Electric fields and low temperatures for the treatment of cancer

Motivation 

Cancer is the 2nd most leading cause of death in the United States. This is one of the many reasons it is paramount to pursue focal tissue ablation techniques. Current techniques include radiofrequency ablation, HIFU, radiation/brachytherapy, chemotherapy as well as countless others.
However, there are still challenges with each procedure. RF ablation and HIFU are thermal ablation modalities, which means they ablate all tissue in the treatment zone indiscriminately, which can be dangerous for adjacent nerves, blood vessels and organs. Brachytherapy, while more targeted than radiation, still is most effective only when used in conjunction with other treatments methods. Chemotherapy has side effects that are detrimental to quality of life. A new tissue ablation method, Non-thermal Irreversible Electroporation, has recently emerged as a promising method of minimally invasive surgery, for treatment of cancer, as well as other soft tissue lesions. I developed cryoelectroportion, a combination treatment using electroporation and cryosurgery, as a novel method to ablate malignant tissue.

Mechanism of Electroporation

Electroporation is the use of high voltage pulses delivered through electrodes to create an electrical field across cellular membranes. This field is capable of permeabilizing the membrane and exposes the cytoplasm to the extracellular space through hydrophilic, toroidal pores.

There are two kinds of electroporation. The first is reversible electroporation. It is characterized by temporary permeability: the cell membrane reseals and reversible electroporation has occurred. This is used for drug delivery and gene therapy [1]. Electric fields for reversible electroporation are within the following bounds:

3.6E4V/m < E < 6.37E4V/m

Irreversible electroporation is the second kind of electroporation. It is characterized by permanent permeability, which results in cell death. This is used for focal tissue ablation for cancerous tissue, as well as ablation of undesirable tissue such as vascular smooth muscle cells in restenosis as well as water and food bacterial sterilization. Electric fields for irreversible electroporation are above the following bounds:

E > 6.37E4V/m

Advantages of Electroporation

1) Electroporation is minimally invasive as compared to surgery

2) It only affects the cellular membrane, so molecular scaffolding is left undamaged (such as collagen and elastin) [2]

3) Nerves, blood vessels [3] and lactiferous ducts have been shown to also be unaffected by the fields. This is advantageous in comparison to thermal ablation modalities such as RF and HIFU because they do not have this cellular selective ablation capability.

Cryosurgery Background

Cryosurgery, on the other hand, is a thermal ablation technique which utilizes subzero temperatures to ablate malignant tissue. Applications include treating skin, liver, lung and prostate cancers. One advantage of cryosurgery is that because freezing occurs on the order of minutes, unlike electroporation, a physician has real time control over the procedure.

Cryosurgery Disadvantages

1) It is difficult to control temperature distribution during cryosurgical procedures because of the convective effect of blood vessels. 

2) Cells can survive freezing at temperatures above -40˚C. So cells on the outer rim on the frozen region can survive. Ultrasound, the typical imaging modality for cryosurgery, can only discriminate between frozen and unfrozen tissue. This is problematic because the region seen as frozen during imaging can contain surviving cells. Therefore, accuracy is compromised. Finding ways of overcoming this limitation is currently a subject of intensive investigation in cryosurgery research.

Electroporation Disadvantages

1) No imaging techniques exists that can show ablated tissue during electroporation procedures in real time

2) Procedure time scale is so rapid that is precludes real time control. Therefore, it requires careful pre-surgical treatment planning. Even so, accuracy is compromised.

3) Applied voltages can cause peripheral nerve stimulation which results in muscle contractions during a procedure.

If electroporation and cryosurgery were combined (termed cryoelectroporation), it is possible to eliminate  all the individual disadvantages of electroporation and cryosurgery when the two are combined.

Methods

The goal of this first order study was to model cryoelectroporation and examine the effect of change in temperature on electric fields and the subsequent implications for ablating tissue such as cancerous tumors. A coupled thermal and electrical model was used to determine temperature and potential distributions respectively.

Enthalpy Method

The enthalpy method was utilized to model the phase transformation occurring during freezing. The term for specific heat was modified to account for latent heat of fusion in order to model the phase transition [4],[5],[6]. In the above equation, λ is latent heat of fusion and D is a term that accounts for H, which represents the volume fraction of liquid in the media. H is the smoothed Heaviside function. This interpretation assumes a mushy zone in solidification: that phase transition occurs over a range of temperatures. This is actually a very good approximation for biological tissues, because more so than other materials, tissue freezes over a larger range of temperatures

Electrical Model

I then used the temperature distribution determined from the heat conduction equation as a dependent variable of the electrical conductivity to solve for the potential distribution associated with an electric pulse (essentially the Laplace equation). Electrical permittivity is a function of temperature. It has been experimentally determined at low frequency (as in typical electroporation parameters) [7].

Tissue Properties

Properties for physiological saline solution were used as a first order simulation for biological tissue in the electrical model, since electrical property data for tissues in the entire range of temperatures of interest is not available in the literature. I derived the electrical conductivity for saline at subzero temperatures analytically using composite theory. The equation for freezing point depression was used to calculate the volume of solution as a function of temperature. Data for electrical conductivity above 0˚C was curve fitted to achieve the following piecewise function: 

Model 1: Proof of Concept

I used a one dimensional Cartesian geometry to illustrate the most fundamental trends of cryoelectroporation, which operated as a proof of concept. I modeled a 6cm slab of tissue between two parallel plates with boundary conditions of 268.15K and physiological temperature. 268.15K was used because in very conservative estimates cell survival occurs at temperatures above 258.15K in cryosurgery, which means we will retain the selective cellular ablation of electroporation.

 

Investigated at:

1. Freezing , 90sec

2. Thawing, 90sec

3. Control

The voltage pulses were set to 100μs and 1Hz.

The resulting temperature distribution during freezing was as expected with a region of phase change (0.2cm) nonlinear behavior at 272.5K.

 Compared to one another, it is clear temperature and electric field are inversely proportional.

This inversely proporational relationship is because of the relationship between electrical conductivity and temperature. This means that a cryoprobe simultaneously delivering freezing temperatures and an electric field will create a frozen region with low conductivity that as a result acts like an insulator. 

Notice that the highest electric field occurs in the region of lowest temperature. Beyond the frozen region, in tissue at normal temperature, fields are substantially lower than those in the frozen/cooled regions, also as a result of this relationship. The electric field has a point of inversion at 0.2cm, which is the same as temperature plot. This is the approximate location of the edge of the frozen lesion.

Control Study

 

I completed the control study with the same electrical parameters with no cold temperatures applied. From the plot below, electric field in frozen/cooled regions is substantially higher than the electric field produced in the control study. But, at a distance from the frozen region, in the location of normal body temperatures, the control electric field is higher. This suggests that not only does freezing/cooling boost the electric field, but it also confines the electric field to the frozen/cooled region.

You can read about subsequent studies I completed on electroporation in my publications:
Cryosurgery with Pulsed Electric Fields
Temperature Modulation of Electric Fields in Biological Matter
Electric Field and Temperature Model of Non-Thermal Irreversible Electroporation in Heterogeneous Tissues


References

[1] Miklavcic 2000 

[2] Daniels 2009

[3] Onik 2010 
[4] Voller 1987
[5] Dantzig 1989
[6] Rubinsky 1981 
[7] Kaatze 1989 
[8] Arps 1953
[9] Hobbs 1975
[10] Mazzoleni 1986