ARTIGO PUBLICADO RS_DGG_MB JUL2012.pdf

G

J

Md

Ra

b

c

a

ARRA

KMCCSA

C9

H0

d(

1h

ARTICLE IN PRESS Model

JBE-2121; No. of Pages 12

Medical Engineering & Physics xxx (2012) xxx– xxx

Contents lists available at SciVerse ScienceDirect

Medical Engineering & Physics

jou rna l h omepa g e: www.elsev ier .com/ locate /medengphy

ioLab: Simulator for cardiac myocyte contractile force of rat based on theynamics of calcium

obson R. Silvaa,b,∗, Daniel G. Gorosoa,c,∗∗, Marcia A.S. Bissacoa

Mogi das Cruzes University, Research and Technology Center – Modeling Biological Systems, Mogi das Cruzes, Sao Paulo, BrazilUnited Faculty of Suzano – Research Center and Extension (NUPE), Suzano, Sao Paulo, BrazilPhysical Medicine and Rehabilitation Institute of the Hospital das Clinicas – FMUSP, São Paulo, Sao Paulo, Brazil

r t i c l e i n f o

rticle history:eceived 22 August 2011eceived in revised form 20 March 2012ccepted 16 May 2012

eywords:athematical modeling

ontractile forcealcium dynamicsimulationpplication of drugs

a b s t r a c t

Background: The calcium ion (Ca2+) is essential in cardiac electrical activity since it is the direct activatorof myofilaments, which cause contraction. For this reason, irregular Ca2+ flow in the cardiac myocyteis one of the main causes of cardiac arrhythmias and contractile dysfunction. In this sense, the formu-lation of mathematical and computational models of the mammalian ventricular myocyte has playedan important role in understanding cardiac physiology. This paper proposes a biophysical model forthe rat cardiac myocyte in order to reduce the number of degrees of freedom and provides a mathe-matical framework that makes computation simpler for our understanding of the complex process ofexcitation–contraction–relaxation (ECR), uses low-order lumped parameter of the myofilaments andCa2+handling. The model allows the calculation of contractile force mainly based on the dynamics ofCa2+, provides data on transient Ca2+andenables the analysis of the effects of drugs used in the treatmentof cardiac arrhythmias.Methods: The mathematical model which describes the kinetics of cytosolic Ca2+ and dynamic cross-bridges, was implemented through nine differential equations, auxiliary equations, three 47 biophysicalparameters. Each was implemented using C++ programming and its user-friendly interface in the pro-gramming language Delphi. The results of each simulation were stored in a text file and its analysis wasshown in a graphical interface using executable programs in Matlab®. Additionally, the validation modelwas performed by comparing both the experimental data of Ca2+ transient and several drug tests.Results: The model satisfactorily reproduced the Ca2+ transient, as well as the effects of drugs that causebeta-adrenergic stimulation and the inhibition of the Ca2+ uptake mechanism (SERCA). Changes in theparameters regulating Ca2+ entry through L-type channels produced the oscillation amplitude of the Ca2+

transient known as the syndrome of pulses alternans. Changes in parameters related to the Na+–Ca2+

2+
exchange has already stabilized the transient Ca and produced a decrease in amplitude of the contractileforce.Conclusion: The simulator proved to be a tool to study and understand the mechanisms that involve thekinetics of Ca2+ and the dynamics of cross-bridges in the unit heart muscle, as well as a tool to analyze thepossible factors that may cause arrhythmias and study the effects of drugs that are used in the treatmentof cardiovascular diseases in general.
Please cite this article in press as: Silva RR, et al. MioLab: Simulator for cardMed Eng Phys (2012), http://dx.doi.org/10.1016/j.medengphy.2012.05.010

∗ Corresponding author at: Mogi das Cruzes University, Research and Technologyenter, Av. Cândido Xavier de Almeida, 200, Mogi das Cruzes, Sao Paulo, CEP 08780-11, Brazil. Tel.: +55 11 4798 7107; fax: +55 11 4799 2069.∗∗ Corresponding author at: Physical Medicine and Rehabilitation Institute of theospital das Clinicas – FMUSP, Street Diderot, 43, São Paulo, Sao Paulo, CEP 04116-30, Brazil. Tel.: +55 11 5549 0111; fax: +55 11 5549 7511.

E-mail addresses: [email protected], [email protected] (R.R. Silva),[email protected], [email protected] (D.G. Goroso), [email protected]. Bissaco).

350-4533/$ – see front matter © 2012 IPEM. Published by Elsevier Ltd. All rights reservettp://dx.doi.org/10.1016/j.medengphy.2012.05.010

© 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

1. Introduction

According to the World Health Organization (WHO), car-diovascular diseases (CVD), including cardiac arrhythmias, areresponsible for about 17.5 million deaths worldwide every year,where 80% occur in developing countries, including Brazil [1]. Infact, according to the American Heart Association (AHA), cardio-vascular diseases affect 1 out of 3 Americans, and represent the

iac myocyte contractile force of rat based on the dynamics of calcium.

main cause of sudden cardiac death with nearly 36.6% of registereddeaths in 2004 [2]. In Brazil, according to a report by the BrazilianSociety of Cardiology (BSC), about 315,000 people died in 2009 fromheart diseases, out of which 75.000 cases were due to infarction [3].

d.

dx.doi.org/10.1016/j.medengphy.2012.05.010


http://www.sciencedirect.com/science/journal/13504533

http://www.elsevier.com/locate/medengphy

mailto:[email protected]






IN PRESSG Model

J

2 eering & Physics xxx (2012) xxx– xxx

Fhap

Ccmma

tiIothtorri

topopadam

aaLstavStcfaot

Mitpga

2

2

sclhad

ARTICLEJBE-2121; No. of Pages 12

R.R. Silva et al. / Medical Engin

or that reason, increasingly more studies concerning the normaleart performance are required in order to understand the causesnd impact of cardiovascular disease, and thus contribute to itsrevention and the development of new therapies.

Among the ions involved in the complex functioning of the heart,a2+ is considered perhaps the most important. It is essential inardiac electrical activity as the direct activator of the myofila-ents to cause contraction, and its irregular flow in the cardiacyocyte is one of several central causes of contractile dysfunction

nd arrhythmias [4].However, development of new mathematical and compu-

ational models of mammalian ventricular myocyte providesmportant tools for understanding the Ca2+ release mechanisms.t also enables an in-depth analysis of the causes of different typesf cardiac arrhythmias, among other research topics. In addition,hese models provide data on Ca2+ transient, contractile force ineart cells, and allow for the reproduction of experiments to inves-igate the effects of new drugs used to treat arrhythmias, whichtherwise would be impossible or prohibitive to conduct in a labo-atory setting. In fact, some models are already producing reliableesults and have contributed to the development of new drugs usedn treating heart disease [5].

The aim of this paper is to present a biophysical model forhe rat cardiac myocyte in order to reduce the number of degreesf freedom, provide a mathematical framework and make com-utation simpler for our understanding of the complex processf excitation–contraction–relaxation (ECR),uses low-order lumpedarameter of the myofilaments and Ca2+ handling. The modelllows the calculation of contractile force mainly based on theynamics of Ca2+,provides data on transient Ca2+andenables thenalysis of the effects of drugs used in treatment of cardiac arrhyth-ias.This new model is based on Negroni and Lascano equations [6]

nd Tang and Othmer [7], but it has added NCX dynamics, suchs. Ca2+ pump(Ca2+-ATPase) from sarcolemma, Ca2+ influx through-type channels, CICR process, and Ca2+ drain channel located inarcolemma and sarcoplasmic reticulum (SR) and Ca2+ content inhe cardiac muscle. Thus, with these new dynamics, the new modelllows for simulations that enable the study of blockers and acti-ators that act in the NCX exchanger of the Ca2+ pump from eitherR or L-type channels. The new model enables an understanding ofhe effect of drugs used for the treatment of arrhythmias. Moreover,hanges can be made in application parameters of the pulse trainor simulating Ca2+ entry through L-type channels (e.g., frequency,mplitude, duration (length of open channel), and appearance timef maximum peak), allowing even the study of the effect of drugshat act on these channel types.

Through the mathematical description of this new model, aioLab simulator (Virtual Laboratory of Cardiac Myocyte) was

mplemented. Its user-friendly interface enables changing not onlyhe biophysical parameters, but also the graphic display to com-are the results of two simulations (between control and chronicroups). It allows for full integration between the MioLab simulatornd Matlab® (see Appendix A).

. Methods

.1. Description model

The new heart muscle model is made up of an arrangement of aarcomeres series unit defined by volume, which is determined byross-sectional and mid length (L), and its ends are given by edge


ine (Z) and center line (M) (see Fig. 1) [6]. Thus, this new modelas been implemented with nine coupled differential equations, 15uxiliary equations, and 47 specific parameters about biophysicalata of rats.

Fig. 1. Description of the sarcomere unit. Sarcomere unit consists of thick and thinfilaments arranged in a parallel elastic element representing the collagen mesh ofthe cell.

2.2. Calcium influx via L-type channel

Depolarization of sarcolemma during cardiac action potential(APC) results in the opening of the Ca2+ channel voltage dependent(CCVD), in particular L-type Ca2+ channels which, when activated,allow for entry of Ca2+ currents by depolarization [8]. Therefore,the influence of Ca2+ on L-type Ca2+ channels was described by thefunction time, t (in seconds).

ICa2+ = A0

(t

t1

)m

em(1−(t/t1)) (1)

The previous equation, although simplistic from a mathemati-cal point of view, allows the simulation of the entry of Ca2+ into thecell through L-type channels and also allows changes to parame-ters representing the pulse amplitude A0 (in �M/s), the time t1 ofoccurrence of peak Ca2+ in seconds, and a parameter exponentialfit m related to the time of opening and closing of the channel.

In that case, the leak influx of cytosolic Ca2+ from an extra cellu-lar medium is proportional to the concentration gradient betweenthese compartments.

Ivaz = g1([Ca2+]e − [Ca2+]i) (2)

where g1 is the leakage coefficient (in s−1), [Ca2+]i is the free calciumconcentration of myoplasm, and [Ca2+]e is the external calciumconcentration (in �M).

2.3. Calcium-induced calcium release (CICR)

Already, the Ca2+ entry through L-type channels induces moreCa2+ release from the sarcoplasmic reticulum (SR), which is a repos-itory of these ions within the cells [8]. Hence, this biophysicalprocess named CICR was described in the Tang and Othmer model[7] as a system of three coupled differential equations:

dx1

dt= L−1x2 + L−4(1 − x1 − x2 − x3) − L1x1x4 − L4x1x4 (3)

dx2

dt= −L−1x2 + L−2x3 + L1x1x4 − L2x2x4 (4)

dx3

dt= −L−2x3 − L−3x3 + L2x3x4 + L3(1 − x1 − x2 − x3)x4 (5)


where x1, x2 and x3, respectively indicate the fraction of receptorsin the active, open and closed states and x4 the concentration offree Ca2+ in the mioplasma. Already, L1, L−1, L2, L−2, L3, L−3, L4 andL−4 are constants of association and dissociation of Ca2+.


IN PRESSG Model

J

eering & Physics xxx (2012) xxx– xxx 3

lr

Q

wta

w(

Q

w

2

fcg

F

wrbid

F

wa

[

F

caccta

2

iafbtwg

gat(fa(raC

Fig. 2. The kinetics of Ca2+ from the myofilaments. Schematic representation of thekinetics of Ca2+ in the myofilaments. The model utilizes the following set of chemicalkinetics: the association constants of Ca2+ to troponin T (Y1) and the complex T* (Z3),


R.R. Silva et al. / Medical Engin

Therefore, the Ca2+ release rate from the sarcoplasmic reticu-um (Qrel) is proportional to the concentration gradient and theeceptors fraction found in the open state:

rel = ch × x2([Ca2+]SR − [Ca2+]i) (6)

here ch is the Ca2+ release rate (by time), x2 is the fraction of recep-ors in the open state, [Ca2+]SR is the Ca2+ concentration within SR,nd [Ca2+]i is the Ca2+ concentration within the cell cytoplasm.

Furthermore, calcium release from ryanodine channels (RyRs)as also included in our model as Ca2+ leak influx rate from SR

Qvaz):

vaz = g2([Ca2+]SR − [Ca2+]i) (7)

here g2 is the leakage coefficient (in s−1).

.4. Contractile force generator

According to the Negroni and Lascano model [6], where the totalorce (F) implemented by the single muscle is normalized with therosscutting section of the corresponding muscle area, which isiven by:

= Fb + Fp (8)

here Fb is a normalized force with a cross-sectional areaespective to the muscle as a result of the actions of all cross-ridges located in the muscle unit, and Fp is the resultant force

mplemented by an elastic element in parallel according the Lan-esberger and Sideman model [9], described as:

p = k(L − L0)5 (9)

here k is an equation parameter, L is the mid-sarcomere length,nd L0 is a measure of L reduction due to the force action Fp.

Thus, in the model structure described by Negroni and Lascano6], the force Fb is given by:

b = A([TCa∗] = [T∗])(L − X) (10)

Accordingly, (7) provides the total force developing in the mus-le unit (by a cross-sectional area unit respective to the muscle)s a function of length (L) variation (X) sarcomere, and [TCa*] con-entrations (troponin complex + Ca2+ + myosin) and [T*] (troponinomplex + Ca2+). Moreover in (7), A is an adjustment parameter andhe evaluation of concentrations [TCa*] and [T*], which depend on

detailed study of Ca2+ kinetics within the cell myofilaments.

.5. Calcium kinetics in the myofilaments of cells

Fig. 2 shows Ca2+ kinetics in the myofilaments of cells, whichs described by means of four kinetic states of thin myofilamentsssociated with troponin (C). Specifically: (i) troponin places withree C (T); (ii) Ca2+ places bound to C troponin (TCa); (iii) Ca2+ placesound to C troponin and which involved cross-bridges for contrac-ile force generator (TCa*); and (iv) troponin C places not associatedith Ca2+ and which involved cross-bridges for contractile force

enerator (T*) [6].Thus, each of the TCa* and T* units act as an independent power

enerator. Likewise, reactions involving the formation of TCa, TCa*,nd T* are reversible processes that use chemical kinetic conceptso describe the following variation rates: Ca2+ net rate binding to TQb); cross-bridges attachment net rate (Qa); Ca2+ release net raterom TCa* (Qr); T* detachment rate to give Ca2+ and T (Qd); anddditional T* and TCa* detachment rates during filament sliding


Qd1 and Qd2). The mathematical description of the rates previouslyeported [6] use Ca2+ association and dissociation constants, as wells attached and detached cross-bridges. Therefore, according to thea2+ kinetics scheme (see Fig. 2) and the rate described above, the

dissociation constants of Ca2+ complex TCa (Z1) and TCa* (Y3); constant attachmentof cross bridges to form TCa* (Y2); and constant shutdown of cross bridges (Z2, Y4

and Yd).

concentration variation rate of [TCa], [TCa*] and [T*] used (10) tocalculate the contractile force is described by coupling differentialequations:

d[TCa]dt

= Qb − Qa (11)

d[TCa∗]dt

= Qa − Qr − Qd2 (12)

d[T∗]dt

= Qr − Qd − Qd1 (13)

2.6. Heart-cell relaxation

Reduction of [Ca2+]i to basal levels is an event that deter-mines the end of contraction. In order to relax the cardiac cells,several Ca2+ carriers compete for cytosolic Ca2+ removal frominside cytoplasmic organelles and to extracellular environment [8].Hence, this model includes the following carriers: Ca2+ pump of SR(Ca2+-ATPase) whose calcium removal rate was indicated by QSR;Na+–Ca2+ exchange (NCX) from sarcolemma was indicated by QT,and Ca2+ pump of sarcolemma (Ca2+ATPase) whose rate is QSL. Asthe purpose of the model is to reduce the degree of freedom of thesystem and relate the contractile force of the cell based solely on thedynamics of Ca2+, these carriers were modeled using the equationof chemical kinetics (Hill equation):

Q = Vmax

1 + (Km/[Ca2+])n (14)

where Vmax is the maximal rate of Ca uptake, Km is a dissociationconstant (Ca2+ concentration for which the maximal rate of Ca2+

uptake accounts for 50% of the maximal rate), [Ca2+] is the freeCa2+ concentration in cell-cytoplasm, and n is the Hill coefficient.

2.7. Calcium concentration inside the sarcoplasmic reticulum andcell cytoplasm


Now, using Eqs. (1) and (7), and the following rates: Qb rateof Ca2+, which is bound to C troponin, Qr rate of Ca2+ release toTCa* complex to form T*, Qd2 rate to detachment of cross-bridges,


ARTICLE IN PRESSG Model

JJBE-2121; No. of Pages 12

4 R.R. Silva et al. / Medical Engineering & Physics xxx (2012) xxx– xxx

F nsientw f 0.65f

QAea

2

dtshSsa[

3

3

i

ig. 3. Validation of the model: the Ca2+ transient and contraction force. TheCa2+ traith the Ca2+ transient simulated pulse of the Ca2+ amplitude 133 �M/s frequency o

rom the simulated data used in the simulation of the Ca2+ transient.

SR rate to Ca2+ removal for SR pump, QSL Ca2+ removal for Ca2+-TPase pump of sarcolemma, and QT rate to Ca2+ removal for NCXxchange, rate of free Ca2+ concentration in cell-cytoplasm ([Ca2+]i)nd ([Ca2+]SR) inside of SR, described as follows:

d[Ca2+]i

dt= ICa2+ + Ivaz − QT − RRS − QSL − Qb

+ Qr + Qd2 + Qvaz + Qrel (15)

d[Ca2+]RS

dt= QRS − Qvaz − Qrsl (16)

.8. Virtual experiments and model validation

Through the validation process of this model, experimentalata from Ca2+ transient obtained by electrical stimulation inhe cardiac myocyte of rats, and drug applications which causetimulation (isoproterenol) and inhibition (2.5-di(tert-butyl)1.4-ydroquinone–tBQ) of the SERCA protein (pump Ca2+-ATPase fromR) in vesicles isolated from rats [2] were compared. In addition,imulation experiments were conducted to establish the anti-rrhythmic effects of drugs (such as those derived from the heparin)10].

. Results


.1. Validation model

For the validation model incorporating the new dynamicsmplemented, first we applied a Ca2+ pulse representing the Ca2+

obtained experimentally by electrical stimulation (Redraw: [2]) and its comparison Hz is shown at the bottom of the figure. At the top, we have the force of contraction

flow through L-type channels with a frequency of 0.65 Hz, ampli-tude of 133 �M/s, duration of 20 s, and appearance peak time of0.0285 s. Besides, change in rest state of Ca2+ ([Ca2+]r) was 0.10 �M.Fig. 3 shows the Ca2+ transient given by the model and a comparisonwith the experimental data reported [2].

Fig. 3 shows that amplitude, rise time, fall time (required by Ca2+

transient fall to half of the peak value), peak occurrence time andCa2+ transient peak match experimental data. Table 1 shows com-parative data between electrical stimulation [2] and Ca2+ transientsimulation.

Furthermore, through the simulator it is also possible to esti-mate the contractile force generated on the muscle unit for theCa2+ transient (see Fig. 3).

3.2. Application and effects of some drugs

MioLab allows for new dynamic simulations like the studyof Ca2+ blockers and activators on Na+–Ca2+ Exchange (NCX), onpump Ca2+ from SR, on L-type channels, or ryanodine channels(RyRs).

3.2.1. Inhibition of pump Ca2+-ATPase from SRThe tBQ (2.5-di(tert-butyl)1.4-hydroquinone) is a blocker of

pump Ca2+-ATPase from SR [11], and it decreases the uptake rateof Ca2+ from the cytosol. Recent experiments show that application


of 5 �M of tBQ has produced decreased amplitude and increasedfall time of the Ca2+ transient [2]. In order to simulate this drug itwas necessary to change the parameters from the SR pump (reduc-tion in maximal rate of Ca2+ uptake) and Ca2+ kinetic parameters


ARTICLE ING Model


R.R. Silva et al. / Medical Engineering

Table 1Model validation: simulated versus experimental data.

Experiment Simulation Unit

�[Ca2+]i 0.38 0.39 �Mt1/2 0.16 0.17 smax[Ca2+]i 0.49 0.49 �Mtp 18.4 18.4 s�ts 0.08 0.08 s

Comparison between experimental data obtained by electrical stimulation [2] andsimulation of the Ca2+ transient. Amplitude of Ca2+ transient (�[Ca2+]i), timer 2+ 2+

((

ia

os

osrt

3

tcaida

TP

(h(Tc

equired for the Ca transient declined to half their peak value (t1/2), Ca peakmax [Ca2+]i), time of occurrence of Ca2+ peak (tp) and rise time of the Ca2+ transient�ts).

n myofilaments (reduction in dissociation rate from Ca2+), whichre shown in Table 2(A).

Table 3 shows the output variables of the control group (absencef tBQ) and the chronic group (presence of tBQ) obtained from theimulator and its comparison with experimental data [2].

Fig. 4A shows the Ca2+ transient of the control group (absencef tBQ) and the chronic group (presence of tBQ) obtained from theimulator through the changes made to the parameters of maximalate of Ca2+ uptake from the cytosol by the Ca2+-ATPase pump andhe SR and Ca2+ dissociation from the myofilaments.

.2.2. Beta-adrenergic stimulation with isoproterenolPrevious studies [12,13] report that isoproterenol (ISO) acts on

he Ca2+ pump (Ca2+-ATPase) from SR resulting in decreasing Ca2+

oncentration by equal to half of the uptake maximal rate (Km),


nd it allows for an increased maximal rate of Ca2+ uptake (Vmax)n isolated vesicles from SR. Moreover, the isoproterenol allows forecreased Ca2+ myofilaments affinity, which enables its dissoci-tion from the thin filament via phosphorylation, and produces

able 2arameters used to simulate the application of drugs and the syndrome of pulsus alterna

Parameters Description

(A) Application of tBQ [Ca2+]r Ca2+ concentration at rVmax Maximum uptake rateKm Dissociation constant

n Hill coefficients

Z1 Dissociation constant oY3 Dissociation constant o

(B) Application of isoproterenol Vmax –

Km –

Y1 Binding constant of CaZ1 –

Y3 –

tp Time of occurrence of

channels of the L-typeM Coefficient of exponen

time of opening and clL-type

A Pulse amplitude of calcL-type

(C) Syndrome of pulsus alternans M –

A –

Vmax –

Km –

Y1 –

Z1 –

Y3 –

(D) Heparin Vmax Maximum rate Ca2+ byKm –n –

A) Parameters used in the simulation of Ca2+ transient in the control group (absence) anave changed the parameters related to Ca2+ pump of the SR (Ca2+-ATPase), the kinetics oC) Parameters related to Ca2+ influx through the channels of the L-type pump of SR Ca2+

o simulate the application of heparin fragments was decided to increase the maximumoefficient (n) and the concentration of Ca2+ (Km) for which the removal rate is half the m

PRESS & Physics xxx (2012) xxx– xxx 5

an increase in the Ca2+ current [8,14]. By using the MioLab Sim-ulator, it was possible to apply isoproterenol to change the Ca2+

pump parameters (Ca2+-ATPase) from SR, Ca2+ kinetic parametersin myofilaments, and Ca2+ uptake via L-type channels. These areshown in Table 2(B).

Table 3 shows a comparison between the amplitude and declinein the Ca2+ transient simulated (see Fig. 4B) from the control group(absence of ISO) and the chronic group (presence of ISO), and itscomparison with reported data [2].

3.3. Isoproterenol applications and the syndrome of pulsusalternans (SPA)

So far, no one knows to what extent the application of drugssuch as isoproterenol or tBQ can change the Ca2+ release processfrom SR. Although other studies [15–17] have reported that theapplication of isoproterenol may produce increased sensitivity toryanodine receptors (RyRs) in Ca2+ associated with its phosphory-lation of protein kinase (PKA), it could increase the release of thision after drug application.

In the same vein, Eisner et al. [18] also studied the destabiliza-tion process of the Ca2+ release channels from SR with experimentaldata from isolated rat cardiac myocyte. These experiments showedthat changes in the charge from SR produced instability in the intra-cellular concentration of Ca2+. In turn, such instability is responsiblefor a SPA, where alternation in amplitude of Ca2+ transient occurred.

In an attempt to adjust the model for it to reproduce experi-mental data on the use of drugs such as isoproterenol and tBQ, we


changed Ca2+ entry parameters through L-type channels, whichcaused destabilization of the Ca2+ release channels from SR (seeFig. 5) and a consequential alternation in amplitude of the Ca2+

transient (see Fig. 6A).

ns.

Control Chronic Unit

est in the SR 10 10 �M SRCa2+-ATPase 207 187 �M/s

0.17 0.17 �M2 2 –

f Ca2+ complexes TCa 1600 410 s−1

f Ca2+ complexes TCa* 1600 410 s−1

207 227 �M/s0.17 0.15 �M

2+ to troponin T 39 29 �M−1 s−1

1600 3200 s−1

1600 3200 s−1

Ca2+ peak through the 0.0285 0.0288 s

tial fit related to theosing of channels of the

2 6 –

ium by channels of the 133 195 �M/s

2 4 –133 180 �M/s207 227 �M/s

0.17 0.15 �M39 29 �M−1 s−1

1600 3200 s−1

1600 3200 s−1

the NCX exchanger 27 36 �M/s0.26 0.26 �M3.4 3.4 –

d control group (presence of tBQ). (B) To simulate the effect of isoproterenol (ISO)f Ca2+ in the myofilaments and the Ca2+ influx through the channels of the L-type.and the kinetics of Ca2+ and that produced the syndrome of pulsus alternans. (D)

rate (Vmax) of Ca2+ removal by the NCX exchanger. Parameters related to the Hillaximum rate not changed.


Please cite this article in press as: Silva RR, et al. MioLab: Simulator for cardiac myocyte contractile force of rat based on the dynamics of calcium.Med Eng Phys (2012), http://dx.doi.org/10.1016/j.medengphy.2012.05.010




Fig. 4. Inhibition and stimulation of Ca2+ pump of the SR. Inhibition and stimulation of Ca2+ pump (Ca2+-ATPase) of SR. (A) Comparison between the Ca2+ transient in thecontrol group (absence) and chronic group (presence of tBQ). (B) Comparison between the Ca2+ transient in the control group (absence) and chronic group (presence ofisoproterenol) obtained with the simulator MioLab.

Fig. 5. Destabilization of the release channels of SR Ca2+. The fraction of ryanodine receptors (RyRs) that are in the active, open, closed and refractory states to the controlgroup (normal state) are shown at the top of the figure. Changes in the parameters that govern the entry of Ca2+ channels by L-type channels destabilized the release of SRCa2+ (chronic group), which can be seen at the bottom of the figure.

Fig. 6. Applications of isoproterenol and the syndrome of pulsus alternans. The irregular oscillation amplitude of the Ca2+ transient (Fig. 6A) is directly related to themechanism of cell contraction and contributes to the onset of arrhythmias (Fig. 6B) as the syndrome of pulsus alternans.




R.R. Silva et al. / Medical Engineering & Physics xxx (2012) xxx– xxx 7

Table 3Inhibition and stimulation of the Ca2+ pump of the SR Ca2+-ATPase.

Control Inhibition (tBQ) Stimulation (ISO)

Chronic Simulation Experiment Chronic Simulation Experiment

�[Ca2+]i (�M) 0.39 0.27 30% 25% 0.74 90% 90%t1/2[Ca2+]i (s) 0.17 0.30 76% 74% 0.14 18% 25%

O SO) obtained from the simulator and its comparison with experimental data taken froml the decline (t1/2) of the Ca2+ transient.

toi

cma

3

radlfhs

ra

fttmNh

3

tesa

m(Nsse

TPt

Tcrc

Table 5Effects of heparin derivatives on force of contraction.

Control Chronic Simulation Experiment

Force (mN/mm2) 53.83 33.64 37.5% 37.5%t1/2 (s) 0.263 0.42 59.7% 40%

Experiments conducted at the Laboratory of Electrophysiology UMC report that frag-

ments, a fact that can now be considered in the new model. Already,the model developed by Negroni and Lascano [6] describes the

utput variables of the control group (absence) and chronic (presence of tBQ and Iiterature [2]. It also indicated a decrease in amplitude (�[Ca2+]i) and an increase in

Furthermore, as Ca2+ transient is directly related to the con-ractile mechanism of the cells [8] in its oscillation amplitudescillations produced in contractile force, which can be observedn the simulation (see Fig. 6B).

Additionally, parameters related to Ca2+ influx through L-typehannels, Ca2+ pump (Ca2+-ATPase) from SR and Ca2+ kinetics inyofilaments, which were amended and thus produced the SPA,

re shown in Table 2(C).

.3.1. Anti-arrhythmic effects of heparin and its derivativesIn this sense, experiments by Shinjo et al. [19] on cultured

at vascular myocyte showed that fragments derived from hep-rin were able to reduce the contractile response of these cells byecreasing Ca2+ intracellular concentration. This experiment estab-

ished the hypothesis that the reduction effect of the contractileorce might be caused by the activation of exchanger NCX by botheparin derivatives and the consequent acceleration of Ca2+ extru-ion into vascular myocyte.

In fact, by using the MioLab simulator, a 74% increase in Ca2+

emoval maximal rate by protein NCX was established, along with reestablishment of the normal oscillation of Ca2+ transient.

As a result (see Fig. 7A), it shows a simulation of Ca2+ transientor the control group (normal state of cells). Specifically, the Ca2+

ransient for the chronic group (in SPA state, see Fig. 7B), and finallyhe amplitude recovery of Ca2+ transient after the increase in the

aximal control rate parameter for Ca2+ removal from cytosol viaCX protein (see Table 4), thus simulating the use of drugs (likeeparin fragments) that act directly on NCX protein (see Fig. 7C).

.3.2. Effects of heparin derivatives on the contraction strengthA test implemented in the Cardiac Electrophysiology Labora-

ory at the Technological Research Center (NPT-UMC) studied theffect of a heparin derivative named disaccharide trissulfate on thetrength of isometric contraction from the isolated right atria of andult male Wistar rat [10].

Therefore, to simulate the effect of heparin through this newodel, the control group (without heparin) and the chronic group

with heparin) were considered, where the Ca2+ removal rate by the


CX exchanger is 27 and 36 �M/s, respectively. As a result of thisimulation (see Fig. 7D), Table 5 shows a comparison between theimulation and experimental data. Finally, NCX exchanger param-ters are shown in Table 2(D).

able 4arameters of NCX exchanger used to simulate the application of derivatives in thereatment of heparin-induced arrhythmias.

Parameters Normal state SPA Drug Unit

Vmax 27 27 47 �M/sKm 0.26 0.26 0.26 �Mn 3.4 3.4 3.4 –

o simulate the application of drugs acting on the exchanger NCX, we decided tohange the parameter (Vmax) that controls the rate of extrusion of Ca2+. Parameterselated to the Hill coefficient (n) and the concentration of Ca2+ (Km) for which thelearance rate is half the maximum speed is not changed.

ments of heparin produced a decrease in the peak force of contraction and relaxationtime (t1/2). In the simulation, there is a drop in the peak force of contraction and anincrease in the relaxation time.

3.4. Calcium transient obtained by prolonged action of caffeine

The Ca2+ transients evoked by rapid pulses of caffeine are dueto the experimental procedure to study Ca2+ uptake by SR. In thisprocedure, the exchanger NCX becomes inoperative by removingthe sodium (Na+) and extracellular Ca2+, which eliminates the flowof Ca2+the sarcolemma assigned to the main competitor of SERCA(pump Ca2+-ATPase from SR) in the removal of Ca2+ the cytosol.Caffeine was used to elicit short episodes of Ca2+ release from theRS, whose removal will be done mainly by SERCA [2].

Under conditions where the concentration of extracellularCa2+ was aborted ([Ca2+]e = 0) and means of extrusion cross-sarcolemmal Ca2+ (NCX and Ca2+ pump sarcolemma) wereconsidered dead (Vmax = 0), the effect of caffeine was simulated bychanges in the rates of transition between states rianodinas recep-tor (see Table 6) so as to favor the stay in the open state during theapplication time of caffeine. Fig. 8 shows a comparison betweenthe simulation and the experimental data of the time course of theCa2+ transients evoked by application of caffeine.

4. Discussion

The model proposed by Tang and Othmer [7], though it includesin its modeling the complex process Ca2+-induced Ca2+-release(CICR) is a simplified approach, as well as ignore the electrical phe-nomena of the membrane that lead to entry Ca2+ in the cytosol,does not include in its modeling the kinetics of Ca2+ in myofila-


relationship between sarcomere dynamics and kinetics of Ca2+ in

Table 6Parameters of process CICR used to simulate the application of caffeine.

Parameters Control Chronic Unit

L1 13.5 70 �M−1 s−1

L−1 7.2 1 s−1

L2 0.8 0.1 �M−1 s−1

L−2 0.84 4 s−1

L3 13.5 30 �M−1 s−1

L−3 7.2 1 s−1

L4 0.8 1.6 �M−1 s−1

L−4 0.84 0.1 s−1

Parameters related to transition between states of RyRs in the control group(absence) and chronic (presence of caffeine). The parameters L1, L−1, L2, L−2, L3, L−3,L4 and L−4 are related to the association and dissociation of Ca2+ receptors RyRs.





Fig. 7. Simulation of the anti-arrhythmic effects of heparin derivatives. Simulation of the anti-arrhythmic effects of heparin derivatives: (A) Simulation of Ca2+ transient int try of( in valc rength

mtCnpnran

Lpc

Ft

he control group (normal state). (B) Changes in the parameters that govern the enchronic group). (C) Reestablishment of the amplitude of the Ca2+ transient increaseytosol via NCX protein. (D) The effects of heparin derivatives on the contraction st

yofilaments, this model allows the calculation of the force con-raction in the muscle unit, but even upgrading the kinetics ofa2+ myofilaments in the model of Negroni and Lascano [20] doesot include in its modeling in exchange Na+–Ca2+ (NCX), the Ca2+

ump (Ca2+-ATPase) of the sarcolemma, Ca2+ influx through chan-els L-type and the process of Ca2+ release from the sarcoplasmiceticulum (SR), known as the CICR, not allowing simulations withgents that act on these components. With the development of theew model, these elements were included in the modeling.


Moreover, the model Puglisi and Bers [21] and the simulatorabHEART is based on experimental data and rabbit describes theroperties of ion currents of sodium (Na+), potassium (K+) andalcium (Ca2+), pumps and exchangers Ca2+ and especially, the

ig. 8. Ca2+ transient evoked by pulses of caffeine: simulation versus experiment. Compransient evoked by application of caffeine.

Ca2+ by L-type channels produced a transient oscillation in the amplitude of Ca2+

ue after the parameter that controls the maximum rate for removing Ca2+ from the.

geometric model of Ca2+ release from the SR. Even the model isvery realistic, also does not take into account the kinetics of Ca2+ inmyofilaments and the dynamics of cross-bridges, not thus provid-ing data on the contractile force of cardiac cell, as can be seen withthe new model (based only on dynamics of Ca2+) MioLab using thesimulator (see Appendix A).

The new deployments undertaken in relation to the Negroniand Lascano model [6] and the Tang and Othmer model [7] enablesimulations to study the action of blockers and activators in the


NCX exchanger of the Ca2+ pump (Ca2+-ATPase) from SR or L-typechannels based mainly on the dynamics of calcium.

The validation new model was performed through experimen-tal data established in the literature and laboratory tests [1,2]. Our

arison between simulation and experimental data of the time course of the Ca2+





Fig. 9. Secondary screens of the simulator MioLab: calcium influx and efflux. Secondary screens of the simulator MioLab: (A) pulse of Ca2+ through the channels of the L-typechannels and leak: allow changes in the parameters of Ca2+ influx through the channels of the L-type and frequency (F1, F2), amplitude A, simulation time (Tsim), maximumtime for application pulse (Tmax), time of occurrence of peakCa2+ (tp), delay (D1 and D2), coefficient of exponential fit (m), as well as changes in external concentration of Ca2+

([Ca2+]e) Ca2+ at rest ([Ca2+]r) and the leakage coefficient (g). On this screen there is the possibility to display graphs, compare two simulations (control and chronic group)and inserting experimental data, saved in files with.* txt for further validation of the Ca2+ transient and contraction forces. (B) Ca2+ pump (Ca2+-ATPase) of the sarcolemma:change the maximum rate (Vmax) of uptake of Ca2+ by Ca2+-ATPase of the sarcolemma, the coefficient of Hill (n) and Ca2+ concentration at which the rate of uptake is thehalf-maximum (Km). The same parameters can also be changed (in similar screens) for the Ca2+ pump (Ca2+-ATPase) and the SR exchanger NCX.(C) Ca2+ release from SR:allows changes in Ca2+ concentration at rest inside the SR ([Ca2+]r), leakage coefficient (g) and coefficient of Ca2+ release from the SR (ch), and changes in the parametersa ) usina yanod

motitietsa

vsosuAfdtditTniCpdiAmt

ssociation and dissociation of Ca2+ receptor RyRs (L1, L2, L3, L4, L−1, L−2, L−3, and L−4

nd uptake of Ca2+by the SR and the states (active, open, closed and refractory) of r

odel effectively reproduced the amplitude, peak and rise timef the Ca2+ transient (see Fig. 3) and even the decline of the Ca2+

ransient (t1/2 required time for Ca2+ transient is reduced to halfts peak value), which showed a small difference (0.01 s) but con-inues within the error margin (20%) for experimental data, shownn Table 1. Simulation of the force of contraction using the param-ters that were validated for the Ca2+ transient is shown at theop of Fig. 3. It is observed that the power transient appears to belower than expected for rat cardiac myocyte, which demonstrates

limitation of the model.Similarly, considering the Ca2+ transient simulation used for the

alidation model with the control group, we implemented newimulations (e.g., study of the effects of blockers and activatorsn the Ca2+ pump (Ca2+-ATPase) from SR, the NCX exchanger inarcolemma and L-type channels). Making it clear that these sim-lation results were compared with experimental data [1,2,18].dditionally, to simulate the inhibition of Ca2+ pump (Ca2+-ATPase)

rom SR (with tBQ) based on experimental data reported [2], weecided to reduce the control parameter rate of Ca2+ removal fromhe cytosol. Moreover, this change produced an increase in theecline time of the Ca2+ transient (t1/2), which matched the exper-

mental data, but also resulted in an increased (compared withhe reduction observed experimentally) Ca2+ transient amplitude.hus, to generate a reduction in the Ca2+ transient amplitude, it wasecessary to change some parameters related to the Ca2+ kinet-

cs in the myofilaments (reduction in dissociation constants ofa2+), which is shown in Table 2(A). The changes made in thesearameters resulted in a 76% increase in the Ca2+ transient timeecline (versus 74% obtained experimentally) and a 30% reduction


n Ca2+ transient amplitude (versus 25% obtained experimentally).lthough the changes in parameters related to the kinetics of Ca2+ inyofilaments produced a satisfactory result when compared with

he experimental data, we cannot forget that these changes are

g the model described by Tang and Othmer [7]. You can also view charts on releaseine receptors (RyRs).

just tweaking the model, and have no further confirmation withexperimental data, so only a theoretical hypothesis that served tocircumvent the limitations of a model.

Additionally, in the case of beta-adrenergic stimulation withisoproterenol (ISO) to simulate the drug effects, alternation ofthe parameters for Ca2+ pump (Ca2+-ATPase) from SR, Ca2+ entrythrough L-type channels of Ca2+ kinetics in myofilaments [8,12–14]were made. Thus, these changes shown in Table 3 resulted in anincreased Ca2+ transient amplitude equal to 90% of the amplituderecorded experimentally and a drop of 18% in decline time t1/2(versus 25% of fall time obtained experimentally). It is notewor-thy that the increased Ca2+ transient amplitude was only obtainedwhen it doubled the parameters related to the dissociation of Ca2+

in myofilaments (see Table 2B). These changes are consistent withthat of other authors [8].

In addition, to stimulate the Ca2+ pump (Ca2+-ATPase) from SR,we have chosen an increase in the maximal rate of Ca2+ uptake(Vmax = 207 �M/s for the control group against 227 �M/s for thechronic group) and its reduction in Ca2+ concentration to obtain aremoval rate of half the maximum (Km = 0.17 �M for the controlgroup against 0.15 �M for the chronic group).

Moreover, in an attempt to adjust the model to reproduce exper-imental data on the use of drugs such as isoproterenol and tBQ,we have done some changes in the parameters governing the Ca2+

entry through L-type channels that produced a destabilization ofchannels for Ca2+release from SR (see Fig. 5) and also the con-sequent alternation in the Ca2+ transient amplitude (see Fig. 6).These results are consistent with experimental data [18]. Based onthe outcome of the last simulation, we tried to correct the alterna-


tion in the Ca2+ transient amplitude through adjustments in modelparameters, resulting in a 74% increase in the maximal rate of Ca2+

extrusion by the NCX exchanger, which achieved restoration of theCa2+ transient amplitude (see Fig. 7C). Briefly, our results verified





Fig. 10. Secondary screens of the simulator MioLab: calcium kinetics and force generation. Secondary f the simulator MioLab: (A) kinetics of Ca2+ in the myofilaments, thisscreen may be changing the parameters of association (Y1 and Y3) and dissociation (Z1 and Z3) of Ca2+ in the myofilaments, parameters of annexation (Y2) and shutdown (Z2,Y4 and Yd) of the bridges crossed, the total concentration of troponin ([T] and parameters used for calculating the concentration of TCa (La, R). In the graphic you can see thec 2+ 2+ e gent s-brids

teArptMein

lttci

oncentrations of Ca , TCa, TCa* and T* and still validate the Ca transient. (B) Forche calculation of the force of muscle contraction in the unit (A, B and K), initial crosee the force of contraction.

he hypothesis from the research group of the UMC who studied theffects of anti-arrhythmic drugs such as heparin derivatives [10].ccording to these researchers, the anti-arrhythmic drugs wereesponsible for blocking a protein known as “exchange inhibitoreptide” (XIP) and reducing the rate of cytosolic Ca2+ removalhrough the NCX exchanger, located in the sarcolemma of cells.

eanwhile, as a result of the inhibition of the XIP protein, the Ca2+

xtrusion rate was increased by the NCX exchanger, thereby reduc-ng the intracellular concentration of this ion and reestablishing theormal Ca2+ transient amplitude.

Nevertheless, new tests also showed that heparin derivativesead to amplitude reduction in the contractile force and relaxation


ime of cells. Therefore, to simulate the effect of heparin throughhis new model, the control group (without heparin) and thehronic group (with heparin) were considered, where the changento the maximal rate of Ca2+ removal by the NCX exchanger was

eration: in this screen, you can change the parameters of proportionality related toge elongation (ho), shortening of L produced by the force fp (L0) and also to visually

33% higher in the chronic group compared to the control group. Asa result of this simulation (see Fig. 7D), the experimental data isquite similar. In fact, the difference is a reduction in the contractileforce; however, the model was not able to reproduce the decreasein t1/2 of relaxation time (the time required for force contraction isreduced to half its peak value).

To simulate the transient Ca2+ evoked by rapid pulses of caf-feine, changing the parameters governing the transition states ofRyRs has been successful in maintaining a sustained increase in thefraction in the open state, which consequently resulted in a sus-tained increase in Ca2+ release SR and the concentration of freeCa2+. It is observed that the model was capable of evoking tran-


sient Ca2+in a manner similar to that observed experimentally. Thedifference between the initial values in transient Ca2+are causeddue to the stabilization period model, but is within the experimen-tal standard deviation. It is important to remember that changes





Fig. 11. Main screen of the simulator MioLab. Main screen of the simulator MioLab where you have access to secondary screens of the program: Parameters of the pulse ofCa2+ through the channels of leakage of the sarcolemma, and channel L-type; process CICR; kinetics of Ca2+ in myofilaments; parameters of the force of contraction; pumpC ma an

irs

nrmAu

5

tiMDidpTtiiad

adaf

dwd

ac

ssn

a2+ (Ca2+-ATPase) in SR; exchanger NCX; Pump Ca2+ (Ca2+-ATPase) of the sarcolem

n parameters related to the association and dissociation of Ca2+

eceptor RyRs were performed by trial and error after successiveimulations, thus allowing a better fit of the model.

In respect the application of some simulations on drugs, it isoteworthy that these are preliminaries and partial, since thesearely work in injecting drug unique mechanism of cell, i.e., theodel does not reproduce the action of the drug in complete detail.nyway, even noting the limitations of the model, its results can besed to collaborate on experiments to be performed.

. Conclusions

Overall, we have presented a new biophysical model to describehe contractile force of rat cardiac myocyte based on the dynam-cs of Ca2+. The new model was specifically implemented with the

ioLab simulator. MioLab was implemented in Visual C++ and theelphi user-friendly interface. MioLab describes the Ca2+ kinetics

n cytosol and the cross-bridge dynamics through a system of nineifferential equations, 15 auxiliary equations and 47 biophysicalarameters. The main novelty is a new dynamics of performance.he model has proved to be a useful tool for simulations that enablehe study of blockers and activators that act on the NCX exchangern the Ca2+ pump (Ca2+-ATPase) from SR or L-type channels. It wasmplemented to better understand the effects of drugs used to treatrrhythmias, thus making the simulator to be used as a tool for heartisease prevention.

Briefly, this simulation model can effectively reproduce themplitude, peak, rise time and Ca2+ transient. In addition, it repro-uces the effects of beta-adrenergic stimulation (with drugs suchs isoproterenol) and inhibition of the Ca2+ pump (Ca2+-ATPase)rom SR (with tBQ) on the Ca2+ transient.

Finally, the simulations made to reproduce the effects of heparinerivatives on the contractile strength are somewhat consistentith experimental data. However, the model was not able to repro-uce the decrease in t1/2 of relaxation time.

New applications of MioLab may be related to blood pressurend heart rate studies, with the purpose of providing a new tool forardiovascular accident prevention.


The simulations with changes in the parameters used were rea-onably successful in reproducing the experimental data, althoughome limitations have been observed. These limitations suggest theeed to adapt the theoretical model employed.

d sarcomere length.

As a future research project aims to after the new model fittingto adapt it so that you can not describe the contractile force at thelevel of the cell but to a cardiac fiber.

Authors contribution

RRS contributed to literature review, search for experimentaldata, mathematical model development, analysis and interpreta-tion of results. DGG is RSS’s mentor. He contributed to the dataanalysis and provided support for writing the present paper. MABcontributed to informatics support. All authors have read andapproved this paper.

Conflicts of interest

The authors claim that there are no financial and personal rela-tionships with other people or organizations regarding the presentwork.

Acknowledgment

The authors appreciate the support of the staff of the Mogidas Cruzes University, Research and Technology Center – Model-ing Biological Systems (MOSIBI/NPT/UMC) and the United Facultyof Suzano –Research Center and Extension (NUPE). The São PauloResearch Foundation (FAPESP – Process 2006/02830-7), the Foun-dations that Support Education and Research (FAEP) and PhysicalMedicine and Rehabilitation Institute of Hospital das Clinicas –FMUSP, Sao Paulo, Brazil, supported and promoted this research.Finally, the authors acknowledge the support of Leonardo JuanRamirez Lopezin writing this paper.

Appendix A. MioLab: virtual simulator for the contractileforce of rat cardiac myocyte

The new mathematical model was implemented by couplingnine differential equations, 15 auxiliary equations, and 47 bio-physical parameters. Moreover, the model was solved by the


fourth-order Runge–Kutta method with 10−5 s as the integrationstep. The results of each simulation were stored in a text fileand its analysis was shown in a graphic interface implementedin Matlab®. Its user-friendly interface was implemented in Delphi


ING Model

J

1 eering

patos

R

[

[

[

[

[

[

[

[

[

[

[cle response experiments with a Huxley-based contraction model. J Mol Cell


2 R.R. Silva et al. / Medical Engin

rogramming that allows changes both in biophysical parametersnd graphics display to compare the simulations results betweenhe control and chronic groups. Given this, Mio Lab is a Virtual Lab-ratory of Cardiac Myocyte, which shows the various secondarycreens (see Figs. 9–10) on a main screen (see Fig. 11).

eferences

[1] Alves BJ. Inhibitory effect of heparin derivatives in electrically induced arrhyth-mias in the right atrium of the rat. Dissertation. University of Mogi das Cruzes,Center for Research and Technology; 2009.

[2] Soriano DC: Experimental model and instrumentation to study the function ofsarcoplasmic reticulum Ca2+ transport in the heart. Dissertation. State Univer-sity of Campinas, Department of Biomedical Engineering; 2007.

[3] World Health Organization. Health and health-related statistical information(WHOSIS): annual report. Genebra; 2009.

[4] Bers DM. Cardiac excitation–contraction coupling. Nature 2002;415:198–205.

[5] Fink M, Noble PJ, Noble D. Mathematical models in cardiac electrophysiologyresearch: implications for the 3Rs. In NC3Rs 2009;19:1–8.

[6] Negroni JA, Lascano EC. A cardiac muscle model relating sarcomere dynamicsto calcium kinects. J Mol Cell Cardiol 1996;28:915–29.

[7] Tang Y, Othmer HG. A model of calcium dynamics in cardiac myocytesbased on the kinetics of ryanodine-sensitive calcium channels. Biophys J1994;67:2223–35.

[8] Bers DM. Excitation–contraction coupling and cardiac contractile force. TheNetherlands: Kluwer, Academic Publishers; 2001.

[9] Landesberg A, Sideman S. Mechanical regulation cross-sectional area of cardiacmuscle by coupling calcium kineticswith Fs cross-bridge cycling: a dynamic


model. Am J Physiol 1994;267:H779–95.10] Duarte J, Caricati NA, Godoy CMG. Use of electrical stimulus strength in rat

atrium as parameter for in vitroquantification of drug anti-arrhythmic effect.In: Anais da XXI Reunião Anual da Federac ão de Sociedades de Biologia Exper-imental: 23–26 Agosto. 2006.

[

PRESS & Physics xxx (2012) xxx– xxx

11] Wictome M, Michelangeli F, Lee AG, East JM. The inhibitors thapsigargin and2.5-di (tertbutyl)-1, 4-benzohydroquinone favor the E2 form of the Ca2+, Mg2+-ATPases. FEBS Lett 1992;304:109–13.

12] Carvalho BMR, Bassani RA, Franchini KG, Bassani JWM. Enhanced calciummobilization in rat ventricular myocytes during the onset of pressure overload-induced hypertrophy. Am J Phys 2006;291:H1803–13.

13] Li L, Desantiago J, Chu G, Kranias EG, Bers DM. Phosphorylation of phospholam-ban and troponin I in �-adrenergic-induced acceleration of cardiac relaxation.Am J Phys 2000;278:H769–79.

14] Ginsburg KS, Bers DM. Modulation of excitation–contraction coupling by iso-proterenol in cardiomyocytes with controlled SR Ca2+ load and Ca2+ currenttrigger. J Physiol 2004;556:463–80.

15] Valdivia HH, Kaplan JH, Ellis-Davies GCR, Lederer WJ. Rapid adaptation of car-diac ryanodine receptors: modulation by Mg2+ and phosphorylation. Science1995;267:1997–2000.

16] Marx OS, Reiken S, Hisamatsu Y, Jayraman T, Burkhoff D, Rosemblit N. PKAphosphorylation dissociates FKBP12.6 from calcium release channels: defectiveregulation in failing hearts. Cell 2000;101:365–76.

17] Wehrens XH, Lenart SE, Huang F, Vest JA, Reiken SR, Mohler PJ, Sun J, GuatimosinS, Song LS, Rosemblit N, D’Armiento JM, Napolitano C, Memmi M, Priori SG,Lederer WJ, Marks AR. FKBP12.6 deficiency and defective calcium release chan-nel (ryanodine receptor) function linked to exercised-induced sudden cardiacdeath. Cell 2003;113:829–40.

18] Eisner DA, Diaz ME, Li Y, O’Neill SC, Trafford AW. Stability and instability ofregulation of intracellular calcium. Exp Biol 2004;90:3–12.

19] Shinjo SK, Tersariol ILS, Oliveira V, Nakaie CR, Oshiro MEM, Ferreira AT, SantosIAA, Dietrich CP, Nader HB. Heparin and heparan sulfate disaccharides bind tothe exchanger inhibitor peptide region of Na+/Ca2+ exchanger and reduce thecytosolic calcium of smooth muscle cell lines. J Biol Chem 2002;277:48227–33.

20] Negroni JA. Lascano EC: simulation of steady state and transient cardiac mus-


Cardiol 2008;45:300–12.21] Puglisi JL, Bers DM. LabHEART: an interactive computer model of rabbit ven-

tricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol2001;281(6):C2049–60.


ARTIGO PUBLICADO RS_DGG_MB JUL2012.pdf

Documents

Transcript of ARTIGO PUBLICADO RS_DGG_MB JUL2012.pdf