Abstract
The thermal environment of developing embryos in Assisted Reproduction clinics is important to achieving a successful outcome, yet it is poorly understood due largely to measurement difficulties. This work developed a finite element model of heat transfer in a Petri dish typically used in assisted reproduction labs to house embryos and validated it against experimental scenarios similar to those used in clinical practice. This included the collation and measurement of model parameters. The model was successfully validated at the location of the embryo, showing good agreement with experimental data. It was found that for the Petri dish system investigated, temperature equilibration from ambient conditions to 37 °C took approximately 35 min in an incubator and that the thermal environment an embryo experiences with the lid on whilst on a heated stage is approximately 2 °C warmer than with the lid off. This suggests that current practice in Assisted Reproduction may routinely expose embryos to temperatures considered detrimental to viability as a result of fluctuations caused by the addition and/or removal of the lid of the dish and the subsequent alteration of heat transfer resistance in the system. The model presented here serves as a starting point to identify other steps in the embryo culture process which may present suboptimal temperatures and hence establish design guidelines to ensure a stable and desirable thermal environment for the embryo.
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Abbreviations
- Ra:
-
Rayleigh Number, \(\frac{{g\beta (\theta_{\text{s}} - \theta_{\infty } )x^{3} c\rho }}{\mu \lambda }\)
- Bi:
-
Biot Number, \(\frac{hL}{\lambda }\)
- α :
-
Thermal diffusivity = λ/(ρc), m2 s−1
- g :
-
Acceleration due to gravity, m s−2
- β :
-
Thermal expansion coefficient, °C−1
- λ :
-
Thermal conductivity, W m−1 K−1
- μ :
-
Kinematic viscosity, m2 s−1
- x :
-
Thickness, m
- L :
-
Characteristic dimension, (x/2) m
- r :
-
Radius, m
- H :
-
Height, m
- c :
-
Heat capacity, J kg−1 K−1
- ρ :
-
Density, kg m−3
- h :
-
Convective heat transfer coefficient, W m−2 K−1
- θ :
-
Temperature, °C
- θ stage :
-
Stage surface temperature, °C
- T :
-
Temperature, K
- q :
-
Heat flux, W
- t :
-
Time, s
- Ø:
-
Diameter, μm
- a :
-
Air
- f :
-
Floor of dish
- i :
-
Initial
- ∞ :
-
Ambient
- m :
-
Media
- o :
-
Paraffin oil
- p :
-
Polystyrene
- s :
-
Surface
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No human studies were carried out by the authors for this article. No animal studies were carried out by the authors for this article.
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Associate Editor Anubhav Tripathi oversaw the review of this article.
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Blomfield, S., Redding, G.P., Bronlund, J.E. et al. A Model for Characterisation of the Thermal Environment of Embryos in a Petri Dish During In Vitro Culture. Cel. Mol. Bioeng. 9, 546–555 (2016). https://doi.org/10.1007/s12195-016-0454-7
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DOI: https://doi.org/10.1007/s12195-016-0454-7