TY - JOUR
T1 - Applicability of cable theory to vascular conducted responses
AU - Hald, Bjørn Olav
AU - Jensen, Lars Jørn
AU - Sørensen, Preben Graae
AU - von Holstein-Rathlou, Niels-Henrik
AU - Jacobsen, Jens Christian Brings
PY - 2012
Y1 - 2012
N2 - Conduction processes in the vasculature have traditionally been described using cable theory, i.e., locally induced signals decaying passively along the arteriolar wall. The decay is typically quantified using the steady-state length-constant, ¿, derived from cable theory. However, the applicability of cable theory to blood vessels depends on assumptions that are not necessarily fulfilled in small arteries and arterioles. We have employed a morphologically and electrophysiologically detailed mathematical model of a rat mesenteric arteriole to investigate if the assumptions hold and whether ¿ adequately describes simulated conduction profiles. We find that several important cable theory assumptions are violated when applied to small blood vessels. However, the phenomenological use of a length-constant from a single exponential function is a good measure of conduction length. Hence, ¿ should be interpreted as a descriptive measure and not in light of cable theory. Determination of ¿ using cable theory assumes steady-state conditions. In contrast, using the model it is possible to probe how conduction behaves before steady state is achieved. As ion channels have time-dependent activation and inactivation, the conduction profile changes considerably during this dynamic period with an initially longer spread of current. This may have implications in relation to explaining why different agonists have different conduction properties. Also, it illustrates the necessity of using and developing models that handle the nonlinearity of ion channels.
AB - Conduction processes in the vasculature have traditionally been described using cable theory, i.e., locally induced signals decaying passively along the arteriolar wall. The decay is typically quantified using the steady-state length-constant, ¿, derived from cable theory. However, the applicability of cable theory to blood vessels depends on assumptions that are not necessarily fulfilled in small arteries and arterioles. We have employed a morphologically and electrophysiologically detailed mathematical model of a rat mesenteric arteriole to investigate if the assumptions hold and whether ¿ adequately describes simulated conduction profiles. We find that several important cable theory assumptions are violated when applied to small blood vessels. However, the phenomenological use of a length-constant from a single exponential function is a good measure of conduction length. Hence, ¿ should be interpreted as a descriptive measure and not in light of cable theory. Determination of ¿ using cable theory assumes steady-state conditions. In contrast, using the model it is possible to probe how conduction behaves before steady state is achieved. As ion channels have time-dependent activation and inactivation, the conduction profile changes considerably during this dynamic period with an initially longer spread of current. This may have implications in relation to explaining why different agonists have different conduction properties. Also, it illustrates the necessity of using and developing models that handle the nonlinearity of ion channels.
U2 - 10.1016/j.bpj.2012.01.055
DO - 10.1016/j.bpj.2012.01.055
M3 - Journal article
C2 - 22455918
VL - 102
SP - 1352
EP - 1362
JO - Biophysical Journal
JF - Biophysical Journal
SN - 0006-3495
IS - 6
ER -