and terminated with resistances that give a reflection coefficient of 0.5. A driving function, in which a linearly increasing left ventricular pressure provided a transient input to an aortic root of relatively low impedance, gave the best simulation of the experimental results.

Echographic application of the Gorlin formula for assessment of aortic stenosis: correlation with cardiac catheterization in pediatric patients.

We have investigated the use of M-mode echocardiography for the diagnosis of aortic valve stenosis by application of the Gorlin formula. The hemodynamic parameters which enter this formula are shown to derive wholly from noninvasive measurements. The predicted valve areas correspond with those derived by classical catheterization studies at a level of r = 0.89, SE = 0.11 cm2, n = 10. These results suggest that the Gorlin formula for aortic stenosis may have application in a noninvasive context.

Cardiac valve area formula for the assessment of aortic stenosis based upon evaluation of left ventricular wall stress in diastole.

We have investigated the application of an hydraulic orifice equation employing aortic valve pressure gradient derived from ventricular diastolic wall stress measurements to estimate obstructive orifice area in aortic stenosis. The expression is given by A = SV square root (D/W)/(750t), where A is the aortic valve area in cm2, SV is the stroke volume in ml, D is the left ventricular minor axis dimension in diastole, W is the left ventricular posterior wall thickness in diastole and t is the systolic ejection period in sec. Valve areas computed by this expression using diastolic wall stress measurements correspond with valve areas derived from the Gorlin formula at a level characterized by a correlation coefficient of r = 0.95 and a standard error of SE = 0.16 cm2, N = 13 for a series of catheterization studies. All the parameters that enter the new expression may be estimated by conventional echocardiographic techniques.

Doppler ultrasonic investigation of Raynaud's phenomenon: effect of temperature on blood velocity.

We have used spectral analysis of signals from a pulsed, range-gated Doppler ultrasonic instrument to make quantitative measurements of arterial blood flow velocity in the hands of normal subjects and persons with Raynaud's phenomenon. We measured the peak velocity during the cardiac cycle and the time integral of the velocity signal over the cardiac cycle. This latter parameter gives a sensitive indication of the degree of vasoconstriction in response to cold. Our preliminary results, based on findings in 13 subjects, suggest that Doppler ultrasound can differentiate persons with Raynaud's phenomenon from normal subjects.

Two-dimensional echocardiographic method for the estimation of cardiac output independent of left ventricular geometry. Comparison with cardiac catheterization in mitral stenosis.

An hydraulic formula for the estimation of cardiac output independent of the geometric status of the left ventricle was studied by comparing the predictions based upon echographic and catheterization data with the results of the standard Fick principle method for cardiac output. The formula tested specifies cardiac output as Q = (1/21) RAT2, where Q is the cardiac output in ml, R is the heart rate, A is the mitral valve area in cm2 and T is the diastolic filling period in seconds per minute. Cardiac output estimated by this equation corresponds with cardiac output as determined by the Fick principle method at a level characterized by a correlation coefficient of r = 0.92 and a standard error of SE = 0.15 L/min for N = 26. The results suggest that the new expression may be useful for estimating cardiac output from echographic data.

An orifice formula independent of mitral pressure gradient for the evaluation of prosthetic mitral valve obstruction.

We have studied an hydraulic orifice equation capable of quantifying the obstructive properties of mitral prostheses from data of a potentially less invasive nature than is required by conventional methods. The results indicate that effective prosthetic orifice area may be computed by the pressure independent equation A = 21SV/DFP2, where A is the effective prosthesis orifice area in cm2, SV is the stroke volume in ml and DFP is the diastolic filling period in s min-1. Areas computed with the pressure independent equation correlate with the results of the modified Gorlin formula (given in the appendix) at a level of r = 0.91 for a series of 17 cases within a range of effective valve areas of 0.50 cm2 to 1.60 cm2. These results suggest that simplified nontraumatic procedures may be developed to screen and follow patients with prosthetic valve implants.

Echocardiographic aortic valve area formula for the estimation of obstruction in stenosis.

We have investigated the use of M-mode echocardiography for the quantification of aortic valve stenosis through the application of a hydraulic orifice equation using only noninvasively determined hemodynamic variables. The new equation is A = (2/5)SV/(t3/2 dP1/4HR), where A is the effective aortic valve area in cm2, SV is the stroke volume in ml, t is the systolic ejection period in seconds, dP is the echographically estimated aortic valve gradient and HR is the heart rate. The predicted valve areas correspond with those derived by conventional cardiac catheterization studies at a level of r = 0.84, SE = 0.14 cm2, N = 10. The results suggest that M-mode echocardiography may have application to the quantitative diagnosis of aortic stenosis.

Elementary echographic estimation of cardiac output independent of the symmetry and kinetic state of the left ventricle in mitral stenosis. Potential application to the determination of the circulation of pregnancy.

An orifice equation is demonstrated which is independent of the symmetry and kinetic state of the left ventricle. The expression allows calculation of the cardiac output in conditions of mitral stenosis when the mitral valve area is known. This equation is Q = (1/21) R A T2, where Q = cardiac output in ml/min, R = heart rate, A = mitral valve area and T = diastolic filling period in sec/min. Ten patients whose gynecologic or obstetric exam suggested a diagnosis of mitral stenosis were evaluated by conventional cardiac catheterization and M-mode echocardiography. Cardiac output computed using the new equation and the Fick principle corresponded at r = 0.95, SE = 340 ml, N = 10. These results suggest that cardiac output may be conveniently estimated for serial studies by the readily measurable echographic variables of heart rate and diastolic filling period once the mitral valve area has been measured by conventional catheterization or bi-dimensional echographic methods.

A pressure independent orifice equation for the estimation of diastolic mitral valve area in mitral insufficiency: correlation with cardiac catheterisation data using a radioactive Krypton indicator method for the determination of regurgitant filling volume.

We have investigated the application of an hydraulic orifice equation for the computation of diastolic mitral valve area in conditions of regurgitation. The new equation is given by Af = 21 Vf/T2, where Af is the total forward flow mitral valve area in cm2, Vf is the diastolic filling volume in ml, T is the diastolic filling period and 21 is a discharge coefficient derived from clinical haemodynamic data. Areas computed by the new formula correlate with valve areas as computed by the Gorlin formula at a level given by r = 0.93, n = 27. The results suggest that the new formula may be utilised in the context of mitral insufficiency and further, considerating the nature of the haemodynamic variables involved, an echographic quantification of this condition by M-mode or bidimensional echocardiography may be possible.

Echocardiographic formula for computation of left ventricular volume and stroke volume. Comparison with cardiac catheterization and the Teichholz formula.

An elementary computational formula for estimating cardiac volume and stroke volume from either M-mode or bi-dimensional echographic data is developed from an analysis of retrospective catheterization, angiographic and echographic data. The proposed equation has the form, V = 0.01 D12/5, where V is the cardiac volume in ml, 0.01 is a unit conversion constant and D is the ventricular dimension in mm. The new model assumes the validity of the Teichholz correction factor to the volume of an ellipsoid of revolution as an approximation of left ventricular cardiac volume. Application of this model to retrospective echographic data reveals that the new formula enjoys an identical domain of validity as the Teichholz formula, deviating from this model by less than 1% over a range of cardiac volumes from 20 to 180 ml. Comparison of this cardiac volume formula with a series of 37 echographic and catheterization measurements of stroke volume yields a correlation of r = 0.95 with a standard error of S.E. = 14.3 ml in comparison with the Fick principle method for cardiac stroke volume. The results of this study suggest that the present expression offers a computational simplification of the Teichholz formula, facilitating modifications for other configurations while retaining this expressions favorable correlation with invasive measurements of cardiac volume.

Non-invasive determination of the aortic valve area in stenosis: hydraulic orifice formula for application to echocardiography and correlation with catheterization.

We have investigated the validity of a hydraulic orifice formula which specifically excludes explicit dependence on the aortic valve pressure gradient in aortic stenosis. The new equation requires knowledge of stroke volume and systolic ejection periods (s/min) and is expressed as, A = 7 V/T2, where A is the effective aortic valve area in cm2, V is the stroke volume in cm3, T is the systolic ejection period in s/min and 7 is a clinically derived orifice coefficient. The data base consisted of 33 pediatric patients undergoing cardiac catheterization for the quantification of aortic stenosis. Additionally 12 of these patients had a conventional M-mode echographic investigation offering sufficient information to test the orifice formula in a non-invasive context. Using potentially non-invasive portions of the catheterization data, the new formula correlated with the classical Gorlin formula at a level of r = 0.85, s.e. = 0.22 cm2. In the M-mode echographic context with stroke volume computed from left ventricular dimensions by the Teichholz equation, the new formula yielded an area correlation with classical methods given by r = 0.87 and s.e. = 0.21 cm2. Additionally five cases each of subvalvular and supravalvular aortic stenosis were studied revealing significant differences in the flow parameters in these two cases. These initial results suggest that non-invasive methods may be of value in quantification, screening and follow-up of patients with stenotic aortic valve disease.

Echographic method for the estimation of cardiac output from mitral-valve area, heart rate, and diastolic-filling period in conditions of mitral stenosis: correlation with cardiac catheterization.

An orifice equation for the non-invasive measurement of mitral-valve area is demonstrated. It is shown that by combining this expression with the assumption of mitral-valve area invariance an orifice equation for the non-invasive assessment of cardiac output in conditions of mitral stenosis using simple echographically measureable variables can be developed. This equation is V = (21)-1 R X A X T2, where V = cardiac output in ml, R = heart frequency, A = mitral-valve area in cm2 and T = diastolic-filling period in sec X min-1. These results suggest that when mitral-valve area is accurately measured at one point in time, cardiac output may be measured at subsequent times at a clinically useful level from a knowledge of the echographically measurable variables of heart rate and diastolic-filling period.

Hydraulic orifice formula for echographic measurement of the mitral valve area in stenosis. Application to M-mode echocardiography and correlation with cardiac catheterisation.

A mitral valve orifice equation has been formulated which allows the computation of mitral valve area (A) from the echographically measurable variables of stroke volume (SV) and diastolic filling period (DFP) in seconds per minute by the formula, A=21 (SV)/(DFP)2. Mitral valve areas computed from M-mode echographic measurements are shown to correlate with areas computed by the Gorlin formula (r-0.90) for resting state conditions of predominant mitral stenosis of clinical grades 2 to 4. The results suggest that, in the absence of wall motion irregularities, M-mode echocardiography can quantitatively assess the mitral valve area in stenosis.

Noninvasive determination of the mitral valve area in stenosis: a computational model and correlation with autopsy and open heart measurements.

An analytical formulation has been developed which allows the computation of mitral valve area (A) from the potentially noninvasive paramaeters of hear rate (R), cardiac output (CO) and diastolic filling period (DFP) by the equation A = 21 CO/R x DFP2. The computed areas correlate with autopsy and open heart measurements (r = 0.91) for resting state conditions of moderate to severe mitral stenosis. These results suggest that noninvaasive methods can have an application in mitral valve determinations.

Medulloblastoma: example of late adult onset with statistical correlation relative to etiology.

A case of histologically verified medulloblastoma occurring in an 88-year-old woman is described. A search of the literature indicates that with respect to age this case is unique. Further, 33 histologically verified cases of medulloblastoma reported in the literature are analyzed with respect to incidence and prognosis as a function of histological type, tumor location, age and sex. The statistical study has confirmed the relative relationships found by Chatty and Earle in their analysis of 105 cases in 1971 and has further indicated a tendency for male desmoplastic differentiation. A survey of an additional 216 cases in the literature reveals an improvement in average survival from 25 to 27 months since 1971, possibly reflecting refined therapeutic techniques. The changing survival expectany with surviving interval has been computed at 10 months per survival year.