Analysis of Contact Stability and Contact Safety of a Robotic Intravascular Cardiac Catheter under Blood Flow Disturbances

Abstract

This paper studies the contact stability and contact safety of a robotic intravascular cardiac catheter under blood flow disturbances while in contact with tissue surface. A probabilistic blood flow disturbance model, where the blood flow drag forces on the catheter body are approximated using a quasi-static model, is introduced. Using this blood flow disturbance model, probabilistic contact stability and contact safety metrics, employing a sample based representation of the blood flow velocity distribution, are proposed. Finally, the contact stability and contact safety of a MRI-actuated robotic catheter are analyzed using these models in a specific example scenario under left pulmonary inferior vein (LIV) blood flow disturbances.

Fig. 1.

Illustration of the robotic catheter ablation procedure [8].

Fig. 2.

The MRI-actuated robotic catheter with two sets of tri-axial actuation coils subject to the perturbation forces resulting from blood flow drag forces and the tissue surface constraint. The catheter base frame S is given as shown. Ψ denotes the surface parametrization. The contact frame C is chosen such that its origin is located at the contact point of the catheter and the z-axis is the outward normal of the tissue surface.

Fig. 3.

(a) The left inferior pulmonary vein (LIV) blood flow velocity profile calculated from the data reported in [35] using a distal diameter of 1.8 cm. The minimum and maximum blood flow velocities are 0.21 m/s and 0.57 m/s, respectively. (b) Histogram of the 10,000 blood flow velocity samples drawn from the blood flow velocity profile in (a).

Fig. 4.

(a) The illustration of the blood flow directions in the tangential plane. The directional angle α_ǁˊ is sampled in [0°, 360°]. (b) The illustration of the blood flow directions in the plane perpendicular to the tangential plane at α_ǁˊ = 90°. α_⊥ is varied in [30°, 150°]. At α_⊥ˊ = 90°, the blood flow direction is parallel to the tangential plane.

Fig. 5.

Results for nominal contact normal force magnitude of 0.25 N. (a) The probabilistic contact stability metric k_s for blood flow directions α_ǁ ∈ [0°, 360°] and α_⊥ ∈ [30°, 150°]. (b) The probabilistic contact safety metric k_f for blood flow directions α_ǁ ∈ [0°, 360°] and α_⊥ ∈ [30°, 150°]. The catheter-tissue contact remains stable for all blood flow directions, but, contact forces can fall outside the specified limits for some blood flow directions.

Fig. 6.

Results for nominal contact normal force magnitude of 0.2 N. (a) The probabilistic contact stability metric k_s for blood flow directions α_ǁ ∈ [0°, 360°] and α_⊥ ∈ [30°, 150°]. (b) The probabilistic contact safety metric k_f for blood flow directions α_ǁ ∈ [0°, 360°] and α_⊥ ∈ [30°, 150°]. The catheter-tissue contact remains stable and within specified contact force limits for all blood flow directions.

Fig. 7.

Results for nominal contact normal force magnitude of 0.1 N. (a) The probabilistic contact stability metric k_s for blood flow directions α_ǁ ∈ [0°, 360°] and α_⊥ ∈ [30°, 150°]. (b) The probabilistic contact safety metric k_f for blood flow directions α_ǁ ∈ [0°, 360°]and α_⊥ ∈ [30°, 150°]. The catheter-tissue contact remains stable for all blood flow directions, but, contact forces can fall outside the specified limits for some blood flow directions.

Fig. 8.

Results for nominal contact normal force magnitude of 0.09 N. (a) The probabilistic contact stability metric k_s for blood flow directions α_ǁ ∈ [0°, 360°] and α_⊥ ∈ [30°, 150°]. (b) The probabilistic contact safety metric k_f for blood flow directions α_ǁ ∈ [0°, 360°] and α_⊥ ∈ [30°, 150°]. The catheter-tissue contact may lead to slippage for some blood flow directions as there are regions of flow directions where the probability of stable contact drops below 1; Contact forces can fall outside the specified limits for all flow directions, since contact safety metric never reaches to 1 for any of the flow directions.

Fig. 9.

(a) The histogram of the resulting normal contact forces when the LIV blood flow direction is varied in the tangential plane (α_ǁ ∈ [0°, 360°] with α_⊥ ∈ [30°, 150°]), for a nominal normal contact force of 0.12 N. The lowest resulting normal contact force occurs at α_ǁ = 104°. (b) The histogram of the resulting normal contact forces when the blood flow is varied in the perpendicular plane (α_⊥ ∈ [30°, 150°]) for α_ǁ = 104°. (c) The histogram of the resulting normal contact forces when the LIV blood flow direction is varied in the tangential plane (α_ǁ ∈ [0°, 360°] with α_⊥ = 0°), for a nominal normal contact force of 0.23 N. The highest resulting normal contact force occurs at α_ǁ = 281°. (b) The histogram of the resulting normal contact forces when the blood flow is varied in the perpendicular plane (α_⊥ ∈ [30°, 150°]) for α_ǁ = 281°.