Permittivity, Conductivity, and Loss Tangent: The Dielectric Trio

Why Some Tissues Are "Visible" to Microwaves

Microwave imaging works because different tissues interact with electromagnetic waves differently. This difference is described by three related properties: permittivity, conductivity, and loss tangent. Together, they form the "dielectric signature" of a tissue.

1. Permittivity (ε) – The Energy Storer

Permittivity measures how well a material stores electrical energy when exposed to an electric field.

ε=εrε0​

Where:

• ε₀ = permittivity of free space (8.85 × 10⁻¹² F/m)

• εᵣ = relative permittivity (compared to vacuum)

High permittivity = material stores more electrical energy. Water has very high permittivity (εᵣ ≈ 80). Most biological tissues have εᵣ between 40 and 70.

For our experiment:

Tissue	Relative Permittivity (εᵣ at 2.5 GHz)	Why
Air	1	Reference
Healthy lung tissue	≈ 45–50	Moderate water content (~70%)
Tumor tissue	≈ 55–60	Higher water content (~85%)

This difference (Δεᵣ ≈ 10) is what makes tumors detectable. Higher permittivity means microwaves slow down more and interact more strongly with the tissue.

2. Conductivity (σ) – The Energy Conductor

Conductivity measures how well a material allows electric current to flow.

σ = J/E​

Where J is current density and E is electric field strength.

High conductivity = material conducts electricity well. Saline water has high conductivity. Tumors have slightly higher conductivity than healthy tissue due to increased ion content.

For our experiment:

Tissue	Conductivity (σ at 2.5 GHz)	Effect
Healthy lung	≈ 1.5 S/m	Moderate attenuation
Tumor	≈ 2.5 S/m	Higher attenuation (~5 dB drop)

Higher conductivity means more signal loss. When we measured S21 for healthy vs. tumor phantom, we saw approximately 4.9 dB of additional attenuation—that's our detection signal.

3. Loss Tangent (tan δ) – The Energy Waster

Loss tangent is the ratio of energy lost (conductivity) to energy stored (permittivity):

tan⁡δ = σ/ωε​

Where ω = 2πf is the angular frequency.

High loss tangent = material converts more electromagnetic energy into heat. Tumors have slightly higher loss tangent than healthy tissue.

Why Loss Tangent Matters

Even if two tissues have similar permittivity, they might have different loss tangents. This gives us another way to distinguish them. Loss tangent is also frequency-dependent—which is why scanning across 2–3 GHz gives us more information than a single frequency.

The Complete Dielectric Picture

Here's how all three properties compare for our phantoms (measured at 2.5 GHz):

Property	Air	Healthy Phantom	Tumor Phantom
Relative Permittivity (εᵣ)	1	≈ 48	≈ 58
Conductivity (σ in S/m)	0	≈ 1.6	≈ 2.4
Loss Tangent (tan δ)	0	≈ 0.22	≈ 0.28

The tumor has:

• 12% higher permittivity (stores more energy)

• 50% higher conductivity (attenuates signal more)

• 27% higher loss tangent (wastes more energy)

All three differences contribute to the detectable ~4.9 dB S21 drop we measured.

How We Use These Properties

We don't measure ε, σ, or tan δ directly. Instead, we measure S21 (transmission). But S21 is determined by these fundamental properties. By extracting frequency-domain and time-domain features, our machine learning model learns to recognize the patterns created by these dielectric contrasts.

The Clinical Relevance

The reason tumors have different dielectric properties is biological:

• Tumors have more water (angiogenesis creates new blood vessels)

• Tumors have higher ion concentration (altered metabolism)

• Tumors have different cell density (more cells packed together)

These biological differences create the electromagnetic differences we detect. That's why microwave imaging works—it's not measuring the tumor directly, but measuring the physiological changes caused by the tumor.

What's Next?

Now that we understand how microwaves interact with tissue, let's look at the other side of THORACIS AI: how we analyze lung sounds using YAMNet.