Characterization of Aging-Associated Cardiac Diastolic Dysfunction

Transcription

1 Chrcteriztion of Aging-Associted Crdic Distolic Dysfunction Wei-Ting Chng 1,2., Jung-Sn Chen 3., Yung-Kung Hung 3, Wei-Chun Tsi 1, Jer-Nn Jung 3 *, Ping-Yen Liu 1,2 * 1 Division of Crdiology, Internl Medicine, Ntionl Cheng Kung University Hospitl, Tinn, Tiwn, 2 Institute of Clinicl Medicine, Ntionl Cheng Kung University, Tinn, Tiwn, 3 Deprtment of Engineering Science, Ntionl Cheng Kung University, Tinn, Tiwn Abstrct Aims: Distolic dysfunction is common in geritric hert filure. A relible prmeter to predict myocrdium stiffness nd relxtion under similr end-distolic pressure is being developed. We propose mteril nd mthemticl model for clculting myocrdium stiffness bsed on the concept of liner correltion between e=e nd wedge pressure. Methods nd Results: We enrolled 919 ptients (mle: 52:6%½484=919Š). Compred with the younger popultion of controls (men ge: 43:9+11:7 yers; n~211; mle: 62:1% ½131=211Š), the elderly (men ge: 76:3+6:2; n~708; mle: 52:6% ½484=708Š) hd greter prevlence of hypertension, dibetes mellitus, nd coronry rtery disese (ll pv0:05). We collected their M-mode nd 2-D echocrdiogrphic volumetric prmeters, intrventriculr filling pressure, nd speckle trcking imges to estblish mthemticl model. The fesibility of this model ws vlidted. The verge erly distolic velocity of the mitrl nnulus ssessed using tissue Doppler imging ws significntly ttenuted in the elderly (e : 0:09+0:02 vs. 0:08+0:02; p~0:02) nd corresponded to the higher estimted wedge (e=e ) pressure (7:76+2:44 vs. 8:35+2:64; p~0:02) in tht cohort. E (Young s modulus) ws clculted to describe the tensile elsticity of the myocrdium. With the sme intrventriculr filling pressure, E ws significntly higher in the elderly, especilly those with e=e vlues w9. Compred with distolic dysfunction prmeters, E lso presented sentinel chrcteristics more sensitive for detecting erly myocrdil relxtion impirment, which indictes stiffer myocrdium in ging herts. Conclusion: Our mteril nd geometric mthemticl model successfully described the stiffer myocrdium in ging herts with higher intrventriculr pressure. Additionl studies tht compre individul differences, especilly in helth sttus, re needed to vlidte its ppliction for detecting distolic hert filure. Cittion: Chng W-T, Chen J-S, Hung Y-K, Tsi W-C, Jung J-N, et l. (2014) Chrcteriztion of Aging-Associted Crdic Distolic Dysfunction. PLoS ONE 9(5): e doi: /journl.pone Editor: Sudhirnjn Gupt, Texs A & M, Division of Crdiology, United Sttes of Americ Received November 6, 2013; Accepted April 20, 2014; Published My 28, 2014 Copyright: ß 2014 Chng et l. This is n open-ccess rticle distributed under the terms of the Cretive Commons Attribution License, which permits unrestricted use, distribution, nd reproduction in ny medium, provided the originl uthor nd source re credited. Funding: This reserch ws supported in prt by the Hedqurters of University Advncement t the Ntionl Cheng Kung University, which is sponsored by the Ministry of Eduction, Tiwn, ROC. The reserch ws lso grnted from Helth Promotion Progrm: Blood Pressure Control from Helth Promotion Administrtion, Ministry of Helth nd Welfre, Tiwn, ROC nd the grnt from NSC B MY2, sponsored by the Ministry of Science nd Technology, Tiwn, ROC. The investigtor (PY Liu) ws grnted by A Lndmrk Project to Promote Innovtion & Competitiveness of Clinicl Trils by the Excellent Clinicl Tril nd Reserch Center in Ntionl Cheng Kung University Hospitl, Ministry of Helth nd Welfre, Tiwn. The funders hd no role in study design, dt collection nd nlysis, decision to publish, or preprtion of the mnuscript. Competing Interests: The uthors hve declred tht no competing interests exist. * E-mil: jjung@mil.ncku.edu.tw (JNJ); lrry@mil.ncku.edu.tw (PYL). These uthors contributed eqully to this work. Introduction Hert filure is incresingly prevlent mong older dults [1]. Cliniclly,40{50% of ptients with symptomtic hert filure hve preserved left hert function, with preserved ventriculr ejection frction (w50%) [2]. Sometimes this is clled distolic dysfunction with preserved systolic function or distolic hert filure [3]. People with distolic hert filure re generlly older nd femle, nd tend to hve greter incidence of systemic hypertension thn do those with contrctile dysfunction ( systolic hert filure ) [4,5]. Physiologiclly, distolic hert filure occurs when the ventricle cnnot fill properly becuse it cnnot relx or its wll is too rigid [6]. Histologicl evidence supports the notion tht distolic dysfunction is relted to ventriculr hypertrophy, incresed interstitil collgen deposition into the myocrdium [7]. Similrly, ging herts continuously lose myocytes, which is compensted for by rective hypertrophy of the remining cells; thus, these herts re filled with fibrotic or dipose tissue [8]. Histologicl smples for mesuring the exct tensile elsticity of the myocrdium re possible only in niml studies, not humn studies. Some mthemticl models hve been used to describe the dynmics of remodeling in skeletl muscle, rteries, nd even the hert [9,10]. However, mthemticl model to study crdic ging is still lcking. Estblishing model of the ging hert would provide tool for us to understnd underlying mechnisms of crdic ging nd to define the impired myocrdil relxtion process. It remins uncertin whether current vilble invsive nd noninvsive dignostic tools cn ccurtely predict myocrdium stiffness. The time constnt of relxtion (tu, t), which describes PLOS ONE 1 My 2014 Volume 9 Issue 5 e97455

2 the rte of left ventriculr (LV) pressure decy during isovolumic relxtion, is currently the stndrd prmeter for predicting the relxtion function of myocrdium [11,12]. However, severl confounding fctors, when echocrdiogrphy is used to mesure the decelertion time of mitrl inflow, my disturb the equivlence between echocrdiogrphic nd ctheterized results. Despite the rtio of mitrl inflow to nnulus tissue, Doppler imging velocity (e=e ) indictes the intrventriculr pressure, which is within the borderline rnge of elevted pressure (e=e ~9{14), the discrimintion of distolic dysfunction remins dilemm [3]. Therefore, relible nd noninvsive dignostic prmeter is crucil for fcilitting n ccurte dignosis tht indictes whether the stiffness is myocrdil stiffness. Studies [13 21] on the elstic properties of the contrcting left ventricle hve roused gret del of interest mong scientists nd engineers. Mny reserchers hve developed series of experimentl techniques for determining the elstic properties of the left ventricle. A simple nd prcticl pproch for in vivo determintions of the properties of the cnine left ventricle, proposed in 1972 [13], estblished the reltionship between the effective elstic modulus nd the circumferentil stress throughout the isovolumetric systolic period. After the concept on the elstic properties of the left ventricle ws ccepted, some reserchers reported tht the effective modulus E mesured from experiments could lso be viewed s n dditionl indiction of the left ventricle hving djusted to the hert disese [14], which showed tht norml vlues of E during the systole directly indicte tht the strength of the left ventricle contrction is norml. The nomogrm, cliniclly usble closed-chest procedure for determining the elstic modulus, ws introduced in 1975 [15]. Using hert-soundfrequency nlysis followed by determintion of E, the loss of muscle-medium elsticity cn be roughly delineted. In ddition to improving dt-cquisition techniques, the modeling of the left ventricle is becoming more importnt fctor for determining myocrdil elsticity. These findings showed tht the stiffness of the complete ventricle should be considered function not only of myocrdil stiffness but lso of the cvity shpe, dimensions, nd structure of the vessel [16]. A better pproximtion for ventriculr modeling requires ssuming tht myocrdil stiffness is function of geometry nd stress. In other words, the geometry of the left ventricle is essentil for simulting it in model. Thick-wlled models re commonly nd widely used to study the dynmics of the ventricle. Severl studies [17 19] on crdic muscle mechnics, LV pump function, nd LV wll thickening view the left ventricle s thick-wlled cylindricl composite. They report tht the thick-wlled cylindricl frmework seems to be good nd prcticl pproximtion sufficient for simulting the left ventricle. One study [20] presented simple nlyticl model to describe the reltionship between ge-relted chnges in the structure nd function of mouse crdic muscle. It suggested tht ge-relted crdic srcopeni likely contributes to depressed LV function in the bsence of overt crdiovsculr disese. Recently, n lterntive mthemticl model for investigting crdic ging chrcterized by distolic dysfunction of the left ventricle ws introduced [21]. In contrst to the previous study, sphericl thick-wlled model nd stretch-induced tissue-growth postulte were used to predict LV dimension nd wll stiffness chnges in ging mice. The Young s modulus of the left ventricle ws determined by introducing smooth monotonic function to fit the experimentl dt nd simplified version of the liner mixture theory of composite mteril. It ws ssumed tht the pressure difference nd the Young s modulus of the left ventricle re two independent fctors tht ffect end-distolic dimension/dimeter nd wll thickness. The importnce of the ging effect on the lrge vessels nd crdic structure cn be lso seen from study [22] on the effect of hypertension on the dimeter nd elstic modulus of the ortic rch; it showed tht the elstic modulus ws significntly correlted with ge in ptients with, but not without, hypertension. In ddition, both the ortic rch dimeter nd the elstic modulus re lrger in ptients with sustined uncomplicted essentil hypertension. Bsed on the proven liner correltion between mitrl e velocity, corrected for the influence of relxtion (e=e rtio) nd intrventriculr pressure (similr to wedge pressure; r~0:87; pulmonry cpillry wedge pressure (PCWP)~1:24 ½e=e Šz1:9) [23], we hve creted crdic mthemticl model to simulte the remodeling process under vrious pressures during the ging process. Unlike other reserch groups, we hypothesized tht the pressure, elstic modulus, nd LV dimension re mutully influenced, tht the reltionship of the elstic modulus to pressure, wll thickness, nd ge cn be estblished with the mthemticl model, nd tht the ging effect on LV wll thickness cn lso be determined using the fixed pressure. Mterils nd Methods Ptients We enrolled 919 ptients (mle: 52:6% ½484=919Š) nd divided them into two cohorts: (1)Echo z : ptients given echocrdiogrphy on physicl exmintion t our university hospitl between Februry 2012 nd June 2013, nd (2) TOP (Echo { ): the Tinlio Old People (TOP) study between July 2010 nd August 2012 [24,25]. Echocrdiogrphic prmeters bsed on the recommendtions of the Americn Society of Echocrdiogrphy [26], medicl records, nd clinicl questionnires were collected from ptients in the cohort. Ptients with poor imge window, LV systolic dysfunction, or significnt (.moderte severity) vlvulr hert disese were excluded. This study ws pproved by the Institutionl Review Bord of Ntionl Cheng Kung University Hospitl (IRB no: ER ), nd ech ptient signed n informed consent form before the physicl exmintion. Echocrdiogrphy Stndrd echocrdiogrphy ws done (Vivid I; GE Vingmed Ultrsound AS, Horten, Norwy) using 3.5-MHz multiphserry probe. The chmber dimensions nd LV mss were mesured using the two-dimensionlly guided M-mode method, nd the LV ejection frction (LVEF) ws mesured with the twodimensionl M mode (Figure 1A). Intrventriculr septl width (IVSd), LV internl dimension (LVIDd), LV posterior wll width (LVPWd), nd LV internl dimension (LVIDs) were mesured sequentilly to clculte geometry nd ejection frction. Trnsmitrl Doppler flow velocity ws obtined from n picl fourchmber view, nd pek erly filling velocity (e), pek tril velocity (), nd the E=A rtio were recorded. Erly distolic nnulr velocity (e ) nd tril nnulr velocity ( ) were lso mesured to estimte the LV end-distolic pressure (e=e ). The verge of medil nd lterl e=e ws used to represent the estimted intrventriculr pressure. To mesure the circumferentil strin, 20 ptients were rndomly selected from the Echo z cohort to receive speckletrcking echocrdiogrphy (STE) (Figure 1B). Short-xis views t the ppillry muscle level were recorded in digitl loops for deformtion nlysis of the left ventricle. The imges were cquired t frme/sec nd stored for three cycles. The imges were nlyzed offline using computer softwre (EchoPAC 09; GE-Vingmed Ultrsound AS, Horten, Norwy). After trcking the mrgin of endocrdium, the softwre detected the myocrdil PLOS ONE 2 My 2014 Volume 9 Issue 5 e97455

3 Stiffer Aging Herts with Distolic Dysfunction muscle level. C: The model of the cylinder, gross nd cross-section. doi: /journl.pone g001 motion during the entire crdic cycle. The circumferentil strin of six segments ws verged nd used in the computtion for the condition tht ehh =0. Sttisticl nlysis SPSS 18.0 (SPSS Inc., Chicgo, IL) ws used for dt mngement nd sttisticl nlyses. Dt re mens 6 stndrd devition (SD). Continuous vribles were compred using Student s t test for normlly distributed vlues. Significnt fctors in univrite nlysis were entered into multivrite nlysis. Multivrite logistic regression nlysis ws used to identify the independent significnce of E in ptients with distolic dysfunction. A Person s prtil correltion coefficient (r) between E nd e=e ws clculted. Sttisticl tests were 2-sided; significnce ws set t pv0:05. Mthemticl modeling In this section, mthemticl model for computing the myocrdium stiffness of the left ventricle is presented. The left ventricle is ssumed to be mde of elstic, isotropic, nd homogeneous tissue tht will completely recover its ntive form when the forces re removed. To cpture LV wll dynmics, thick-wlled cylindricl pressure vessel ws used (Figure 1C). The cylinder llows resonbly complex motions of the left ventricle, viz., rdil infltion, xil extension, torsion, nd trnsmurl sher reflecting cross-sectionl view of the cylinder. The uniform internl (pi ) nd externl (po ) pressures re respectively pplied to the inner nd outer surfces of the cylinder. The interior rdius nd exterior rdius of the cylinder re denoted by nd b, respectively. The quntity r denotes the rdius t n rbitrry position between nd b [27]. For simplifiction, the strin norml to the cross-sectionl plne (r2h plne), ezz, nd the sher strins crz nd chz re ssumed to be zero. Hence, the present three-dimensionl problem cn be reduced to n equivlent two-dimensionl one involving pproximtion. In ddition, the cylinder is ssumed to be xisymmetric, i.e., the deformtion nd loding conditions of the cylinder re independent of h. Then the rdil stress srr nd circumferentil stress shh cn be redily obtined s srr ~ p {p z ð p {p Þ i o o i 2 2 r2 1{ =b2 b ð1þ ð Þ p {p { p {p o o i 2 2 i r2 1{ =b2 b ð2þ shh ~ The corresponding strins cn be cquired from the constitutive reltion (stress-strin reltion), nmely Figure 1. The echocrdiogrphic prmeters nd the mthemticl model for computing the myocrdium stiffness of the left ventricle. A: The mesured echocrdiogrphic prmeters. IVSd: intrventriculr septl width in distole; LVIDd: left ventriculr internl dimension in distole; LVPWd: left ventriculr posterior wll width in distole; nd LVIDs: left ventriculr internl dimension in systole. B: The mesuring circumferentil strin in the short-xis, t the ppillry PLOS ONE 3 1zn ½srr {n(srr zshh ) err ~ E ð3þ 1zn ½shh {n(srr zshh ) ehh ~ E ð4þ My 2014 Volume 9 Issue 5 e97455

4 Tble 1. The clinicl nd echocrdiogrphic chrcteristics of the younger nd older cohorts. Vrible Younger cohort n = 211 (22.9%) Older cohort n = 708 (77.1%) p-vlue Age (yers) ,0.001 Mle 131 (62.08) 484 (68.82),0.001 HTN 21 (9.95) 349 (49.22),0.001 DM 11 (5.21) 122 (17.2),0.001 CAD 6 (2.84) 71 (10.01) 0.02 ECHOCARDIOGRAPHIC PARAMETERS IVSd (cm) LVPWd (cm) LVIDd (cm) LVIDs (cm) LVEF (%) e (m/s) e/ e9 (m/s) e/e IVRT DT E (Young s modulus) Dt re n% ð Þ or men or + stndrd error; HTN = hypertension; DM = dibetes mellitus; CAD = coronry rtery disese; IVSd = inter-ventriculr septl dimeter in distolic phse; LVPWd = left ventriculr posterior wll dimeter in distolic phse; LVIDd = left ventriculr internl distolic dimension; LVIDs = left ventriculr internl systolic dimension; e = erly distolic mitrl inflow velocity; e/ = the rtio of erly to lte distolic mitrl inflow velocity; e9 = the verge erly distolic velocity of mitrl nnulus in tissue Doppler; LVEF = left ventriculr ejection frction. doi: /journl.pone t001 where e rr is the rdil strin, e hh is the circumferentil strin, n is Poisson s rtio, nd E is the Young s modulus. Solving Eq. (3) nd Eq. (4) yields E~ s ð rrz2s hh Þð1{s hh Þ e rr ðs rr zs hh Þ ð9þ n~ s hhe rr {s rr e hh ðs rr zs hh Þðe rr {e hh Þ " # E~ ð s rre rr {s hh e hh z2s hh e rr {2s rr e hh Þðe rr {e hh {s hh e rr zs rr e hh Þ e rr ðs rr zs hh Þðe rr {e hh Þ 2 ð6þ Substituting Eqs. (1) nd (2) into Eq. (6) gives E~ nh i h i o 2 b 2 { 2 2 b 2 p i{p o z 2 r 2 ð p o{p i Þ ðe rr {2e hh Þz 2 b 2 p i{p o { 2 r 2 ð p o{p i Þ ð2e rr {e hh Þ h i 2e 2 rr b 2 p i{p o { 2 r 2 ð p o{p i Þ ð7þ n h i h io e 2 hh : b 2 p i{p o z 2 r 2 ð p o{p i Þ {e 2 rr b 2 p i{p o { 2 r 2 ð p o{p i Þ h i 2e 2 rr b 2 p i{p o { 2 r 2 ð p o{p i Þ ð5þ Then the Young s modulus for e hh ~0 cn be redily derived s 1 E~ 32 2e 2 rr b 2 p i{p o b 2 p i{3p o { 2 r 2 ð p o{p i Þ : 1{ b2 2 b 2 { 2 b 2 p i{p o { 2 r 2 ð p o{p i Þ ð10þ The prmeters, b, p i, nd p o cn be cquired from experiments nd shown s follows: ~ LVIDd 2 b~ LVIDdz2LVPWd 2 ð11þ ð12þ If e hh is not considered, Eqs. (5) nd (6) cn be reduced to n~ s hh s rr zs hh ð8þ p i ~ 1:9z1:24e=e0 0:0075 ð13þ PLOS ONE 4 My 2014 Volume 9 Issue 5 e97455

5 Figure 3. The reltionship between E nd echocrdiogrphic intrventriculr pressure in the younger nd older cohorts. A: The reltionship between e=e nd E vlue in vrious ge group. B: The exponentil correltion between ge nd E in the regression nlysis. doi: /journl.pone g003 p o ~ 1:9z1:24e=e0 10 ð14þ 0:0075 Also, e rr is the rtio of the rdil elongtion to the distolic rdius, i.e., e rr ~ ðlvidd{lvidsþ=lvidd, nd e hh is n verge strin for six segments in the circumferentil direction. For computtion, the prmeter r in Eqs. (7) nd (10) ws chosen s zb=2. Results Figure 2. The correltions between e=e nd E both in the clinicl sttistics nd the mthemticl models. A nd B: The reltionship between e=e nd E in clinicl sttistics, nd C: in the mthemticl model. e=e = estimted intrventriculr pressure by the rtio of erly distolic mitrl inflow velocity nd the verged erly distolic velocity of mitrl nnulus in tissue Doppler imging; E~Young 0 s modulus. doi: /journl.pone g002 The clinicl nd echocrdiogrphic chrcteristics of the younger nd older cohorts The elderly cohort (w65 yers old) were significntly older (men ge~76:26+6:2 vs. 43:88+11:67 yers), hd higher prevlence of hypertension (49:2% vs. 10:1%), dibetes mellitus (17:2% vs. 5:2%), nd coronry rtery disese (9:9% vs. 2:74%; ll pv0:05) (Tble 1) thn did the younger cohort (n~211; mle~62:08%). All of them worked nd lived independently. Bsed on our previous questionnire in the TOP study [25], most lived n ctive life (11:8+7:61 h of wlking/week). PLOS ONE 5 My 2014 Volume 9 Issue 5 e97455

6 Tble 2. Multivrite regression nlyses for the independence of E vlue in younger ptients with distolic dysfunction. Vrible Odds Rtio 95% Confidence Intervl p-vlue Age Dibetes Mellitus IVSd IVRT E (Young s modulus) Abbrevitions: see Tble 1. doi: /journl.pone t002 To estblish model for predicting the stiffness chrcteristics of myocrdium, we used the M-mode nd 2-D echocrdiogrphic volumetric prmeters, intrventriculr filling pressure, nd STE from ll clinicl ptients nd the 2 cohorts. The fesibility of this model ws vlidted. Despite slight but significnt (p~0:01) difference in intrventriculr dimeter between the two cohorts (LVIDd~5:03+0:63 vs. 4:78+0:53), the LV systolic ejection frction ws within the norml rnge in ll ptients (LVEF~68:20+8:39 vs. 70:02+6:72; p~0:09). The men erly distolic velocity of the mitrl nnulus in tissue Doppler imging ws significntly ttenuted in the elderly cohort (e ~0:09+0:02 vs.0:08+0:02; p~0:02), which corresponds to the higher estimted wedge (e=e ) pressure (7:76+2:44 vs. 8:35+2:64; p~0:02). E (Young s modulus) ws clculted to describe the tensile elsticity of the myocrdium, which ws lso significntly (p~0:001) elevted in the elderly cohort (E~28,872: :74 vs. 31,325: :77). Insted of liner reltionship, the regression nlysis illustrted nonliner ssocition between ge nd E (E~10,000e 0:0162ge ; r 2 ~0:61) After excluding ptients with hypertension, dibetes mellitus, nd coronry rtery disese, the correltion between E nd distolic dysfunction remined significnt (pv0:05) in the helthy elderly compred with other echocrdiogrphic prmeters (Tble S1). The reltionship between E nd echocrdiogrphic intrventriculr pressure in the younger nd older cohorts There ws positive correltion between e=e nd E (E~7699:07e=e 0 z2806:7; r~0:87; pv0:001) both in the clinicl sttistics (Figure 2A,B) nd in the mthemticl models (Figure 2C). The slope of the trend line shown in Figure 2B is very close to the one obtined by directly using the mthemticl model in Figure 2C. In the group with n e=e v5, E ws estimted s 18,042(P), but once the pressure elevted (e=e w11), E significntly incresed (45,030 P). Ctegorizing ptients by ge groups (20 45y=o, 45 60y=o, w60 y=o) showed tht, lthough under the sme intrventriculr filling pressure, E ws significntly higher in the elderly (w60 y=o), especilly with higher e=e (w9) (E~34,633 in yer-old group, 33,778 in yer-old group, nd 42,726 in.60-yer-old group) (Figure 3A). However, the difference ws not significnt in younger ptients or between genders. Regression nlysis showed tht n exponentil correltion between ge nd E could be summrized to delinete the soring E in older ptients (Figure 3B). Multivrite nlysis, compred with other trditionl prmeters for dignosing distolic dysfunction (decelertion time [DT]; isovolumic relxtion time [IVRT]), E lso showed independent elevtion for detecting erly myocrdil relxtion impirment in both younger (odds rtio ½ORŠ~1:12; 95% confidence intervl ½CIŠ~1:03{1:47; p~0:04) nd older ptients (OR~1:48; 95% CI~1:22{1:94; p~0:01), which indictes stiffer myocrdium in ging herts. (Tble 2 nd 3; Tble S2 nd S3) The corresponding trend in vrious models To simulte the humn hert, we creted model to obtin the circumferentil strin. In ddition to the rdil strin, the circumferentil strin of the ctul myocrdil contrction ws mesured using STE Besides grossly ttenuted E, the model reflected similr trend of geometric nd pressure chnge, regrdless of whether the circumferentil strin ws considered (Figure 4 A,B). Thus, if the mjor question is the reltionship between pressure nd the tensile elsticity of the myocrdium, rther thn the exct vlues of E, the simpler cylinder model my replce the complex ellipticl model to reduce mesurement nd clcultion errors. The reltionship between E nd echocrdiogrphic wll thickness in the younger nd older cohorts LV hypertrophy ws more prevlent in the elderly thn in the younger nd middle-ged ptients; it led to poor complince nd to difficulty in shpe chnging; thus, it impired distolic function. Although the ssocition between thicker wll nd higher intrventriculr pressure hs been frequently reported, suitble model to illustrte it in ptients of vrious ges is lcking. Our mthemticl model depicted positive ssocitions between IVSd Tble 3. Multivrite regression nlyses for the independence of E vlue in older ptients with distolic dysfunction. Vrible Odds Rtio 95% Confidence Intervl p-vlue Coronry Artery Disese e/ E (Young s modulus) Abbrevitions: see Tble 1. doi: /journl.pone t003 PLOS ONE 6 My 2014 Volume 9 Issue 5 e97455

7 Figure 4. Vrious models to simulte ctul herts with different conditions. A: The positive ssocition between e=e nd E, nd B: between ge nd E in the mthemticl model, whether or not considering circumferentil strin. e hh ~circumferentil strin. doi: /journl.pone g004 nd E, long with the incresing e=e (Figure 5A). It lso indicted tht in the sme LV wll width, higher intrventriculr pressure correlted to higher vlue of E. In ddition, by inputting the representtive E (30,000, 35,000, nd 40,000 for the 20 45, 45 60, nd w60 y=o groups, respectively), we discovered tht higher vlue of E, long with ging, ws ssocited with thicker ventriculr wll under the sme intrventriculr pressure (Figure 5B). This my explin the deteriorting myocrdil relxtion nd higher incidence of signs of hert filure signs in the elderly, who re more vulnerble to the sme pressure. Discussion This is the first evlution of the distolic dysfunction in the ging humn hert tht uses physiologic nd echocrdiogrphic ssessments combined with mthemticl modeling. Our most importnt findings re tht: (1) E (Young s modulus), the tensile elsticity of the myocrdium, cn be used cliniclly to describe myocrdil relxtion nd to noninvsively detect erly distolic dysfunction; (2) ging myocrdium becomes thicker, stiffer, nd Figure 5. The reltionship between E nd echocrdiogrphic ventriculr wll thickness in the younger nd older cohorts. A: In the mthemticl model, the positive ssocition between IVSd nd E when the vlue of e=e is low, moderte, nd high. B: The positive correltion between e=e nd IVSd with different verge vlues of E (E ve ~30,000, 35,000, nd 40,000 for the 20 45, 45 60, nd w60 y=o ge groups, respectively). Becuse circumferentil strin = 0, (internl dimension), pressure, E = f (LVPWd), or E = f (IVSd) ws fixed. IVSd = intrventriculr septl width in distole; LVPWd = left ventriculr posterior wll width in distole. doi: /journl.pone g005 less expndble, which grees with previous clinicl findings. Even under the sme intrventriculr filling pressure, E ws significntly higher in elderly ptients (w60 y=o), especilly with higher e=e (w9); (3) our mthemticl model similr trends of geometric nd pressure chnges, regrdless of whether circumferentil strin ws considered. The criteri for dignosing distolic dysfunction nd distolic hert filure remin imprecise [3,11]. Although there re severl prmeters tht indicte myocrdil relxtion, none directly describe the tensile property of myocrdium. In ddition to some mesurement errors, the current dignostic criteri re nsufficient when the borderline vlue of estimted intrventriculr pressure (e=e ~9{14) is considered [12]. Another dilemm is the coexistence of systolic nd distolic dysfunction [27]. Different PLOS ONE 7 My 2014 Volume 9 Issue 5 e97455

8 Tble 4. Comprison of our model nd the previous Yng et l. model. Yng et l. model [21] Our model Geometric ssumption Sphere Cylinder Stress-strin reltion Hook s lw Plne elsticity Mteril Composite mteril Isotropic mteril Fctors influencing Young s modulus Young moduli of collgen Interior nd exterior pressure (mesured from experiment) Young moduli of muscle Initil dimension (mesured from experiment) Volume frction of collgen (dt fitting) Strins (mesured from experiment) doi: /journl.pone t004 from distolic dysfunction, which remins preserved in myocrdil structure nd contrctions, systolic dysfunction leds to ftigue nd filure of dequte deformtion. Becuse echocrdiogrphic prmeters re too limited to precisely delinete distolic function in systolic hert filure, using E offers the physicin new opportunity to distinguish it from other types of hert filure bsed on the chnge in myocrdil stiffness [28]. Reserchers hve discovered continuous loss of myocytes surrounded by the dipose nd fibrotic tissue deposited in the extrcellulr mtrix (ECM) in the ging process [7]. Therefore, myocrdil stiffness is determined by the volume rtio nd the combined mechnicl properties of the myocytes nd ECM. To prove tht the ge-relted increse of collgen content shifts myocrdil mechnicl properties from myocyte-bsed stiffness to collgen-bsed stiffness, reserchers hve creted number of mthemticl models [13 21]. To describe myocrdil stiffness in vrious stges, the histologicl components of myocytes nd ECM were trnsformed to different input numbers in those models. Yng et l. [21] creted mthemticl model of LV remodeling in ging mice. Becuse humn myocrdil smples re insufficient to support similr models of the ging humn hert, we replced the histologicl prmeters with clinicl dt. Other studies [22 23] hve reported tht the e=e rtios is highly correlted with intrventriculr pressure, enbled us to illustrte the geometric nd tensile chnges under different pressures. In Yng et l. [21], sphericl thick-wlled model nd stretchinduced tissue-growth postulte were used to predict left ventricle dimensions nd wll stiffness chnges in ging mice. A generlized Hook s Lw ws considered nd used for clculting the strin in the rdil direction. The Young s modulus of the left ventricle ws determined by introducing smooth monotonic function to fit the experimentl dt nd simplified version of the liner mixture theory of composite mteril. It ws ssumed tht the modulus depends only on the volume frction of collgen nd the Young s moduli of collgen nd muscle. Also, the pressure difference nd the Young s modulus of the left ventricle were ssumed to be two independent fctors ffecting wll thickness nd end-distolic dimension nd dimeter. The chnges in left ventriculr mss nd pressure with time re importnt throughout the whole study. It ws concluded tht senescent mice tend to hve higher modulus nd pressure thn do young mice. In our study, the left ventricle considered s pressurized thickwlled cylinder is ssumed to be mde of one type of elstic, isotropic, nd homogeneous tissue tht will be completely restored its ntive form when the forces re removed. We restricted the equtions (stress-strin reltions) to the cse of plne elsticity. Strins in the rdil direction nd in the circumferentil direction cn be tken into ccount when determining the stiffness of myocrdium. The rdil nd circumferentil strins mesured from experiments were directly used to clculte the Young s modulus (E), which is currently regrded s prcticl indictor for evluting crdic distolic dysfunction. Also, in our mthemticl model, the pressure, elstic modulus, nd left ventricle dimensions re mutully influenced. We found tht when using the sme intrventriculr filling pressure to compre the elderly nd younger ptients, the former hd tendency to hve higher E vlue. (Tble 4) Becuse dt-fitting techniques were not used in our computtion, more ccurte results could be obtined. In summry, our mthemticl model offers n dditionl prcticl pproch to evlute crdic distolic dysfunction. STE is n emerging technique, with ngle- nd lod-independent chrcteristics, for evluting subtle myocrdil dysfunction [29,30]. A close reltionship between myocrdil strin nd longterm outcome in ptients with myocrdil dysfunction hs been reported in number of studies [31]. In ddition, STE recognizes not only the different directions of myocrdil strin but lso the precise phse of the crdic cycle [30]. To the best of our knowledge, STE hs never been used to develop mthemticl model of the hert; thus, this is the first study tht includes circumferentil strin in rdil-directed thick-wll model. In contrst to the mthemticl model, which does not consider strin, the mechnicl model dded the lower vlue of E cused by circumferentil strin even while the positive reltionship between E nd e=e persisted. If the min purpose is to chrcterize the ging process of the humn hert, the simpler cylinder model is dequte. Otherwise, more delicte fctors should be considered (e.g., longitudinl strin). The present study clerly showed tht E ws significntly higher in the elderly cohort thn in the younger cohort, even under the sme intrventriculr pressure. E, which hs never been used to describe the distolic function using clinicl dt, hs the potentil to detect erly distolic dysfunction with high sensitivity. This will help us understnd chnges in myocrdil stiffness with ging; therefore, we should be ble to detect occult distolic dysfunction in the erly stge of systemic chronic diseses like hypertension disorder dibetes mellitus. This study hs severl limittions. First, the min hypothesis ws bsed on the liner correltion between the e=e rtio nd intrventriculr pressure, but some confounding fctors my interfere when mesuring e=e (e.g., tchycrdi, frme rte, nd different ngles when smpling) [23]. Second, lcking sensitive circulting crdic mrkers (e.g., troponin nd brin ntriuretic peptide), vlidting these formuls might underestimte overestimte symptomtic hert filure [32,33]. However, most of our ptients were reltively helthy, ccording to the TOP study questionnires [25]. Moreover, lifestyle-ssocited informtion ws recorded for ptients recruited from the TOP study but not for those given the helth exmintion. Third, in ptients without PLOS ONE 8 My 2014 Volume 9 Issue 5 e97455

9 pericrdil disese, extrcrdic pressure ws fr lower thn intrventriculr pressure. One study [34] on 11 dogs with chronic hert filure reported tht the pressure in the pericrdil spce ws usully beneth 10 mmhg or 1=3 of the right tril pressure. Thus, in most LV models, the extr crdic pressure hs been neglected. In our study, E in both models, whether or not extrcrdic pressure ws considered, showed trend of chnges similr to tht of intrventriculr pressure or IVSd. Fourth, we ssumed the LV to be hollow xisymmetric cylinder with plne strin, stte of strin in which the strin norml to the x2y plne, e z, nd the sher strin c xz nd c yz, re ssumed to be zero. The deformtion in the xil direction (z direction) is ignored, nd the strins in the rdil nd circumferentil directions re independent of h. In relity, the left ventricle does not hve constnt crosssection nd does not deform uniformly t different orienttions. In ddition, the left ventricle ws ssumed to be mde of elstic, isotropic, nd homogeneous tissue when we determined the Young s modulus of the myocrdium. Nonetheless, the left ventricle usully contins t lest two bsic rw mterils, viz., muscle nd collgen. Although mthemticl model hs limittions, it enbles us to illustrte the quntittive reltionships between structurl nd functionl chnges. becuse distolic nd systolic hert filure shre similr poor outcomes [35] detecting distolic dysfunction erly helps to llow erly interventions, which my led to better prognosis [36]. Furthermore, this model uses echocrdiogrphic prmeters insted of histologicl dt, nd it is noninvsive, it mkes erly detection more fesible. References 1. Butler J, Klogeropoulos A, Georgiopoulou V, Belue R, Rodondi N, et l. (2008) Incident hert filure prediction in the elderly: the helth ABC hert filure score. Circ Hert Fil 1: Bhti RS, Tu JV, Lee DS, Austin PC, Fng J, et l. (2006) Outcome of hert filure with preserved ejection frction in popultion-bsed study. N Engl J Med 355: Mor-Avi V, Lng RM, Bdno LP, Belohlvek M, Crdim NM, et l. (2011) Current nd evolving echocrdiogrphic techniques for the quntittive evlution of crdic mechnics: ASE/EAE consensus sttement on methodology nd indictions endorsed by the Jpnese Society of Echocrdiogrphy. Eur J Echocrdiogr 12: Tresch DD, McGough MF (1995) Hert filure with norml systolic function: common disorder in older people. J Am Geritr Soc 43: Jrsm T, Hlfens R, Abu-Sd HH, Drcup K, Stppers J, et l. (1999) Qulity of life in older ptients with systolic nd distolic hert filure. Eur J Hert Fil 1: Own TE, Hodge DO, Herges RM, Jcobsen SJ, Roger VL, et l. (2006) Trends in prevlence nd outcome of hert filure with preserved ejection frction. N Engl J Med 355: Anvers P, Hiler B, Ricci R, Guideri G, Olivetti G (1986) Myocyte cell loss nd myocyte hypertrophy in the ging rt hert. J Am Coll Crdiol 8: Khn AS, Sne DC, Wnnenburg T, Sonntg WE (2002) Growth hormone, insulin-like growth fctor-1 nd the ging crdiovsculr system. Crdiovsc Res 54: Fung Y (1990) Biomechnics: motion, flow, stress, nd growth. New York: Springer. 569 p. 10. Tber LA (1998) Biomechnicl growth lws for muscle tissue. J Theor Biol 193: Nishimur RA, Tjik AJ (1997) Evlution of distolic filling of left ventricle in helth nd disese: Doppler echocrdiogrphy is the clinicin s Rosett Stone. J Am Coll Crdiol 30: Myreng Y, Smiseth OA (1990) Assessment of left ventriculr relxtion by Doppler echocrdiogrphy. Comprison of isovolumic relxtion time nd trnsmitrl flow velocities with time constnt of isovolumic relxtion. Circultion 81: Gotteiner NL, Hn G, Chndrn KB, Vonesh MJ, Bresticker M, et l. (1972) In vivo determintion of elstic modulus of cnine crdic muscle. J Bsic Eng 94: Ghist DN, Sndler H, Vyo WH (1975) Elstic modulus of the humn intct left ventricle determintion nd physiologicl interprettion. Med Biol Eng 13: Ghist DN, Advni SH, Ro BN (1975) In vivo elstic modulus of the left ventricle: its determintion by mens of left ventriculr vibrtionl model nd its physiologicl significnce nd clinicl utility. Med Biol Eng 13: In conclusion, this is the first report to document using mthemticl model to delinete distolic dysfunction in the ging humn hert. The vulnerbility of the elderly to higher pressure my contribute to their developing erlier signls for hert filure. E is useful for the erly nd noninvsive detection of distolic dysfunction. Supporting Informtion Tble S1 After excluding ptients with hypertension, dibetes mellitus, nd coronry rtery disese, the correltion between E nd distolic dysfunction remined significnt in the helthy elders. (DOC) Tble S2 Multivrite nlysis on the reltionship between E nd echocrdiogrphic intrventriculr pressure in younger ptients. (DOCX) Tble S3 Multivrite nlysis on the reltionship between E nd echocrdiogrphic intrventriculr pressure in older ptients. (DOCX) Author Contributions Conceived nd designed the experiments: JNJ PYL. Performed the experiments: WTC JSC YKH WCT. Anlyzed the dt: WTC JSC YKH. Wrote the pper: WTC JSC JNJ PYL. 16. Yettrm AL, Grewl BS, Gibson DG (1992) Modelling the left ventricle for determintion of the elsticity of the myocrdium. J Eng Med 208: Arts T, Renmn RS, Veenstr PC (1979) A model of the mechnics of the left ventricle. Ann Biomed Eng 7: Dumesnil JG, Shoucri RM, Lurenceu JL, Turcot J (1979) A mthemticl model of the dynmic geometry of the intct left ventricle nd its ppliction to clinicl dt. Circultion 59: Ohyon J, Chdwick RS (1982) Mechnics of the left ventricle. Biophys J 39: Lin J, Lopez EF, Jin Y, Vn Remmen H, Buch T, et l. (2008) Age-relted crdic muscle srcopeni: combining experimentl nd mthemticl modeling to identify mechnisms. Exp Gerontol 43: Yng T, Chio YA, Wng Y, Voorhees A, Hn HC, et l. (2012) Mthemticl modeling of left ventriculr dimensionl chnges in mice during ging. BMC Syst Biol 6: Isnrd RN, Pnnier BM, Lurent S, London GM, Diebold B, et l. (1989) Pulstile dimeter nd elstic modulus of the ortic rch in essentil hypertension: noninvsive study. J Am Coll Crdiol 13: Ngueh SF, Middleton KJ, Kopelen HA, Zoghbi WA, Quinones MA (1997) Doppler tissue imging: noninvsive technique for evlution of left ventriculr relxtion nd estimtion of filling pressures. J Am Coll Crdiol 30: Chng CS, Chng YF, Liu PY, Chen CY, Tsi YS, et l. (2012) Smoking, hbitul te drinking nd metbolic syndrome in elderly men living in rurl community: the Tinlio old people (TOP) study 02. PLOS One 7: e Chng CL, Lee PT, Chng WT, Chng CS, Chen JH, et l. (2013) The interply between inflmmtion, physicl ctivity nd metbolic syndrome in remote mle geritric community in Southern Tiwn: the Tinlio Old People (TOP) study 03. Dibetol Metb Syndr 5: Lng RM, Bierig M, Devereux RB, Flchskmpf FA, Foster E, et l. (2005) Recommendtions for chmber quntifiction: report from the Americn Society of Echocrdiogrphy s Guidelines nd Stndrds Committee nd the Chmber Quntifiction Writing Group, developed in conjunction with the Europen Assocition of Echocrdiogrphy, brnch of the Europen Society of Crdiology. J Am Soc Echocrdiogr 18: Reismnn H, Pwlik PS (1980) Elsticity theory nd pplictions. New York: John Wiley & Sons. 28. Tei C, Ling LH, Hodge DO, Biley KR, Oh JK, et l. (1995) New index of combined systolic nd distolic myocrdil performnce: simple nd reproducible mesure of crdic function study in normls nd dilted crdiomyopthy. J Crdiol 26: Liu YW, Su CT, Lin CC, Chen JH (2009) Evidence of left ventriculr systolic dysfunction detected by utomted functionl imging in ptients with hert filure nd preserved left ventriculr ejection frction. J Crdic Fil 15: PLOS ONE 9 My 2014 Volume 9 Issue 5 e97455

10 30. Perk G, Kronzon I (2009) Non-Doppler two dimensionl strin imging for evlution of coronry rtery disese. Echocrdiogrphy 26: Bertini M, Ng AC, Antoni ML, Nucifor G, Ewe SH, et l. (2012) Globl longitudinl strin predicts long-term survivl in ptients with chronic ischemic crdiomyopthy. Circ Crdiovsc Imging 5: Lukowicz TV, Fischer M, Hense HW, Döring A, Stritzke J, et l. (2005) BNP s mrker of distolic dysfunction in the generl popultion: importnce of left ventriculr hypertrophy. Eur J Hert Fil 4: Hung XP, Du JF (2004) Troponin I, crdic distolic dysfunction nd restrictive crdiomyopthy. Act Phrmcol Sin 12: Horne SG, Belenkie I, Tyberg JV, Smith ER (2000) Pericrdil pressure in experimentl chronic hert filure. Cn J Crdiol 5: Wrren SE, Grossmn W (1991) Prognosis in hert filure: is systolic or distolic dysfunction more importnt? Herz 16 Spec No 1: Glderisi M (2005) Distolic dysfunction nd distolic hert filure: dignostic, prognostic nd therpeutic spects. Crdiovsc Ultrsound 3: 9. PLOS ONE 10 My 2014 Volume 9 Issue 5 e97455