Figure 1 – (a) Schematic depicting cell lysis by tip sonication: (i) sonicator tip is inserted into the sonication vessel, submerging tip in liquid. (ii) Controller for specifying pulse, amplitude & duration iii) The tube sits in ice-bath for cooling iv) Input energy from controller (ii) is set as a function of signal amplitude (translates to tip power based on fluid volume and vessel), pulse durations, and total sonication time v) Thermal energy transfers to ice-bath from cell suspension domain vi) The sonicated liquid is divided into circulated zone & dead zone (b) Axis-symmetric models (right half) of common laboratory tubes: i) 1.5 mL microcentrifuge tube ii) 5 mL microcentrifuge tube iii) 15 mL Falcon tube iv) 50 mL Falcon tube
It is also important to note that adverse temperature effects of sonication extend beyond this paper’s focusing example of cell lysate preparation. For example, mass loss of graphene nano particles is caused by temperature rise in sonication (Baig et al., 2018). In ultrasonic extraction of corn, overexposure causes reduction of glucose release due to denaturation of enzyme due to temperature rise. There is a reduction in taste, vitamin content and loss of texture in foods that over processed with ultrasonic extraction (Tobergte & Curtis, 2013). In another example, single walled carbon nanotubes (SWCNT) bundle ends are frayed due to temperature rise caused by ultrasonic exposure (Hassan, Reddy, Haque, Minett, & Gomes, 2013; Strano et al., 2003). Thus, a model for mixing and temperature rise caused by sonication will find uses in broader biotechnology applications.
Sonication protocols are designed to mitigate this influence of temperature rise and improve mixing; however, they currently require much empirical testing to determine. Typically, the probe is operated in a pulsed fashion with defined on and off cycles. Additionally, the sonication vessel is submerged in an ice bath or chiller line. There is a tradeoff between the number of cells lysed and the extract viability which decreases when over-sonicated. From a physical standpoint, it is logical that there exists a threshold temperature for each type of extract, and corresponding sets of optimum parameters to stay below this threshold, but in practice, finding this threshold and controlling temperature rise experimentally can be difficult. The sonicator parameters of input power, pulse durations, and total sonication times are empirically optimized for a given vessel, often necessitating a large number of experiments to cover the design space (Kwon & Jewett, 2015). Characterization tools can help direct such experiments, but their utility for small volume lysate preparations are limited (Sutkar & Gogate, 2009). The velocity field inside a sonoreactor can be monitored by particle image velocimetry (PIV) techniques (G. S. B. Lebon, Tzanakis, Pericleous, Eskin, & Grant, 2019; Donato Rubinetti, Weiss, Wahlen, & Müller, 2016), but for opaque lysate in a small tube such techniques cannot be used to conveniently measure the velocity pattern. It is also difficult to routinely measure temperature in such small volumes by thermocouple and as the vessel is seated in an ice bath, it is also difficult to monitor the inner vessel temperature by NIR imaging. Thus, to more efficiently design optimal sonication protocols for thermally sensitive procedures like cell extract preparation, we propose finite element modeling of mixing and thermal effects.
Finite element modeling of ultrasound systems has been demonstrated in literature, especially for larger reactors. Fluid flow in large sonoreactor (> 500 mL) has been extensively studied (B. Lebon, Tzanakis, Pericleous, & Eskin, 2019; D. Rubinetti & Weiss, 2018; Xu, Yasuda, & Koda, 2013). The temperature-rise in large reactors, however, is less prevalent, likely due to temperature rise being negligible in a large vessel when subjected to low power density input and having a larger surface area for thermal dissipation (Trujillo & Knoerzer, 2011). Effects of ultrasound (temperature rise and fluid streaming) are mostly studied for medical applications of high-intensity, focused ultrasound (Moriyama, Yoshizawa, & Umemura, 2012; Solovchuk, Sheu, Lin, Kuo, & Thiriet, 2012). Conversely, in cell extract preparation, much smaller, laboratory scale tubes (Fig 1b) are used and both mixing and temperature effects will need to be managed. This can be done using a similar framework of finite element modeling.
This paper provides a computational model to predict the effects of tip sonication parameters on mixing and temperature rise in small vessels, commonly used for cell extract preparation. First the relationship between fluid flow patterns and tip immersion depth is modeled; this is used to estimate the optimum tip depth which maximizes mixing. This is done by numerically calculating the stationary velocity field inside the sonication tubes for different tip immersion depths and comparing the fractional volume with regular, circulating streamlines. Next a heat transfer model is used to predict temperature rise over time due to sonication in lab scale tubes which is then experimentally validated. This model is then used to estimate the optimal threshold temperature in a common cell extract strain (BL21 DE3 star) using optimized CFPS experiments presented in literature (Kwon & Jewett, 2015). This model coupled to experimental data can then provide insight on the effect of sonication temperature on cell lysis yield. A stepwise workflow is then presented for use of these numerical models in obtaining optimized parameters for other novel sonication set ups. Lastly, we provide convenient master-plots for determination of optimal sonication conditions for new temperature thresholds without need of running the modeling code.