Rewarming

Introduction

Magnetic nanoparticle–based warming enables rapid, volumetric rewarming of cryogenically preserved biological systems by coupling magnetic fields to iron-oxide nanoparticles. Recent advances in this method have greatly improved the achievable warming rate for volumetric rewarming of rodent and human-scale organs (Han, Gangwar).

Rewarming from the glass transition temperature to the melting temperature of cryoprotectant-loaded tissue without ice formation requires a tradeoff between cryoprotectant (CPA) concentration and warming rate. High concentrations of CPA slow the rate of ice formation, but can be toxic. Lowering the concentration of CPA demands a faster warming rate to outcompete the rate of ice formation. As a result, optimizing the achievable warming rate is a well-studied mechanism to relax the amount of cryoprotectant that needs to be loaded into the organ.

Nanoparticle-based rewarming addresses this need by magnetically heating nanoparticles distributed in the vasculature in advance of vitrification (see Glass, Not Ice and this video). Where convective and microwave based rewarming can not provide sufficient heating rates nor temperature uniformity for rewarming a human-scale organ, nanoparticle-based warming can. Leveraging the high vascular density of the kidney, well-optimized nanoparticle rewarming unlocks rapid and uniform heating across the organ.

At Until, we’re scaling vitrification technology with the patient at the center of our design process, so when developing our volumetric rewarming system, we prioritized building a highly performant device that could work in a hospital setting. Previous work rewarming human-scale organs made use of power-intensive devices that operate at 120 kW drive power for 35 kA/m and 350 kHz, requiring specialized electrical infrastructure not compatible with standard hospital outlets. As the largest donor organ, the liver weighs around 1.5 kg, and roughly a 3.5J/gC° heat capacity, simple calculation shows that one only needs about 5 kW of heating power to warm this at 50 C°/min and the kidney comes in substantially lower at 400W ^{1, 2}.

heat capacity of liver tissue x mass of avg liver x dT/dt = power

3.5 J/gC° x 1500g x 1 = 5.2 kW

The high power loss in the pre-existing systems is attributable to inefficiency in the magnet itself, with conduction, switching losses, and coil cooling serving as the dominant sources of power consumption for the device.

Total power consumption = Heating Power Delivered + System Losses

Understanding how to improve on this efficiency requires looking first to how the nanoparticles are heating in the first place.

Let’s start there.

How Nanoparticles Produce Heat

We use iron oxide nanoparticles to heat larger biological systems, they are roughly the size of an adenovirus (10^-7 meters). In the simplest view, a magnetic nanoparticle can be seen as a single-domain magnet, meaning all the magnetic moments () are aligned in the same direction. A magnetic moment is a measure of the magnitude and direction of magnetism.

There are two mechanisms through which iron oxide nanoparticles heat in an alternating magnetic field, Brownian relaxation and Néel relaxation. In Brownian relaxation, the magnetic dipole in the particle aligns with the magnetic field through solid-body rotation — the nanoparticle itself rotates — generating heat through viscous losses. In Néel relaxation, the magnetic dipole reorients internally by overcoming the magnetocrystalline anisotropy barrier of the particle. The Néel case tends to be the dominant mechanism for our purposes, so we’ll focus there.

What is the magnetocrystalline anisotropy barrier, you ask? It's the energy barrier that resists reorienting a magnetic moment away from its preferred directions set by the crystal structure.

Iron (Fe) and Oxygen (O) come together to form a crystal lattice. Below you can see a cubic crystal lattice formed by just two Fe₃O₄ units coming together.

This crystalline structure has an and a . The easy axis sets the preferred axis for magnetic moment orientation when there is no applied magnetic field.

The potential energy of the magnetic moment imposed by the magnetocrystalline anisotropy is set by the angle between the magnetic moment and the easy axis. Let’s call this angle Θ.

The magnetocrystalline anisotropy barrier is the energy required completely to flip the magnetic moment.

So, the relevant entities to track are the magnetic moment of the particle (), the and the , and lastly, the applied magnetic field (). Once a magnetic field is applied the energy landscape changes:

With an insufficient Energy applied via a , the magnetic moment cannot overcome the Energy barrier to align with the applied magnetic field.

In order to realign with the applied magnetic field, the magnetic interaction needs to overcome the magnetocrystalline anisotropy barrier. Until that point, there is a metastable local minimum in the energy function.

With sufficient Energy applied via a , the Energy barrier is overcome, and the magnetic moment flips.

This flipping is the “Alternating” in the Alternating Magnetic Field (AMF) Coils that we use to rewarm biological systems after cryopreservation. But most importantly, when the magnetic moment of the crystalline structure flips, a is released.

This is essentially how nanoparticle-based volumetric rewarming works!

The energy released by a single nanoparticle flip is the shown above. Heating power is simply the rate at which these heat packets are released, multiplied by the amount of energy in each packet, which is set by the anisotropy barrier.

As the magnetic field oscillates, the magnetic moment repeatedly overcomes the anisotropy barrier and flips direction, releasing heat each time. Higher frequencies increase the rate of these flipping events.

In short: stronger fields help overcome the anisotropy barrier, while higher frequencies increase how often nanoparticles release heat.

Using this as our guiding principle, we set out to design a Power Electronics System to generate an alternating magnetic field with the highest achievable frequency and an applied magnetic field Energy larger than the magnetocrystalline anisotropy barrier of our in-house particles, all while keeping the power consumption below what would be readily available in a hospital setting.

Engineering an Efficient Power Electronics System

You now have a solid understanding of how nanoparticles are used to rewarm an organ, so we shift our focus to the Power Electronics System that produces the applied magnetic field that makes the magnetic moment of the nanoparticles flip, which then produces heat.

Here, the entities to track are the applied magnetic field () measured in kiloamperes per meter (kA/m), the frequency of flips measured in kiloHertz (kHz), the Power Budget taken from an outlet is measured in kilowatts, and the system losses also measured in kilowatts (kW).

In order to ensure that our system could be easily applied in a hospital setting, we decided that an L15-30 circuit that can supply 10.8 kW of power seemed like a good upper bound for our power budget. If we wanted to eventually do a liver, this would imply:

Power Budget - Heating Power Required = Acceptable System Loss

10.8 kW - 4 kw = 6.8 kW of System Losses

So under hospital-setting constraints, we can afford 6.8 kW of system losses. You might remember previous work rewarming human-scale organs made use of power-intensive devices that operate at 120 kW power budget for 35 kA/m and 350 kHz. But calculation shows that we should only need 5 kW of heating power to warm a liver at 60 C°/min, and the kidney only 400W. This implies that the system loss is over 100kW.

To drive the power budget down to 10.8kW we needed to engineer a system that is extremely efficient at producing a high frequency applied magnetic field.

What are the parts of a Power Electronics System that can generate an alternating magnetic field? A signal, an amplifier, a resonator and the coil.

A low-power-source defines the desired frequency of the alternating magnetic field. That signal is then to the high voltage and current levels that are needed to drive the system. The is a circuit that then sustains the desired frequency and waveform, and maximizes energy transfer to the , which is the physical conductor converting the oscillating current into an alternating magnetic field in space.

By dramatically increasing the efficiency of both the amplifier and the resonator, we have arrived at our first complete rewarming system, the Until Mark 1.

Mark 1 produces a 900 kHz oscillating field at up to 40 kA/m with 7 kW of coil loss. For organ rewarming, we reduce the field strength to 29 kA/m and bring the losses down below 4 kW. At these settings, we have been able to rewarm a vitrified pig kidney loaded with our iron oxide nanoparticles at 50 C°/min while consuming a total of less than 4 kW out of the wall. At this power, the device could run off of a common single phase 208V circuit.

Our System Successfully Rewarms a Pig Kidney

After successful vitrification of a pig kidney, Until Mark I system performance was evaluated during active rewarming of a whole pig kidney at native geometry. Kidney cortex temperature was measured by placing a thermocouple one centimeter depth from the surface of the kidney. The temperature increased at an average rate of 59°C per minute in the deep venous location and 73°C in the cortical location.

Until Mark I: Volumetric Rewarming of a Vitrified Kidney

The central challenge of organ cryopreservation has never been cooling alone, but reliably returning complex biological systems back through the glass transition to normal body temperature, without catastrophic ice formation.

With Until Mark 1, we demonstrate rewarming a vitrified pig kidney while operating from standard electrical infrastructure. This represents a crucial step toward deployable organ cryopreservation systems. By reducing total system power requirements from industrial-scale levels down to a few kilowatts, we’ve placed the realities of hospitals, transplant centers, and patients at the core of our designs. By improving the system’s frequency, we get better heating per nanoparticle and can use less nanoparticles. There is still substantial work ahead, but these results demonstrate that organ-scale rewarming no longer requires massive power budgets to achieve rapid volumetric heating.