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Table 1 Equations for the mathematical models studied, and the general terms of lower and upper asymptotes, inflection point and points of maximum curvature. *The second derivative of model 3 is a transcendental equation, so a general term cannot be calculated.

From: Comparative study of four sigmoid models of pressure-volume curve in acute lung injury

   

Volume

Pressure

Model

Ref.

Equation

Lower asymptote

Upper asymptote

Inflection

LPMC

UPMC

1

21

V = a + b 1 + e − ( P − c ) / d MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGwbGvcqGH9aqpcqWGHbqycqGHRaWkdaWcaaqaaiabdkgaIbqaaiabigdaXiabgUcaRiabdwgaLnaaCaaaleqabaGaeyOeI0IaeiikaGIaemiuaaLaeyOeI0Iaem4yamMaeiykaKIaei4la8Iaemizaqgaaaaaaaa@3DFE@

a

a + b

c

c - 1.317d

c + 1.317d

2

18

V = b 1 + e − ( P − c ) / d MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGwbGvcqGH9aqpdaWcaaqaaiabdkgaIbqaaiabigdaXiabgUcaRiabdwgaLnaaCaaaleqabaGaeyOeI0IaeiikaGIaemiuaaLaeyOeI0Iaem4yamMaeiykaKIaei4la8Iaemizaqgaaaaaaaa@3BD1@

0

b

c

c - 1.317d

c + 1.317d

3

12

V = V 0 − V 0 e − k P 1 + e − ( P − c ) / d MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGwbGvcqGH9aqpdaWcaaqaaiabdAfawnaaBaaaleaacqaIWaamaeqaaOGaeyOeI0IaemOvay1aaSbaaSqaaiabicdaWaqabaGccqWGLbqzdaahaaWcbeqaaiabgkHiTiabdUgaRjabdcfaqbaaaOqaaiabigdaXiabgUcaRiabdwgaLnaaCaaaleqabaGaeyOeI0IaeiikaGIaemiuaaLaeyOeI0Iaem4yamMaeiykaKIaei4la8Iaemizaqgaaaaaaaa@4522@

0

V 0

*

*

*

4

11

V = a + b [ 1 + e − ( P − c ) / d ] s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGwbGvcqGH9aqpcqWGHbqycqGHRaWkdaWcaaqaaiabdkgaIbqaamaadmaabaGaeGymaeJaey4kaSIaemyzau2aaWbaaSqabeaacqGHsislcqGGOaakcqWGqbaucqGHsislcqWGJbWycqGGPaqkcqGGVaWlcqWGKbazaaaakiaawUfacaGLDbaadaahaaWcbeqaaiabdohaZbaaaaaaaa@4196@

a

a + b

c − d ln 1 s MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGJbWycqGHsislcqWGKbazcyGGSbaBcqGGUbGBdaWcaaqaaiabigdaXaqaaiabdohaZbaaaaa@356E@

c − d ln ( 3 s + 1 ) − 5 s 2 + 6 s + 1 2 s 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGJbWycqGHsislcqWGKbazcyGGSbaBcqGGUbGBdaWcaaqaaiabcIcaOiabiodaZiabdohaZjabgUcaRiabigdaXiabcMcaPiabgkHiTmaakaaabaGaeGynauJaem4Cam3aaWbaaSqabeaacqaIYaGmaaGccqGHRaWkcqaI2aGncqWGZbWCcqGHRaWkcqaIXaqmaSqabaaakeaacqaIYaGmcqWGZbWCdaahaaWcbeqaaiabikdaYaaaaaaaaa@4635@

c − d ln ( 3 s + 1 ) + 5 s 2 + 6 s + 1 2 s 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGJbWycqGHsislcqWGKbazcyGGSbaBcqGGUbGBdaWcaaqaaiabcIcaOiabiodaZiabdohaZjabgUcaRiabigdaXiabcMcaPiabgUcaRmaakaaabaGaeGynauJaem4Cam3aaWbaaSqabeaacqaIYaGmaaGccqGHRaWkcqaI2aGncqWGZbWCcqGHRaWkcqaIXaqmaSqabaaakeaacqaIYaGmcqWGZbWCdaahaaWcbeqaaiabikdaYaaaaaaaaa@462A@