Model-Based Optimization of Solid-Supported Micro-Hotplates for Microfluidic Cryofixation

Cryofixation by ultra-rapid freezing is widely regarded as the gold standard for preserving cell structure without artefacts for electron microscopy. However, conventional cryofixation technologies are not compatible with live imaging, making it difficult to capture dynamic cellular processes at a precise time. To overcome this limitation, we recently introduced a new technology, called microfluidic cryofixation. The principle is based on micro-hotplates counter-cooled with liquid nitrogen. While the power is on, the sample inside a foil-embedded microchannel on top of the micro-hotplate is kept warm. When the heater is turned off, the thermal energy is drained rapidly and the sample freezes. While this principle has been demonstrated experimentally with small samples (<0.5 mm${}^2$), there is an important trade-off between the attainable cooling rate, sample size, and heater power. Here, we elucidate these connections by theoretical modeling and by measurements. Our findings show that cooling rates of 10⁶ K s⁻¹, which are required for the vitrification of pure water, can theoretically be attained in samples up to ∼1 mm wide and $5\mathrm{m}$ thick by using diamond substrates. If a heat sink made of silicon or copper is used, the maximum thickness for the same cooling rate is reduced to ∼3 $\mathsf{\mu }$m. Importantly, cooling rates of 10⁴ K s⁻¹ to 10⁵ K s⁻¹ can theoretically be attained for samples of arbitrary area. Such rates are sufficient for many real biological samples due to the natural cryoprotective effect of the cytosol. Thus, we expect that the vitrification of millimeter-scale specimens with thicknesses in the $10\mathrm{m}$ range should be possible using micro-hotplate-based microfluidic cryofixation technology.