**3. Quality of diagnostic testing procedure**

It should be understood that testing the presence of breast tumor (just like any other tumor) is a random experiment with probabilities associated with the outcomes. Therefore, the quality of diagnostic tests can be measured using the probabilities associated with them. A test can be positive (detect tumor) when the tumor is actually present (true positive), and a test can also be positive (detect tumor) when there is no tumor at all (false positive). Likewise, a test can be negative (does not detect tumor) when the tumor is not present (true negative), and a test can also be negative (does not detect tumor) when the tumor is actually present (false negative). Out of these four different probabilities, the two which are normally used to qualitatively access the diagnostic procedure accuracy are *sensitivity* which is the true-positive rate probability and *specificity* which is the true-negative rate probability. If T<sup>+</sup> indicates the test is positive, T<sup>−</sup> indicates the test is negative, C+ indicates existence of cancer, and C<sup>−</sup> indicates the absence of cancer, then the conditional probabilities stated above are shown in **Table 1**.

Sensitivity, specificity, and other probabilities which are used in the test's qualitative measure can be easily calculated using Bayes' theorem. If "a," "c," "b," and "d" indicate the test positive and cancer-carrying persons, test positive and cancer-not-carrying persons, test negative and cancer-carrying persons, and test negative and cancer-not-carrying persons, respectively, then using **Table 2**, the probabilities in **Table 1** and other percentages can be calculated in **Table 3** at any confidence interval (CI).

The statistics of the cancer-detecting modalities in **Table 4** suggests that despite their recognized ability to detect tumors they still have their lackings. False-positive rate and falsenegative rate are not negligible. False-positive rates lead to a number of needless surplus investigations which could produce ionization. In the context of false-negative rate, if a fraction of the tumors are not detected at an early stage, then this could lead to malignancy and


ultimately to metastasis. An important reason for the limitations using the techniques is that the contrast between the tumor and the surrounding tissue sometimes can be as low as a few

**Table 3.** Calculation methods of test statistics as quality metrics of diagnostic tests for 95% confidence intervals (CI).

These and other relevant issues motivated the researchers to seek for an alternative technology which could provide better statistics and also not be harmful at the same time. This alternative technology and methodology is the use of ultra-wide band (UWB) emission and

percent and therefore it adds to the error of diagnostic procedure.

**Cancer tumor Test Present Absent Total** Positive a c a + c Negative b d b + d **Total** a + b c + d a + b + c + d

**Test statistics Computation method Definition/interpretation**

1. Sensitivity a/(a + b) It is the true-positive rate. This shows the probability that a

2. False-negative rate 1⁻Sensitivity = b/(a + b) This shows the probability of a negative test result given that

3. Specificity d/(c + d) It is the true-negative rate. This shows the probability that a

4. False-positive rate 1⁻Specificity = c/(c + d) This shows the probability of a positive test result given that

7. Cancer prevalence (a + b)/(a + b + c + d) This shows total probability of the presence of cancer tumor 8. Cancer absence (c + d)/(a + b + c + d) This shows total probability of the absence of cancer tumor

11. Accuracy (a + d)/(a + b + c + d) This shows the probability that he patient will be correctly classified Authors in [11] surveyed these test statistics of different breast cancer screening tests, and their results are tabulated in

the cancer tumor is present

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the disease is not present

Sensitivity/(1⁻specificity) It is the ratio of the true-positive rate to the false-positive rate.

1⁻Sensitivity/(specificity) It is the ratio of the false-negative rate to the true-negative rate

a/(a + c) This shows the probability that the cancer tumor is present given the test is positive

d/(b + d) This shows the probability that the cancer tumor is absent given the test is negative

test result will be positive when the cancer tumor is present

test result will be negative when the cancer tumor is absent

**Table 2.** Cross tabulation table of conditional probabilities.

**S. no**

5. Positive likelihood ratio

6. Negative likelihood ratio

9. Positive predictive value

10. Negative predictive value

**Table 4**.

imaging system.

**Table 1.** Conditional probabilities associated with cancer diagnostic tests.


**Table 2.** Cross tabulation table of conditional probabilities.

used to see if the breast lump is filled with cyst or if it is solid. Ultrasound can also be used to characterize the type of tumor. They are considered a good extension of physical palpations which use touching the breasts to detect the presence of any tumors. But they are limited to penetration because of lower frequency as compared to MRI and x-ray mammograms.

It should be understood that testing the presence of breast tumor (just like any other tumor) is a random experiment with probabilities associated with the outcomes. Therefore, the quality of diagnostic tests can be measured using the probabilities associated with them. A test can be positive (detect tumor) when the tumor is actually present (true positive), and a test can also be positive (detect tumor) when there is no tumor at all (false positive). Likewise, a test can be negative (does not detect tumor) when the tumor is not present (true negative), and a test can also be negative (does not detect tumor) when the tumor is actually present (false negative). Out of these four different probabilities, the two which are normally used to qualitatively access the diagnostic procedure accuracy are *sensitivity* which is the true-positive rate probability and *specificity* which is the true-negative rate probability. If T<sup>+</sup>

indicates the test is negative, C+

Sensitivity, specificity, and other probabilities which are used in the test's qualitative measure can be easily calculated using Bayes' theorem. If "a," "c," "b," and "d" indicate the test positive and cancer-carrying persons, test positive and cancer-not-carrying persons, test negative and cancer-carrying persons, and test negative and cancer-not-carrying persons, respectively, then using **Table 2**, the probabilities in **Table 1** and other percentages can be calculated in

The statistics of the cancer-detecting modalities in **Table 4** suggests that despite their recognized ability to detect tumors they still have their lackings. False-positive rate and falsenegative rate are not negligible. False-positive rates lead to a number of needless surplus investigations which could produce ionization. In the context of false-negative rate, if a fraction of the tumors are not detected at an early stage, then this could lead to malignancy and

> /C+ )

> /C<sup>−</sup> )

> /C+ )

> /C<sup>−</sup> )

**Probability name Conditional probability**

True positive P(T+

False positive P(T+

False negative P(T<sup>−</sup>

True negative P(T<sup>−</sup>

**Table 1.** Conditional probabilities associated with cancer diagnostic tests.

indicates the absence of cancer, then the conditional probabilities stated above are

indicates existence of cancer,

Ultrasound waves have frequencies above about 20 kHz [9, 10].

**3. Quality of diagnostic testing procedure**

indicates the test is positive, T<sup>−</sup>

4 UWB Technology and its Applications

**Table 3** at any confidence interval (CI).

and C<sup>−</sup>

shown in **Table 1**.


Authors in [11] surveyed these test statistics of different breast cancer screening tests, and their results are tabulated in **Table 4**.

**Table 3.** Calculation methods of test statistics as quality metrics of diagnostic tests for 95% confidence intervals (CI).

ultimately to metastasis. An important reason for the limitations using the techniques is that the contrast between the tumor and the surrounding tissue sometimes can be as low as a few percent and therefore it adds to the error of diagnostic procedure.

These and other relevant issues motivated the researchers to seek for an alternative technology which could provide better statistics and also not be harmful at the same time. This alternative technology and methodology is the use of ultra-wide band (UWB) emission and imaging system.


that the frequency for the UWB technique is from 3.1 to 10.6 GHz in America. However, in Europe, the frequencies include two parts: from 3.4 to 4.8 GHz and from 6 to 8.5 GHz. Applications of UWB radar in health and medicine include human body monitoring, remote sensing, and imaging. Unlikely with x-ray imaging, UWB radar uses non-ionizing electromagnetic waves which have been proved to be harmless to the human body. Additionally, the UWB radar has a very low-average power level, power efficiency, and robustness against noise. Thus, UWB is a cost-effective way of real-time human body imaging. Categorically,

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**Penetrating through obstacles.** UWB uses RF pulses with high gain. Therefore, UWB can penetrate through walls. This makes UWB practicable for wide area presentations where obstacles are sure to be met. This uniqueness of UWB makes it feasible to image organs of the human body.

**High precision ranging at the centimeter level.** UWB provides an effectively precise ranging to the centimeter level because of highly short-pulse characteristics. The short UWB pulse has a very strong temporal and space-resolving capability, which is appropriate for the localiza-

**Low electromagnetic radiation.** UWB also features low electromagnetic radiation because of low radiation power of the emitted pulse. According to the standards, these are less than −41.3 dBm in indoor communications. Again, the low-powered radiation effects the environment very less, which is ideal in medical diagnostic applications involving human body

**Low processing energy consumed.** As UWB utilizes very short-duration pulses, this permits the use of long-life battery-operated devices. These features are quite analogous with the wireless sensor network (WSN) nodes which essentially have to be operable under strict

UWB encompasses numerous utmost sought practical features for any electrical instrumentation used in medical applications. These features include noninvasiveness, low power, noncontact remote operation, biocompatibility, biological friendliness, environmental friendliness, detection, and localization. But in terms of tissue imaging, their physiological understandability by the users, high sensitivity (true-positive rate), and high specificity (truenegative rate), UWB requires more research. In this respect, the way human tissues behave with UWB waves emitted on them, i.e., their channel impulse response, is a very important aspect in the research of UWB applications in health monitoring and diagnostic systems.

The objective of microwave tomography is to use the inverse scattering method in finding the dielectric properties of the tissue under study. This gives a dielectric contrast of it. It produces

In a microwave tomography breast cancer investigation system, the breast is lowered into a cylinder-shaped antenna system which covers the breast completely. Microwave measurements are then made with all possible combination of antennas, acting as both transmitter and receiver, respectively. Since the microwaves are spread, scattered, and reflected when they

a chart of permittivity and conductivity through inversion scattering.

some other features of UWB are enumerated as follows.

where organs are very close to each other.

power control and high power efficiency.

**5.1. UWB microwave tomography**

tion and detection in the medical diagnostic applications of tumors.

**Table 4.** Contrast among different breast cancer detection modalities [11].
