During a radiofrequency ablation (RFA) procedure to destroy a cancerous liver tumor, an electrode catheter is inserted into the tumor and a 55.0 W AC source with frequency 765 kHz is used to generate radio frequency waves in the catheter. A typical electrode catheter is 1.00 cm in length and 8.00 mm in diameter. The deposition of energy into tumor cells by these radio waves is dependent on the specific absorption rate (SAR), measured in watts per kilogram, of the target tissue, given by 1 SAR = PEP m -IE12 where p is the resistivity of the tissue, typically, 2.220 m for liver tumors, Pm is its mass density, typically 1.06 g/ml, and E is the magnitude of the electric field in the catheter. (a) What is the intensity (in W/m2) of radio frequency electromagnetic waves on the surface of the catheter? (Approximate the cathether as a solid cylinder, for which radio waves emanate from both flat faces and the curved surface.) W/m² (b) What is the magnitude of the electric field (in kV/m) for these waves? kv/m (c) What is the SAR (in W/kg) when the device is operated at 55.0 W? W/kg
During a radiofrequency ablation (RFA) procedure to destroy a cancerous liver tumor, an electrode catheter is inserted into the tumor and a 55.0 W AC source with frequency 765 kHz is used to generate radio frequency waves in the catheter. A typical electrode catheter is 1.00 cm in length and 8.00 mm in diameter. The deposition of energy into tumor cells by these radio waves is dependent on the specific absorption rate (SAR), measured in watts per kilogram, of the target tissue, given by 1 SAR = PEP m -IE12 where p is the resistivity of the tissue, typically, 2.220 m for liver tumors, Pm is its mass density, typically 1.06 g/ml, and E is the magnitude of the electric field in the catheter. (a) What is the intensity (in W/m2) of radio frequency electromagnetic waves on the surface of the catheter? (Approximate the cathether as a solid cylinder, for which radio waves emanate from both flat faces and the curved surface.) W/m² (b) What is the magnitude of the electric field (in kV/m) for these waves? kv/m (c) What is the SAR (in W/kg) when the device is operated at 55.0 W? W/kg
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![During a radiofrequency ablation (RFA) procedure to destroy a cancerous liver tumor, an electrode catheter is inserted into the tumor and a 55.0 W AC source with frequency 765 kHz is used to generate radio frequency waves in the catheter. A typical electrode catheter is 1.00 cm in length and 8.00 mm in diameter. The deposition of energy into tumor cells by these radio waves is dependent on the specific absorption rate (SAR), measured in watts per kilogram, of the target tissue, given by
\[ \text{SAR} = \frac{1}{\rho_E \rho_m}|E|^2 \]
where \(\rho_E\) is the resistivity of the tissue, typically 2.22 \(\Omega \cdot \text{m}\) for liver tumors, \(\rho_m\) is its mass density, typically 1.06 \(\text{g/ml}\), and \(E\) is the magnitude of the electric field in the catheter.
(a) What is the intensity (in \(\text{W/m}^2\)) of radio frequency electromagnetic waves on the surface of the catheter? (Approximate the catheter as a solid cylinder, for which radio waves emanate from both flat faces and the curved surface.)
\[ \boxed{\phantom{XXXX}} \, \text{W/m}^2 \]
(b) What is the magnitude of the electric field (in \(\text{kV/m}\)) for these waves?
\[ \boxed{\phantom{XXXX}} \, \text{kV/m} \]
(c) What is the SAR (in \(\text{W/kg}\)) when the device is operated at 55.0 W?
\[ \boxed{\phantom{XXXX}} \, \text{W/kg} \]
(d) How does the wavelength of the RF waves compare to the size of the catheter? (Enter the ratio of the wavelength to the length of the catheter.)
\[ \frac{\lambda_{\text{RF}}}{L_{\text{catheter}}} = \boxed{\phantom{XXX}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f1b7c10-7ca4-413c-bb43-fe1a15020101%2F25c6b838-2e3a-43d1-a36b-bbbd578d100d%2F6sxo4d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:During a radiofrequency ablation (RFA) procedure to destroy a cancerous liver tumor, an electrode catheter is inserted into the tumor and a 55.0 W AC source with frequency 765 kHz is used to generate radio frequency waves in the catheter. A typical electrode catheter is 1.00 cm in length and 8.00 mm in diameter. The deposition of energy into tumor cells by these radio waves is dependent on the specific absorption rate (SAR), measured in watts per kilogram, of the target tissue, given by
\[ \text{SAR} = \frac{1}{\rho_E \rho_m}|E|^2 \]
where \(\rho_E\) is the resistivity of the tissue, typically 2.22 \(\Omega \cdot \text{m}\) for liver tumors, \(\rho_m\) is its mass density, typically 1.06 \(\text{g/ml}\), and \(E\) is the magnitude of the electric field in the catheter.
(a) What is the intensity (in \(\text{W/m}^2\)) of radio frequency electromagnetic waves on the surface of the catheter? (Approximate the catheter as a solid cylinder, for which radio waves emanate from both flat faces and the curved surface.)
\[ \boxed{\phantom{XXXX}} \, \text{W/m}^2 \]
(b) What is the magnitude of the electric field (in \(\text{kV/m}\)) for these waves?
\[ \boxed{\phantom{XXXX}} \, \text{kV/m} \]
(c) What is the SAR (in \(\text{W/kg}\)) when the device is operated at 55.0 W?
\[ \boxed{\phantom{XXXX}} \, \text{W/kg} \]
(d) How does the wavelength of the RF waves compare to the size of the catheter? (Enter the ratio of the wavelength to the length of the catheter.)
\[ \frac{\lambda_{\text{RF}}}{L_{\text{catheter}}} = \boxed{\phantom{XXX}} \]
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