= Chordae tendineae
The \b[chordae tendineae] are collagen-rich tensile cords connecting <valve leaflets> of the <mitral valve> and <tricuspid valve> to <papillary muscles>. Their <tension> helps restrain the leaflets against displacement toward an atrium during ventricular <systole>. They are supports for pressure-loaded leaflets, rather than muscles that pull the valves open. The <aortic valve> and <pulmonary valve> do not have this chordal apparatus.<Anatomy and Physiology 2e by J. Gordon Betts and others>[§19.1, Right Ventricle; Heart Valve Structure and Function]{ref}
An original static model shows why the arrangement matters. Suppose a leaflet attachment experiences a resultant <force> $F=\Delta pA$ from a <pressure> difference $\Delta p$ acting over effective area $A$. Two equal tethers each carry <tension> $T$ at angle $\theta$ to the load axis. Their transverse components cancel and their axial components balance the load:
$$
2T\cos\theta=F,\qquad T=\frac{\Delta pA}{2\cos\theta}.
$$
A stipulated $\Delta p=10$ kPa over $A=1$ cm$^2$ gives $F=1$ N. Changing $\theta$ from $30^{\circ}$ to $60^{\circ}$ raises each tether's <tension> from about $0.577$ to $1$ N without changing the pressure load.
\Image[/valve-tether-angle.png]
{title=Tether angle changes tension under the same applied load}
{description=Original equal-tether force balance. Each panel supports a 1 N load; angles are measured from the opposing load axis. This point-attachment schematic illustrates vector components, not the anatomy or measured forces of a particular valve.}
A primary experiment tested the related geometrical question in a left-heart simulator. Force transducers measured selected <chordae tendineae> while the positions of <papillary muscles> were changed. Different chordal types responded differently.<Effects of papillary muscle position on chordal force distribution: an in-vitro study by Jorge Hernan Jimenez and others>[Abstract, Methods and Results]{ref} Real leaflets distribute loading among many attachments, so the two-tether model explains a mechanism without supplying a universal chordal force. Material behavior, geometry and the timing of ventricular contraction remain separate inputs.
Back to article page
