Fluid dynamics during embryo transfer

Objective : To study fluid dynamics during ET.

Design : Computational fluid dynamics were applied to calculate fluid velocity changes, dynamic pressure differences, and shear stress in the transferred load for the following injection speeds: 0.1, 1, 6, 12, and 20 m/sec.

Setting : Academic research institute of mechanical engineering and reproduction biotechnology and private centers of reproductive medicine.
Patient(s) : None.

Intervention(s) : None.

Main Outcome Measure(s) : Fluid velocity, dynamic pressure, and shear stress during injection of the transferred load.

Result(s) : An increase of injection speed for the transferred load increased the shear stress, dynamic pressure, and velocity differences acting on the embryo. The narrowing of the catheter lumen diameter by 20% amplified the transferred fluid velocity by 78%. An embryo positioned in proximity to the catheter’s wall was exposed to considerably higher shear stress, dynamic pressure, and velocity difference than an embryo in the center of the catheter’s lumen.

Conclusion(s) : The transfer of an embryo should be conducted gently and with minimal injection speed. Any narrowing of the catheter lumen should be eliminated. Preferably the embryo should be kept far from the catheter’s wall during injection of the transferred load. (Fertil Steril 2011;96:324–7. 2011 by American Society for Reproductive Medicine.)

The procedure of ET is the final manual intervention in the IVF procedure.
The fact that high rates of fertilization in the laboratory result in a relatively low pregnancy rate have led investigators to focus their attention on various features of the ET procedure.

Several factors influencing ET success have been described (e.g., development potential
of the embryos, receptivity of the endometrium, instrumentations used, and ability and specific experience of the clinicians) (1–3).
Despite the variety of presently available catheters, the basic idea of delivering an embryo into the uterus remains the same: the pressure generated in the working chamber of the insulin syringe is passed into the catheter, where it causes the ejection of the transferred
load. The study conducted previously by our team demonstrated that ET performed with the standard insulin syringe-catheter complex was able to affect mouse blastocyst viability (4). The abrupt alterations in the embryo’s environment during ETwere the most probable cause for the observed morphological and apoptotic changes in the mouse blastocysts (4, 5).
The physical conditions created inside the catheter during ET are not well understood nor have they been investigated to date.

Therefore, in the current work, the fluid dynamics parameters that are generated inside the transferred load during the injection phase of ET were analyzed, and their possible impact on embryo viability is discussed.

MATERIALS AND METHODS
Simulation of Fluid Dynamics

A numerical approach using computational fluid dynamics was applied in the
present study.
To complete the experimental approach presented in the previous article (5), we studied a numerical model of the ET catheter ending and a model of the uterus during the injection phase of ET. The entire period of injection lasted for 0.02 second.

Water, being a model of embryo culture medium, was injected at a time interval of 0.01 second at a linear rising rate into a uterus model containing glycerin at rest.

After that, the water flow rate was reduced to zero. The diameter of the inner compartment of the catheter used for the experiments and simulations was 0.4 mm. The tip narrowing was assumed to be 20% of the diameter of the inner compartment.

The uterus model was built with 2 rigid walls, set 2 mm apart, according to the experimental
approach presented in the previous article (5).

Embryo culture medium properties were assumed to be those of liquid water (density r ¼ 998.2 kg/m3; dynamic viscosity m ¼ 0.001003 kg/[m/sec]).

To mimic the viscous uterine fluid, the uterus model was filled with glycerin of density r ¼ 1,236.25 kg/m3 and dynamic viscosity m ¼ 0.799 kg/(m/s), which has similar density as that of
uterine fluid (6, 7). A 3-dimensional geometric model of the flow domain was created in ANSYS Modeler (ANSYS, Incorporated).
The average fluid velocity was computed at the cross-sections O and X (Fig. 1A). Dynamic pressure was determined at points O and X (Fig. 1A). Velocity difference, dynamic pressure difference, and shear stress acting on the embryo were calculated for the hypothetical embryo positions I and II (Fig. 1A).

Calculations were performed for the following mean velocities in the catheter inlet cross-section: 0.1, 1, 6, 12, and 20 m/sec.
The flow was assumed to be transient, incompressible and turbulent, described by the Reynolds-averaged Navier-Stokes equations with the shear stress transport k-u turbulence model. The computations were carried out using the computational fluid dynamics code Parallel ANSYS Fluent 12.1 with the segregated solver SIMPLE (semi-implicit method for pressure-linked
equations).

The model was solved in double precision on a control volume unstructured 3-dimensional mesh of 3,961,001 control volumes made in ANSYS Mesher.
The pressure values are expressed in Pa. Dynamic pressure is a pressure resulting from the motion of a medium and is closely related to the kinetic energy of the fluid particles. Shear stress is a stress state in which the stress is parallel to the surface of the material. Shear stress is relevant to the motion of fluids upon surfaces and to the fluid viscosity.
The study was approved by the local ethics committee.

RESULTS
An increase of the injection speed of the transferred load increased the shear stress, dynamic pressure, and velocity differences acting on the embryo (Table 1). The shear stress difference in proximity to the catheter wall (position II) was considerably higher than that in the midstream (position I) (Table 1 and Fig. 1). For the injection velocity of 12 m/sec, the shear stress difference in position II was 557.51 Pa, whereas it was 8.85 Pa in position I.

The detailed data on shear stress difference for the studied embryo positions and injection velocities are presented in Table 1. The dynamic pressure difference acting on the embryo in the midstream was considerably lower
than that in proximity to the catheter wall (Table 1 and Fig. 1).

For the injection velocity of 12 m/sec, the dynamic pressure difference acting on the embryo in position I was 1,321 Pa, whereas it was 100,818 Pa in position II. The detailed data for injection velocities are presented in Table 1.

The velocity difference acting on the embryo in proximity to the catheter wall was considerably higher than that in midstream (Table 1 and Fig. 1). For the mean injection velocity of 12 m/sec, the velocity difference acting on the embryo in position II was 14.3 m/sec, whereas it was only 0.09 m/sec in position I (Table 1).

The narrowing of catheter lumen diameter by 20% increased the transferred fluid velocity by 78% (Table 1). For the injection velocity of 12 m/sec at cross-section X, the fluid velocity at the narrowed cross-section O reached 21.4 m/sec. The detailed data for the injection velocities are presented in Table 1.

The narrowing of the catheter lumen also caused considerable increase in the dynamic
pressure of the transferred fluid. For the injection velocity of 12 m/sec, the calculated dynamic pressure inside the catheter at point X was 101,292 Pa, whereas it was 217,333 Pa in the catheter narrowing, point O.

The detailed data for the particular injection velocities are presented in Table 1.

DISCUSSION
The aim of this study was to investigate the fluid dynamics of the transferred load during the injection phase of ET. The results of the present study indicated that an increase in the injection speed of the transferred load increases the shear stress, dynamic pressure, and velocity difference acting on an embryo during ET.

Furthermore, the narrowing of the catheter tip considerably amplifies the injection
speed of the transferred load, as well as the dynamic pressure and wall shear stress.
The general idea of delivering an embryo into the uterine cavity has not changed much since the early days of IVF. Overall, the pressure generated in the working chamber of the insulin syringe is passed into the catheter where it causes ejection of the transferred load.

The disproportion between the diameters of the syringe plunger and the catheter lumen creates favorable conditions for the fast fluid flow inside the catheter, reaching 12 m/sec on average (5).
According to the concept of fluid flow inside a tube with a circular cross-section, the fluid in the central region moves faster than in the peripheral region of the catheter lumen.

The fluid flow velocity gradient exerts shear stress on any object placed inside the fluid. The
impact of the shear stress on air bubbles, similar in size to an embryo, positioned inside the catheter is presented in Figure 2.

It is evident that the air bubble in proximity to the catheter wall is exposed to higher shear stress than one that stays in the midstream, where fluid flow velocity gradient and shear stress are lower (Fig. 2).
The strength of the shear stress increases with the injection speed of the transferred fluid (Table 1).With high enough injection speeds, the shear stress can be strong enough to injure the vital cell’s organs and impair embryo viability. A recent study indicated that fast ET, with an injection speed of the transferred volume of more than 1 m/sec, could trigger both morphological and apoptotic changes in mouse blastocysts (4, 8).

Alternatively, reduction of the injection speed to less than 0.1 m/sec allowed to avoid morphological changes and significantly decreased apoptosis in embryos (4).
In another experiment, 3 mouse blastocysts were loaded together into an ET catheter (Labotect GmbH) and transferred simultaneously into the uterus model under in vitro conditions (4). When
the embryos were checked 5 minutes after the transfer, one retained normal morphology, one was shrunk, and one was collapsed with a broken zona pellucida. To explain the observed phenomenon, it has to be taken under consideration that the position of the embryo
inside the catheter lumen is random; therefore, exposure to shear stress and pressure changes during the injection phase of ET can differ among embryos (Fig. 1). The embryo with unchanged morphology most likely stayed in the midstream of the fluid flow (arrow I, Fig. 1), where it was exposed to the least shear stress, pressure, and velocity differences (Table 1). On the other hand, the embryo with the highest degree of morphological changes most probably stayed in the peripheral region of catheter lumen (arrow II, Fig. 1), where it was exposed to significant shear stress, pressure, and velocity gradient (Table 1).
Another factor that could have affected the results of the ‘‘3 embryo transfer’’ experiment was the narrowing of the catheter tip (Fig. 1A). It constituted an obstacle for the transferred load, especially for the embryo in the peripheral region of the catheter lumen (arrow II, Fig. 1).

Furthermore, the narrowing of the catheter tip considerably increased injection speed of the transferred fluid and amplified the dynamic pressure and shear stress at the level of catheter
outlet (Table 1). It is known that narrowing of small blood vessels results in distortion and fragmentation of erythrocytes, such as in microangiopathic hemolytic anemia or hemolytic-uremic syndrome (9). Therefore, it would be appropriate to eliminate any narrowing of the catheter lumen. Furthermore, it would be optimal to maintain embryos in the center of the catheter lumen during ET, far from the catheter’s wall, because of the minimal shear stress, dynamic pressure, and velocity difference (Table 1). However, the presently available
catheters do not provide such an option. Therefore, redesigning the present-day catheters or developing novel approaches to ET might be necessary.

Taking the results of the present study into consideration, it would be advised to transfer embryos with minimal injection speed because the strength of the shear stress and the pressure changes increase with the injection speed of the transferred load. It would also be recommended
to eliminate any narrowing of the catheter lumen to assure more favorable conditions for the transferred embryos.