Cardiac systolic index of contractility is modeled by Emax (currently). Emax point(s) selection could be dependent on afterload (AL) resistance during measurement as AL is changing independently and could be influenced by e.g., ventilation, autonomic NS, pharmaceuticals etc., On this slides you can appreciate new approach of modeling of systolic elastance, based on more-physiological End-systolic point selection (ES) points.

2. MODELING OF CARDIAC CONTRACTILITY-
SYSTOLIC INDEX (ESPVR); COMPARISON OF ES (END
SYSTOLIC POINT) VS. EMAX (MAX. PV POINT)
Dr. Filip Konecny

3. Furthermore, on the left side of the slide, additional characteristics are presented. In case of the sum of squares due to error SSE characterizes the curve-linear fit through individual end systolic chamber
elastances. As we are selecting these individual points, we need to know that R VALUE should be higher than 0.7 to obtain reasonable goodness of fit for given preload reduction.
The X axis or volume Intercept IC or (V0) plays a role in acknowledging as to WHERE the chamber's minimal volume lies if hypothetically, we lower chamber's pressure to the minimum P0. This might mean that at
V0 (minimal chamber Volume point) for given ventricle values can not pass this point as all blood would be at this point ejected out. Please note this (V0) or volume IC is very different as compared to minimal
ESV or minimal volume (Vmin) calculated and displayed in the analysis files.
From Emax points created slope Ees (end systolic elastance) indicates how much the LV end-systolic volume (ESV) decreases in response to a decrease of end-systolic pressure (ESP) during temporary preload
reduction. Ees=ESP/ESV Ees units are mmHg/ml
During preload reduction, as venous return decreases by temporary occlusion of inferior vena cava IVC, in this example, the maximal PV ratio and thus individual elastances decreases as chamber voids the
volume through unobstructed aortic outflow (with constant amount of afterload). Volume is not leaving the LV chamber linearly, rather leaves faster as compared to LV pressure as could be seen on the
waveform channel example above the tabulated data (red waveform for P and black for V).
Basic outline of modeling Systolic Index ESPVR
In the PV loop plane (XY plot) green PV loops, where
the Maximal PV ratio occurs is called the end
systolic ventricular elastance E max (for given loop).
When points are connected relationship ESPVR is
created; in this case a curve-linear slope called Ees
(the end-systolic elastance). . At this point the ratio of
P vs. V can be also referred to as end systolic
chamber elastance (to extrapolate it for LV and RV
chamber). This was originally modeled by Suga and
Sagawa as being linear (1, 2)
REF:
1.Suga H, Sagawa K, Shoukas aa. Load Independence of the
Instantaneous Pressure-Volume Ratio of the Canine Left Ventricle
and Effects of Epinephrine and Heart Rate on the Ratio. Circ Res.
Mar; 1973 32(3):314–322. [PubMed: 4691336]
2. Suga H, Sagawa K. Instantaneous Pressure-Volume
Relationships and Their Ratio in the Excised, Supported Canine
Left Ventricle. Circ Res. Jul; 1974 35(1):117–126. [PubMed:
4841253]
Introduction to the modeling of ESPVR, systolic load-independent
index of cardiac contractility

4. 3 ELEMENTARY STATES PRIOR TO PRELOAD REDUCTION
OF LOAD-DEPENDENT PRESSURE-VOLUME LOOP (PVL)
This is graphical representation of left ventricle PVL planes from 3 different hemodynamic conditions before attempting preload reduction by IVC occlusion to obtain indices of load
independent indices of LV contractility. Ideally, the systolic indices of load-independent ESPVR obtained by reducing filling volume should be performed under a stable afterload resistance
(afterload impedance). In this case we could observe that in example A, the ejection phase of the cardiac cycle has to be adjusted to large afterload impedance. In the example C,
situation is opposite. The idealized condition could be seen as condition B, where the systemic vascular impedance is close to being exhibited as a constant.
To note: Afterload impedance during pre-load maneuvers matters; moreover, the position of the PVL on the X-volume axis before the preload reduction is equally important.

5. Example A HR ESP EDP Pmax Pmin dPmax dPmin P@dP/dt max P@dP/dt min
bpm mmHg mmHg mmHg mmHg mmHg/sec mmHg/sec mmHg mmHg
Mean 227 187.36 5.255 192.779 1.648 8992.778 -7771.82 101.259 157.2
SD 6 2.047 1.063 2.301 0.15 184.185 225.714 2.961 3.482
Example C HR ESP EDP Pmax Pmin dPmax dPmin P@dP/dt max P@dP/dt min
bpm mmHg mmHg mmHg mmHg mmHg/sec mmHg/sec mmHg mmHg
Mean 347 85.28 1.433 96.095 -0.802 6178.237 -4670.266 56.588 61.9
SD 2 1.206 0.312 0.788 0.053 99.264 62.618 1.814 2.013
B
A
MAX PV point
MAX PV point
ES point
ES point
3 full cardiac cycles using example from swine are
shown (above).
LVP, LVV, Ao P trace and LV dp/dt channels are
presented while red cursors indicate ejection
phase of cardiac cycle (from dp/dt max to min).
Dp/dt min is associated with closure of Ao valve
which indicates the end of systole in LV. Pressure
at this location is also known as P@dp/dt min (as
shown on the right side of this slide; yellow
highlight).
Data and waveform graphs on the right side of
this slide are from rat following examples A and
B, while locating P@ dp/dt min and comparing its
location at PV loop plane using red and blue
boxes.
Selecting Max PV point-Emax or going with
more physiologically relevant ES ?

6. ESPVR:
Selection Duration: 5.471 sec
Equation: P = -0.016168*V^2 + 3.506851*V + -31.543)
SSE Value = 869.171
Intercept(V0) = 9.402
ESPVR slope (sqrt(b2_4ac)) = 3.203
ESPVR:
Selection Duration: 3.342 sec
Equation: P = -0.084732*V^2 + 14.736189*V + -553.944)
SSE Value = 179.537
Intercept(V0) = 54.957
ESPVR slope (sqrt(b2_4ac)) = 5.423
ESPVR:
Selection Duration: 3.342 sec
Equation: P = -0.031930*V^2 + 5.807375*V + -199.440)
SSE Value = 345.486
Intercept(V0) = 45.953
ESPVR slope (sqrt(b2_4ac)) = 2.873
ES points
ES points
MAX PV points
MAX PV points
A A A
Intercept(V0) = 0.793
SSE Value = 1381.404
Equation: P = -0.015012*V^2 + 3.407630*V + -2.691)
ESPVR:
Selection Duration: 5.471 sec
ESPVR slope (sqrt(b2_4ac)) = 3.384
Modeling of cardiac contractility-systolic indices (ESPVR); comparing ES (end systolic point) vs. Emax (Max. PV point)
B
B B
Comparison ES and
Emax based ESPVR
Comparison ES and
Emax in ESPVR
A and B
Comparison
ES and Emax in ESPVR
ES (point selection dp/dt min) based ESPVR
ES (point selection dp/dt min) based ESPVR

7. CONCLUSION
INDEX (ESPVR); COMPARING ES (END SYSTOLIC POINT) VS. EMAX (MAX. PV POINT)
1. When performing temporary preload reduction by IVCO there will be always presence of an afterload (AL)
impedance. Level of impedance would vary during e.g., single experiment or in-between group of control animals
(slide 3 A, B and C). There is always possibility to perform swift AL occlusion by aortic constriction, if variation is
excessive (detected before IVCO).
2. Similarly, preload reduction differs based on the amount of the initial afterload impedance. Moreover, the quality
of the preload reduction should be judged by e.g., IVCO SSE (sum of squared errors); Time of Preload reduction
by IVCO (sec); ∆ P (mmHg) P (max)- (P end) in mmHg and other parameters please see
3. Lastly, both End Systolic elastance slopes (Ees) within the relationship-ESPV, constructed from (Emax vs. ES points)
should be compared to ensure quality of Emax point as they might not be always determined suitably as
compared to ES points (see slide 4) for details of capture of Emax point.