Visual Servoing for Beating Heart Surgery - Visual Servoing via Advanced Numerical Methods - page 93

these devices can be seen as belonging both to the category of surgical mechatronic
tools. In that sense, the Cardiolock project is a novel and promising approach for
beating heart surgery.
Experimental in vivo results (Figure 6.4) have shown the efficiency of the ap-
proach. Furthermore, the analysis of the contact forces between the stabilizer and
the heart surface shows that the use of an active device does not modify signifi-
cantly the pressure applied on the heart. Taking also into account the safety of the
approach, we think that the medical acceptance of such a device should therefore be
comparable to the one of currently used passive stabilizers.

6.3 Heart Motion Prediction

The cardiac motion is composed of two quasi-periodic components [41]. The slow
component is due to the ventilation and the faster one corresponds to the heartbeats.
The sharp transients of the heart motion correspond to the high frequency harmonics
of the heartbeat. The heartbeat component has been proved to be dependent on the
respiratory cycle [13]. As robotized heart compensation can take advantage of the
knowledge of future cardiac motion, a lot of work has been devoted to heart motion
prediction. A full review of the available prediction algorithms is given in [2]. In
this section we only outline the two methods that explicitly take into account the
coupling between the heartbeat and respiratory components.

6.3.1 Linear Parameter Varying Method

The first step of this prediction algorithm [13] consists in separating the heartbeat
and respiratory components of the heart motion. This is achieved thanks to a gating
technique. In the electrocardiogram (ECG) signal, the QRS complexes, a combina-
tion of three electric waves, denote the beginning of the cardiac cycle. Sampling the
heart motion by the QRS complexes delayed by half a cardiac cycle allows to ob-
serve only the respiratory component at different moments of the respiratory cycle,
since the heart is almost at rest during the second half of the heartbeat cycle. In order
to be able to reconstruct the respiratory motion at each sample k , these samples are
interpolated using a smoothing cubic spline function F . Therefore, the respiratory

motion can be written as

ˆ

M r ( k )= F ( k − k res p ) (6.1)

where k res p is the sample number representing the beginning of the current respi-
ratory cycle. Then, this motion is subtracted from the whole motion to obtain the
heartbeat component:

ˆ ˆ

M c ( k )= M ( k ) − M r ( k ) . (6.2)

The heartbeat component is modeled by a finite impulse response (FIR) to the QRS
complex considered as an impulse. The heartbeat motion at sample k can therefore
be written as a convolution product: