symmetry has long fascinated the great minds in many disciplines from art to theoretical physics . in the field of medicine
the circulation system is powered mainly by cardiac muscle and valves activities , which are specifically the coherent dilation and contraction of right and left ventricles .
today , left ventricular systolic function evaluation has become routine in most clinical settings ; left ventricular diastolic function measurement is getting more and more attentions ; unfortunately , satisfactory assessment of right ventricular function is still a dream by clinicians due to lack of available reliable indexes .
a number of new indexes introduced in this paper as a result of the symmetry concept will enable us to obtain a much better picture of cardiac function .
this is easy to understand with many cardiac clinicians / researchers having already taken advantage of it .
the second level of symmetry is systole and early diastole , which is based on the fact that both systolic and early diastolic processes are active .
this will lead to the finding of counterparts of indexes used only in either systolic or early diastolic process .
however , there is no farther endeavor to systemically explore how far and deep this theory can go . at the beginning of human development , both the ventricles developed from two adjacent segments of the primary heart tube .
the left ventricle will pump up the systemic circulation , while the right ventricle needs to provide energy to the pulmonary circulation . in the pulmonary system ,
the circulation resistance is approximately a third of that in the systemic circulation , which makes the right ventricle wall thickness roughly half of its left neighbor .
since the left ventricle is much stronger , the interventricular septum is captured in the regular daily task of left ventricular contraction and relaxation . in terms of shape and power ,
both ventricles are asymmetric . with our interests focusing on the behavior of contraction and relaxation
echocardiography branches from medical imaging where ultrasound waves are used to exam the structure and function of the heart . here , we are interested in what the symmetry principle will bring us in this rapidly evolving field .
symmetry of both left and right ventricular activity with regard to behavior is supported by some indexes describing both ventricles. in 1989 , bargiggia , et al .
introduced dp / dt to describe left ventricular systolic function , ten years later , oh , et al . pushed it on the right side of the heart .
another example is the tei index , , which is also developed to evaluate both ventricular functions .
symmetry of both diastolic and systolic processes is suggested by the fact that both are active . due to
left ventricular relaxation is active , left ventricular diastolic time constant is discovered and well accepted to be the most established index to describe left ventricular diastolic function . since left ventricular contraction is also an active process ; it is reasonable for us to think that left ventricular systolic time constant exists .
this idea can be tested with a similar experiment conducted by weiss , et al . except focusing on the systolic process .
interestingly , based on the developed computational and mathematical methods , we can prove the symmetry between left ventricular systole and diastole . to introduce the proof ,
we first examine the calculation of tau , which is : tau = 1.2 ( t1  t3 ) , ( t1  t3 ) is the time interval from 3 m / s to 1 ms on the descending branch of continuous wave doppler mitral regurgitation spectrum .
this means , ( t1  t3 ) is the core to evaluate left ventricular diastolic function . in terms of left ventricular systolic function evaluation by dp / dt , we can find that dp / dt = 32/(t3  t1 ) , ( t3  t1 ) is the time interval from 1 m / s to 3 m / s on the ascending branch of continuous wave doppler mitral regurgitation spectrum .
since only ( t3  t1 ) is a variable , it is the key to evaluate left ventricular systolic function .
it is interesting to ponder upon the question as to how much this symmetry of systole and diastole principal can cover .
the systole includes isovolumic contraction and ejection phases . however , there are four phases in diastole : isovolumic relaxation , rapid inflow , diastasis and atrial systole . from the above analysis , we come to a conclusion that there could be symmetric tau and dp / dt , which reveals the symmetry exists between isovolumic contraction and isovolumic relaxation .
it deserves to mention that during isovolumic periods , both the aortic and mitral valve are closed , which makes it the best time to evaluate cardiac function due to relative independence of foreload and afterload .
since the active cardiac muscle movement is still a driving force of these periods , especially in the early stage of the phase , symmetry should still apply .
for example , the color m - mode flow propagation velocity could be measured in both phases . in the late stage of the phases , the active systolic contraction
/ diastolic relaxation comes to an end , which shows that the symmetry is ready to phase out .
the last two phases of diastole , diastasis and atrial systole , can not be found in systole .
so far , there are two levels of symmetry in cardiac function evaluation , one is the symmetry of left and right ventricles , and the other is the symmetry between systole and early diastole . under this principal
, we introduce a list of new indexes that can be valuable in cardiac function evaluation
the dp / dt is used to describe both left and right ventricular systolic function ( figure 1a , c ) . today , dp / dt is integrated into many echo machines on the market for evaluation of left and right ventricular systolic function . with the symmetric contraction and relaxation on mind ,
we can introduce two new indexes to evaluate left and right ventricular diastolic function from dp / dt .
this will be of great interest to clinicians and/or researchers , who have been enthusiastic with the systolic dp / dt ( s ) .
the same measurement can be done on the other branch of the regurgitation spectrum ( figure 1a , c ) . with regards to the methodology , dp / dt measurement
can also be done on aortic or pulmonary regurgitation spectrum ( figure 1b , d ) .
the left ventricular diastolic time constant , tau is the most established index to describe left ventricular diastolic function
. with increasing interests focusing on the non - invasive endeavors in echo lab , and blessed by the fast digital technology progress , tau could be measured in our local clinic in the near future. the non - invasive calculation of tau is based on the measurement performed on either the descending branch of the continuous - wave doppler mitral regurgitation spectrum , or the ascending branch of continuous - wave doppler aortic regurgitation spectrum ( figure 1a , b ) . suggested by the symmetry principle , the following three types of missing tau will come into light : ( 1 ) left ventricular systolic time constant ; ( 2 ) right ventricular diastolic time constant ; and ( 3 ) right ventricular systolic time constant .
ai : aortic insufficiency ; lv : left ventricle ; mr : mitral regurgitation ; pi : pulmonary regurgitation ; rv : right ventricle ; tr : tricuspid regurgitation .
left ventricular diastolic time constant is the most established index to describe left ventricular diastolic function .
right ventricular tau(s ) are even more pragmatic since there are more pulmonary and tricuspid regurgitations , compared with aortic and mitral valve regurgitations .
furthermore , right ventricular tau(s ) are more valuable since few satisfactory indexes exist to describe right ventricular function due to its irregular shape ( dr sherif nagueh , personal communication ) .
ai : aortic insufficiency ; lv : left ventricle ; mr : mitral regurgitation ; pi : pulmonary regurgitation ; rv : right ventricle ; tr : tricuspid regurgitation .
ai : aortic insufficiency ; lv : left ventricle ; mr : mitral regurgitation ; pi : pulmonary regurgitation ; rv : right ventricle ; tr : tricuspid regurgitation .
myocardial performance index or tei index is used to evaluate both the left and right ventricular function . , both the tei indexes focus on systolic elements . following the two level symmetry principle , there should be two more tei indexes focusing on diastolic elements .
this index is measured with color doppler m - mode when the mitral valve opens from the four - chamber view .
the m - mode cursor is placed in the center of the column of mitral valve .
color m - mode flow propagation velocity is used to evaluate left ventricular diastolic function . by applying symmetry principle , we will get three new indexes : ( 1 ) the first one can be used to evaluate left ventricular systolic function with the color doppler m - mode cursor placed in the center of left ventricular outflow tract . (
2 ) the second one can be used to evaluate right ventricular diastolic function with the color doppler m - mode cursor placed in the center of the column of tricuspid valve . (
3 ) the third one can be used to evaluate right ventricular systolic function with the color doppler m - mode cursor placed in the center of the right ventricular outflow tract . all about color m - mode flow propagation velocity
so far , only four doppler major indexes in echocardiography have been analyzed based on the two level symmetry principle .
we are showing another seventeen ( question marks in the tables ) indexes or measurement approaches under symmetry principle in this paper .
clinicians and/or researchers working with other cardiac imaging facilities may try this symmetry principal in their own field as well .
the idea of symmetry in cardiac function assessment will fly when all indexes in the tables are tested one by one in the future .
lv : left ventricle ; lvot : left ventricular outflow tract ; mv : mitral valve ; rv : right ventricle ; rvot : right ventricular outflow tract ; tv : tricuspid valve .
the dp / dt is used to describe both left and right ventricular systolic function ( figure 1a , c ) . today , dp / dt is integrated into many echo machines on the market for evaluation of left and right ventricular systolic function . with the symmetric contraction and relaxation on mind ,
we can introduce two new indexes to evaluate left and right ventricular diastolic function from dp / dt .
this will be of great interest to clinicians and/or researchers , who have been enthusiastic with the systolic dp / dt ( s ) .
the same measurement can be done on the other branch of the regurgitation spectrum ( figure 1a , c ) . with regards to the methodology , dp / dt measurement
can also be done on aortic or pulmonary regurgitation spectrum ( figure 1b , d ) .
the left ventricular diastolic time constant , tau is the most established index to describe left ventricular diastolic function
. with increasing interests focusing on the non - invasive endeavors in echo lab , and blessed by the fast digital technology progress , tau could be measured in our local clinic in the near future. the non - invasive calculation of tau is based on the measurement performed on either the descending branch of the continuous - wave doppler mitral regurgitation spectrum , or the ascending branch of continuous - wave doppler aortic regurgitation spectrum ( figure 1a , b ) . suggested by the symmetry principle , the following three types of missing tau will come into light : ( 1 ) left ventricular systolic time constant ; ( 2 ) right ventricular diastolic time constant ; and ( 3 ) right ventricular systolic time constant .
ai : aortic insufficiency ; lv : left ventricle ; mr : mitral regurgitation ; pi : pulmonary regurgitation ; rv : right ventricle ; tr : tricuspid regurgitation .
left ventricular diastolic time constant is the most established index to describe left ventricular diastolic function .
right ventricular tau(s ) are even more pragmatic since there are more pulmonary and tricuspid regurgitations , compared with aortic and mitral valve regurgitations .
furthermore , right ventricular tau(s ) are more valuable since few satisfactory indexes exist to describe right ventricular function due to its irregular shape ( dr sherif nagueh , personal communication ) .
ai : aortic insufficiency ; lv : left ventricle ; mr : mitral regurgitation ; pi : pulmonary regurgitation ; rv : right ventricle ; tr : tricuspid regurgitation .
ai : aortic insufficiency ; lv : left ventricle ; mr : mitral regurgitation ; pi : pulmonary regurgitation ; rv : right ventricle ; tr : tricuspid regurgitation .
myocardial performance index or tei index is used to evaluate both the left and right ventricular function .
, both the tei indexes focus on systolic elements . following the two level symmetry principle , there should be two more tei indexes focusing on diastolic elements .
this index is measured with color doppler m - mode when the mitral valve opens from the four - chamber view .
the m - mode cursor is placed in the center of the column of mitral valve .
color m - mode flow propagation velocity is used to evaluate left ventricular diastolic function . by applying symmetry principle , we will get three new indexes : ( 1 ) the first one can be used to evaluate left ventricular systolic function with the color doppler m - mode cursor placed in the center of left ventricular outflow tract . ( 2 ) the second one can be used to evaluate right ventricular diastolic function with the color doppler m - mode cursor placed in the center of the column of tricuspid valve .
( 3 ) the third one can be used to evaluate right ventricular systolic function with the color doppler m - mode cursor placed in the center of the right ventricular outflow tract . all about
so far , only four doppler major indexes in echocardiography have been analyzed based on the two level symmetry principle .
we are showing another seventeen ( question marks in the tables ) indexes or measurement approaches under symmetry principle in this paper .
clinicians and/or researchers working with other cardiac imaging facilities may try this symmetry principal in their own field as well .
the idea of symmetry in cardiac function assessment will fly when all indexes in the tables are tested one by one in the future .
lv : left ventricle ; lvot : left ventricular outflow tract ; mv : mitral valve ; rv : right ventricle ; rvot : right ventricular outflow tract ; tv : tricuspid valve .
 both right and left ventricles are developed from two adjacent segments of the primary heart tube . 
 though they are different with regard to shape and power , they mirror each other in terms of behavior . 
 this is the first level of symmetry in cardiac function assessment . 
 both cardiac muscle contraction and relaxation are active . 
 this constructs the second level of symmetry in cardiac function assessment . 
 combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function . in this article , 
 four major indexes from echocardiography were analyzed under this principal , another seventeen indexes or measurement approaches came out of the shadow , which is very helpful in the assessment of cardiac function , especially for the right cardiac function and diastolic cardiac function . 
Introduction
Symmetry in cardiac function assessment
Application in echocardiography
Ventricular contractility assessment (dp/dt)
Left ventricular diastolic time constant
Myocardial performance index
Color M-mode flow propagation velocity