Isoprenaline: A Potential Contributor in Sick Sinus Syndrome—Insights from a Mathematical Model of the Rabbit Sinoatrial Node

Table 1

Model equations of the SAN single cell, 2D tissue, and some channel currents.

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Single cell model of SAN

 𝑑𝑉/𝑑𝑡=−(𝑖_Na+𝑖_Ca,𝐿+𝑖_Ca,𝑇+𝑖_K,𝑟+𝑖_K,𝑠+𝑖_st+𝑖_to+𝑖_sus+𝑖_𝑏,Na+𝑖_𝑏,K+𝑖_NaK+𝑖_NaCa)/𝐶_𝑚

2D intact SAN-atrium tissue model

 𝜕𝑉𝑖𝜕𝑡=∇⋅(𝐷∇𝑉)−^tot𝐶_𝑚

Changes of sodium current induced by mutation

 𝑖_Na=(𝑆_Na×𝑔_Na)𝑚³ℎ[Na⁺]_𝑜𝐹²𝑒𝑅𝑇^{(𝑉−𝐸Na)𝐹/𝑅𝑇}−1𝑒^{𝑉𝐹/𝑅𝑇}𝑉−1 

 𝜏_ℎ1=𝑆_𝜏ℎ13.717×10⁻⁶𝑒^{−0.2815(𝑉+17.11)}1+3.732×10⁻³𝑒^{−0.3426(𝑉+37.76)}+5.977×10⁻⁴ 

 𝜏_ℎ2=𝑆_𝜏ℎ23.186×10⁻⁸𝑒^{−0.6219(𝑉+18.8)}1+7.189×10⁻⁵𝑒^{−0.6683(𝑉+34.07)}+3.556×10⁻³ 

 ℎ_1∞=11+𝑒^{(𝑉−𝑉∗𝑆ℎ+66.1)/6.4}

Effects of Ach on currents

 𝑖_K,Ach=𝑔_K,Ach,max𝑗𝑘[Ach]^𝑛K,Ach𝐾^𝑛K,Ach_0.5,K,Ach+[Ach]^𝑛K,Ach[K⁺]_𝑜10+[K⁺]_𝑜⋅𝑉−𝐸_K1+𝑒^{(𝑉−𝐸K−140)𝐹/2.5𝑅𝑇}

 𝑖_Ca,𝐿=1−𝑏_max[Ach]𝐾_0.5,Ca+[Ach]×𝑔_Ca,𝐿𝑑_𝐿𝑓_𝐿+0.0061+𝑒^{−(𝑉+14.1)/6.0}𝑉−𝐸_Ca,𝐿

 𝑖_𝑓=𝑦[𝑔_𝑓,Na(𝑉−𝐸_Na)+𝑔_𝑓,K(𝑉−𝐸_K)]

 𝑑𝑦=𝑦𝑑𝑡^∞−𝑦𝜏_𝑦

 𝑦_∞=𝑒^{−(𝑉+78.91−𝑠)/26.2}𝑒^{−(𝑉+78.91−𝑠)/26.2}+𝑒^{(𝑉+75.131−𝑠)/21.25} 

 𝜏_𝑦=1000.0𝑒^{−(𝑉+78.91−𝑠)/26.2}+𝑒^{(𝑉+75.131−𝑠)/21.25} 

   𝑠=𝑠_max[Ach]^𝑛𝑓𝐾^𝑛𝑓_0.5,𝑓+[Ach]^𝑛𝑓

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