Our proposed device relies on the principles of electrochemical impedance spectroscopy. In EIS, the impedance of a material is measured in response to a range of suitable frequencies of voltage or current. The most common EIS technique involves what is called a ‘frequency sweep’, which is accomplished by stimulating across a wide range of frequencies with a specific sinusoidal voltage or current at an interface and recording the corresponding frequency and amplitude of the response voltage/current signal at each input frequency value (Moqadam et al 2015). This relatively new technique has been used successfully to measure a range of biological parameters including tissue compression, tissue oxygen saturation.

Complex impedance in biological tissues is due primarily to ion concentrations. The charge separation across the cell membrane causes it to act as a capacitor. Capacitors have infinite impedance at low frequencies, which means that, at low frequencies (~30 Hz), current travels primarily through the extracellular fluid (Moqadam et al 2015). The diagram to the left depicts the most widely used (and simplistic) circuit model for the impedance of biological tissues. The values of the circuit components can be determined computationally from frequency spectra. The pathophysiologic changes associated with compartment syndrome can be directly correlated with the values R_ext and C from the circuit below. More specifically, patients with compartment syndrome will have an increased R_ext at low frequencies due to accumulation of fluid in the compartment and lack of sufficient oxygen perfusion after exercise. The post exercise capacitance value to increase due to compression, because the value of capacitance is proportional to the area of the cell membranes and inversely proportional to the distance between them. Due to the incredible sensitivity of impedance spectra to tissue structure, we anticipate that other features of compartment syndrome such as thickening of the fascia (collagenous wall surrounding muscle compartments) and lack of perfusion in muscle tissue may produce additional features on the impedance spectra of patients with compartment syndrome that would allow this technique to better distinguish between patients with and without the condition. It will be impossible, however, to identify such features without access to real CECS patients.

A diagnostic test for CECS requires a reading of pressure in all four muscle compartments of the lower leg before any surgery can be performed. While impedance spectroscopy will be able to identify differences across all compartments combined, a higher level of specificity is required for the final device to isolate the muscle compartments in each measurement. Therefore, our group proposes the use of electrical impedance tomography (EIT) to form a 2-D impedance image of the lower leg in the axial plane. An example of an EIT setup and output are given in Figure 3.

The fundamental principle of impedance tomography is that a known electrical current source is placed on the surface of the skin and that the current from this source flows non-linearly through the tissue (which is considered to be an inhomogeneous volume conductor) into a current sink at a different position. All of the current is contained within the bounded tissue volume and there are no other sources, making the equation for the potential field as follows due to the conservation of charge (Malmivuo and Plonsey 1995):

(2) ∇⋅(σ∇Φ) = 0

where σ is the tissue conductivity and Φ is the electrical potential. Typically, the current input and voltage sensing leads are confined to a set of equidistant electrode leads. While current is applied at a single pair of leads on the surface of the conductor, the voltage is measured separately at the rest of the lead pairs on the surface of the volume conductor. Then, the position of the current source is changed and the voltage measurements are repeated. The greater the number of electrodes, the higher the resolution of the acquired image. For the application of EIT to CECS diagnosis, our group elected to use a set of 16 electrodes to maximize resolution while also keeping in mind size limitations due to the circumference of the lower leg. We have also chosen to use the adjacent measurement method, which entails injecting current between two adjacent leads, then measuring the voltage between pairs of other adjacent leads along the electrode ring. This leads to a total of 16 x 13 = 204 voltage measurements, as shown in Figure 4.

After the collection of the voltage readings, the next step is to export the data for use in an image reconstruction algorithm. Our group elected to use EIDORS: Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software, an open source program under a general public license that is available for use in MATLAB (Adler and Lionheart 2005). This program is capable of supporting various electrode surface placements and data collection algorithms. It is also able to output the impedance of select regions of the image over time (i.e. muscle compartments), which will be critical for CECS diagnosis. An example of an image reconstruction in EIDORS is given in Figure 5, from one of the program’s demo modules. Furthermore, MATLAB allows for programs to be packaged and used in an executable format without the actual installation of MATLAB, as well as for the customization of a user interface.

The final step is to correlate the 2-D electrical impedance tomography images to whether someone has compartment syndrome. We propose this could be accomplished with a neural network, where the tomographic images from a patient would be the inputs and the diagnosis of whether that person has CECS would be the output. To make such a machine learning algorithm, a training set must first be supplied. This data would have the 2-D electrical impedance tomography images as well as corresponding labels of whether they have CECS as inputs, and the neural network would trained through the data a certain amount of epochs. To avoid over-fitting, a discrete set for the validation data will be used; Over-fitting is the point where the neural network makes correlations that are cannot be generalized, and this is displayed in Figure 5 (More details on over-fitting and model training).

For the construction of the deep learning model, Python integrated with Keras and Tensorflow will be used. A pseudocode of our model is shown in Figure 6, and a convolutional networks is used for our model since it's optimal for image processing. Also, to achieve the highest efficacy, we propose to take 2-D electrical impedance tomographic images both before and after exercise for most accurate results. Measuring changes in impedance will account for patients' baseline impedance measurements when calculating the change in impedance due to exercise. Finally, it should be noted that acquiring a large, diverse sample size would be needed for proper training (n>50). Having too small of a sample size will not allow for best correlation, and baseline impedance readings can differ depending on the patients' physiologies. Having the most diverse group will ensure that the accuracy measurements from the training data best represents the accuracy of the model in a real-world setting. Enlarged version of Figure 6 is shown below.