Christopher W. Vick

Introduction

        Ultrasound is a fast, nondestructive, noninvasive, and relatively inexpensive imaging platform. Ultrasound has many uses in medical diagnosis. Such applications often consist of a skilled technician interpreting an ultrasound image, based on gray-level and texture. Unfortunately, such a process cannot be used to effectively evaluate tissue structure. The human visual system is not capable of discriminating many higher-order textures. This has spurned the development of computer texture analysis methods; these methods cannot be fully effective until we learn more about the intricacies of ultrasound propagation through tissue.

        It has long been known that the velocity and attenuation of ultrasound are characteristics of the medium they travel through. These parameters can be related to the physical properties of the material, such as density, elasticity, composition, and cell microstructure. In 1991, Self et al. (1), proposed the use of ultrasound for texture evaluation of plant tissues. Low frequency ultrasound has been used extensively to characterize the ripeness of fruits. Limited research has been conducted to measure the cell texture of cooked carrots using low frequency ultrasound. And unfortunately, the experiments conducted yielded ambiguous results. It is presumed that high frequency ultrasound carries complex microstructural information about a material; detailed examination of carrot cellular structure using high frequency ultrasound (>1MHz) has not been attempted. 

        The hypothesis of this research is that high frequency ultrasound (5MHz) can be used to characterize and identify the cellular structure of carrots. When properly accounted for, high frequency ultrasound should yield useful cellular texture information unavailable when low frequency ultrasound is used.

        This research focuses on the high frequency evaluation of carrot cell texture. We focus on measuring the frequency response curves of a variety of carrot samples, inducing texture changes through cooking. By statistically examining these functions, parameters for classifying the cell structure of the cooked carrots can be derived. Using these parameters, a program can be devised that can identify how long a carrot has been cooked.

        A number of long term goals will be addressed by this research. First, and foremost, this research will address whether plant texture characterization using high frequency ultrasound is realistic, or even possible. Furthermore, this research will examine the biological devices for the attenuation and propagation of high frequency ultrasound through the carrot cell tissue. Eventually, this could allow for more comprehensive computer texture analysis models. We will discuss the possibility of applying comparable imaging techniques toward human tissue characterization. This could in turn lend toward more accurate medical diagnosis, such as distinguishing healthy liver tissue from diseased liver tissue. Using noninvasive ultrasound for this process will spare a hospital patient the unnecessary pain of a biopsy, and the unnecessary fees associated with other imaging modalities, such as MRI or X-Ray. 

Background

        The use of ultrasound, mechanical waves with a frequency above 20KHz, is becoming increasingly widespread. The ultrasound technique utilizes a transducer which is capable of generating and receiving high frequency ultrasonic vibrations. In application, these very short wavelength sound waves are reflected off very small surfaces inside a material before they are collected. By analyzing these complex reflections, the inside of a material can be imaged. Ultrasound offers a fast, nondestructive, noninvasive, and relatively inexpensive imaging platform. These properties have spawned the application of ultrasound to a variety of materials.

        Ultrasound has long been used in medicine for diagnosis. A gray-value medical ultrasonic image can be made of a human liver section, for instance. A skilled ultrasound technician uses gray-level as well as texture information to interpret the image, such as identifying a lesion. The human visual system is very capable of discriminating different textures from each other, but is hardly perfect (2). The use of computer texture analysis is being thoroughly researched. An artificial neural network has been used to develop an adaptive texture feature extraction method; currently it only exhibits a noticeable importance in a limited number of dataset situations (2). Without a doubt, numerous improvements need to be made to this system. This system needs to more effectively account for imaging artifacts, frequency-dependent attenuation, backscatter, and other inherent imaging effects. Such improvements can likely be derived from a close examination of other ultrasound techniques.

        Ultrasound has been shown to be especially useful for the nondestructive testing of many other materials. The food industry has been using ultrasonic techniques for a number of years. It has been used for processes such as emulsification, cleaning and animal backfat thickness estimation (3). Ultrasound has been used to examine the structure of homogeneous materials, such as metals (4), and inhomogeneous materials , such as wood (5). Ultrasonics has been used to measure ripeness in bananas (1), melons (6) and avocados (7). The use of ultrasound for texture measurements of plant tissues has been proposed (8), but not thoroughly examined. This is the key aim of the proposed research.

        Let us consider the idea of ultrasonic microstructure characterization. This can be done using ultrasonic transmission measurements of wave speed and attenuation through a material. It has been shown that velocity and attenuation are characteristic of the physical properties of the material, such as density, composition, elasticity, and other cellular structure properties (8). Wave speed measurements are relatively insensitive to details of microstructure; attenuation yields a much better examination of microstructural detail(4). Unfortunately, separating attenuation effects due to diffraction, absorption, refraction, and scattering is difficult, if impossible. A lot of theoretical work is conducted in this respect.

        A study was conducted to access the early possibility of using ultrasound to assess the quality of fruits and vegetables (9). It was concluded that the high attenuation in plant samples prevented an effective use of high frequency ultrasound. A subsequent study suggested this high attenuation was due to scattering from plant intercellular air spaces (10). Low frequency (<100kHz) ultrasound has been shown to alleviate high attenuation problems (7), because scattering at long wavelengths is weakest. However, high wavelengths likely carry more information about the microstructure of a material (4).

        The texture of carrots has been under much study. A large number of biological studies have been conducted toward understanding the tissue factors that affect the eating texture of fresh and cooked vegetables (11). Ahmed et al. (12), noted that when a carrot is subjected to thermal processing, its texture undergoes a number of physical and chemical changes. These changes have been observed and measured in a number of different research papers. Recently, an attempt at the texture evaluation of carrots has been made using low frequency ultrasound. A study examined the changes in low frequency (37kHz) velocity and attenuation among cooked carrots (13). In the aforementioned study, transmission changes were correlated with textural changes measured using an electron microscope. The purpose of this study was to detect a difference between fresh and cooked carrots using low frequency ultrasound. Very little signal analysis was conducted in this study; the results are often vague, and overly speculative. In addition, there was a large range of error, and are many factors that this study didn't account for. Carrots are generally homogenous along each axis of symmetry. This allows a number of assumptions to be made about the carrot tissue; this, in effect, allows simplified theoretical considerations to be made about the propagation of sound waves through the cell structure. The above study didn't account for this, nor for frequency dependent attenuation.

        This research expands upon the experiment conducted by Nielsen and Martens (13), making a few careful changes to the methodology they used. Most importantly, higher frequency ultrasound was used (1MHz), as opposed to the 37kHz used by Nielsen and Martens. This substantially increases the attenuation effects, but also likely yields additional microstructure information previously unavailable. In our research, the focus is not the velocity and attenuation of the signal. The frequency analysis of the ultrasound signal is what is important here. With unique responses, carrots of varied cell texture can be differentiated. This research could likely also apply to other homogeneous vegetables (such as potatoes) also. Most importantly, the proposed research will contribute to a more comprehensive understanding of the ultrasonic imaging of cell structure. These signal analysis methods can likely be used to improve the performance of current texture analysis methods; this could allow for more accurate diagnosis and tissue characterization in humans.

Theory

        When digitizing signals, one needs to be careful to avoid introducing aliasing, artifacts, or other undesired features into the recorded function (14). The Whittaker-Shannon sampling theorem states that a sinusoidal function must be sampled at a rate greater than the Nyquist frequency to avoid aliasing. The Nyquist Frequency is defined as:

                e nyq = 1/ (2D x), where D x = sampling interval

        In this project, as will be explained later, a pair of 5MHz transducers will be used. A chirp function will be generated with the transmitting transducer, that scans from about 2 MHz to about 8 MHz. Thus we expect the highest output frequency to be about 8 MHz. So, based on the above equation:

                Given: e nyq = e max = 8 MHz
                Sampling interval = D x = 1/(2e nyq ) = 1/(2 (8 MHz) )
                Thus, D x = 1/(16 MHz cycles/sec)
                D x = 62.5 nanoseconds

        In order to avoid aliasing, the digitizer should be set above this interval. Thus, in this project, the digitizer was set to sample all f(x) at 50 ns.

        The Fourier Transform is an important tool in analyzing the signals in this project. In essence, performing a Fourier Transform on a function decomposes the function into all the separate frequencies that comprise it.

        A flexible version of the Discrete Fourier Transform will be used, called the Fast Fourier Transform (FFT). There is a pre-existing FFT function in IDL that will prove useful for this project.

                Given a function, f(x), the FFT of the function equals F(u). Where:

The result is an array with N elements. Element 0 contains the zero frequency component, which is equal to 1/(NT), where T is the sampling interval. Element 1 contains the 2/(NT) frequency component, etc. All the way up to element N/2, which contains the components from the Nyquist frequency, the highest frequency that can be sampled.

        When imaging a carrot sample, if we characterize the system as linear & shift invariant, it can be modeled as a simple convolution process:

                f_transducer(t) = the transducer function over time
                f_carrot(t) = the carrot function over time
                Sys(t) = the system function over time

        By acknowledging a convolution process:

                f_tr(t)*f_ca(t) = Sys(t)

        By taking the FT of both sides, we arrive at:

                FT[f_tr(t)*f_ca(t)] = FT[Sys(t)]

        By using the Transform of a Convolution property of Fourier Transforms (Gaskill, 1978, p.196), we arrive at:

                F_tr(u) F_ca(u) = Sys (u) (1)

        where,
                F_tr(u) = FT of f_tr(t)
                F_ca(u)= FT of f_ca(t)
                Sys(u) = FT of Sys(t)

        Overall, it would be useful to remove the response of the transducers, so that only the carrot response remained. This can be done by taking Equation (1) into log space:

                F_tr(u) F_ca(u) = Sys (u)
                Log [ F_tr(u) F_ca(u)] =Log [ Sys (u) ] using log mult. rule yields:
                Log[F_tr(u)] – Log[F_ca(u)] = Log [Sys(u)] solve for F_ca(u)
                Log[F_ca(u)] = Log[Sys(u)] + Log[F_tr(u)]
                So, F_ca(u) = 10^( Log[Sys(u)] + Log[F_tr(u)])

        This research will deal mainly with the response of the system as a whole, but it was the above technique that was used to allow the computer program to isolate the carrot frequency response.

Methods

Experimental Setup

       The experimental setup consisted of a clear vertical jar. For measurements, this jar is filled with filtered water. Mounted at opposite ends of the jar were a pair of flat plane 5MHz ultrasound transducers. The transmitting transducer was a Panametrics: 5.0/.25, 113542; the receiving transducer, Panametrics V326, 5.0/.375, 93925. Diagram #2 shows the rest of the laboratory setup. For imaging, a sample is secured between the transducers. For this research, the signal generator (Polynomial Waveform Synthesizer, Model 2020) was programmed to produce a chirp function, using the following function: For 5u SIN(INT(1.5M+1.3M/1u*t)) FOR 5 m 0. This creates a chirp function scan a frequency range of about 1MHz to 9 MHz, centered at the transducers peak sensitivity, 5MHz. This signal is first sent through a (EIN Model 240L RF) power amplifier, then through the transmitting transducer. Next, the signal propagates through the longitudinal axis of the sample in the jar setup, and is captured by the receiving transducer. It is then amplified by a receiving amplifier (RITEC Broadband Reciever BR-640) where the system gain (in dB) can be manually adjusted. Before getting stored to disk, the output signal is digitized to 9 bits using a Data 6500 Digitizer. For all the measurements taken below, the output signals were sampled for 256 points, in 50 ns intervals (as explained above). In addition, the receiver gain for each measurement was recorded, for use in mathematical calculations as stated earlier. 

        Carrot samples were prepared in a method similar to that used by Nielsen and Martens . (13) The carrots used were ordinary supermarket Dole Carrots, bought in 32oz. bags. After purchase, they were stored in a refrigerator. Before preparation, the carrots were cleaned, and sorted according to size. Carrots 19-38 mm in diameter, without noticeable breaks, cuts, or bruises, were used. The tops and bottoms of the carrots were cut off, and discarded. Using a Farberware Ultrapro Apple Corer (#81780), a 1.4cm diameter region of the carrot core was stamped out. This core was carefully cut crosswise, into individual small cylinder samples, 1.1cm in height. Thus the final sample dimensions were 1.1 cm in height, and 1.4cm in diameter (see Diagram #3.) Depending on which segment of the carrot a sample is cut from, the xylem core diameter can vary greatly. As necessary, the size of the xylem cores were measured and recorded. The samples were cut and placed in a plastic bag before cooking.

        For the cooking experiments, the carrot cylinders were boiled at 100 degrees Celsius in filtered water for an appropriate time of between 0 to 16 minutes, in 30 second intervals. This cooking serves to induce textural changes in the structure of the carrot. Immediately after the carrots were done cooking, they were cooled off in filtered water at room temperature. Shortly thereafter, the samples were imaged in the aforementioned ultrasound setup.

There were six main parts conducted for this research:

      Part I: Measuring the response of the transducers

       For the first part, it was important to measure the response curve of the transducers. This was done by filling the jar setup with water, and imaging in the absence of a carrot sample. The water offers no acoustic impediance, thus the ultrasound signal can propagate through the system, unaffected. When the output signal is collected, what results is effectively the response of the transducers. Another factor to consider was the variability of this response curve. In order to test this, the transducer response was measured twenty times, on three different occasions. In each of these trials, the transducer was aligned, the imaging was done, then the transducer was misaligned, and the process was repeated. It is known when the transducers are aligned when a maximum amplitude signal is shown on the digitizer. This means that the transducer plates are parallel, and lined up. 

       Part II: Testing variation among repeated same sample readings

       For the next part, it was desired to examine the amount of variation that has been shown to be inherent to repeatedly imaging the same sample numerous times. For this trial, 18 random segment carrot cylinder samples were prepared, and cooked for a 1 minute interval. These samples were then imaged a total of five times each.

      Part III: Testing variation among different segments of the same carrot

        Along the length of a carrot, the xylem core diameter changes significantly. At the bottom of a carrot, it is only a few millimeter in diameter, while near the top, the xylem core can be over a centimeter in diameter. The effect of the diameter of the xylem core on a carrot sample response curve was measured. To do this, 9 consecutive segment samples were cut from five different carrots from the same harvest. The xylem core diameter for these samples ranged from .1cm to .4 cm. For this part, all these samples were cooked for 1 minute.

      Part IV: Testing variation among different carrots of equal cooking time

        Next, the response curve variance among different carrots was measured. 16 same segments samples were cut from four different carrots of the same harvest. These samples were all cooked for a 1 minute interval, and then subsequently imaged.

      Part V: Imaging samples of various cooking times

       For this part, 64 random samples were cut from 8 different carrots of the same harvest. These samples were separated into two batches of 32 samples. For each batch, one sample was cooked for each of the thirty-two 30 second intervals from 30 seconds to 16 minutes. Using the above setup, all these samples were imaged. 

      Part VI: Unknown sample trial

       For the last section of the experiment, 10 random sample segments were cut from 5 random carrots of the same harvest. These samples were cooked by an assistant, for 'secret' lengths of time. These 10 carrots were labeled a-j. Two were cooked for either 1,2,3,4, or 5 minutes. Another two were cooked for either 6,7,8,9, or 10 minutes. Two more were cooked for 11,12,13,14,15 or 16 minutes. The next two were cooked for a random 30 second interval under 16 minutes. The last two were cooked for any randomly picked time under 16 minutes. All of the a-j samples were mixed up, with their actual cooking times sealed in envelopes. These samples were imaged, in the same process as explained above. The data was then stored for later analysis.

       For the most part, the data obtained was evaluated using my original IDL program, entitled C.U.A.P. The source code for this Carrot Ultrasound Analysis Program can be found in Appendix A. Additional analysis was done using Microsoft Excel.

Diagram #1 : graphical user interface of the CUAP.

      Part I: Transducer Response

        As an initial step of the research, the response of the transducers was characterized. This was done through the aforementioned process. Figure #2 shows the mean magnitude transducer response, averaged over 18 separate measurements. The standard deviation bars across the response curve convey the small variance across the measured response. The average variation was at about 6%.
                           

Figure #2: Mean Transducer Response. Bars show plus/minus one standard deviation.

      Part II: Same Sample Variation

        Next, variation from imaging the same sample repeatedly was measured. This was examined most thoroughly on a carrot cooked for one minute. Figure #3 shows the standard deviation of the mean magnitude system response. For this graph, sample readings were all normalized. This discards overall attenuation information, but still retains relative frequency dependent attenuation data. The average variation here is at 20%. This measurement readily agrees with the 21% replication variation reported by Cheng (1992) and Self et al. (1994). Notice that in the lower half of the frequency range, variation drops below 7%.

Figure #3:Standard Deviation of Normalized System Response with 1 minute cooked carrots.

      Part III: Segment Variation

       Unlike previous studies, the response curve along the length of a carrot was also examined. Figure #4 shows a three-dimensional plot of the system response of a carrot, as the xylem core diameter ranges from 0.2 to 0.4 cm. Particularly notice that the magnitude substantially drops.

Figure #4: Relative System Response along length of a carrot

        As can be seen above, even along the length of the carrot, a characteristically similar response of the carrot is retained. In the above case, the average variation among different carrot segments is 45%. On the other hand, once these functions are normalized, the average variation drops to below 15%.

      Part IV: Carrot Variation
   
        Next, a number of same segment samples were examined from different carrots. Figure #5 shows an example of the wide variation seen among carrots cooked for 2 minutes. Variation can be as high as 80%. Yet even after normalization, as shown, the , different carrots variation averages at 36%. The sources of this large amount of variation will be discussed later on.

Figure #5: Standard Deviation among same segment.

        Part V: Various Cooking Times

        Figure #6 shows a compilation of the response curves of 16 samples, cooked from 1 to 16 minutes, in 1 minute intervals. Again, it is not the exact magnitude that is what is important, but rather the relative comparisons of the response of the different carrot textures. The frequency response changes seen in the plot can be explained by structural changes that were invoked through cooking.   By normalizing this plot, we essentially arrive at a carrot texture look up table. This is shown in Figure #7. As can be seen, it is difficult to make sense of this plot by eye. But, as the hypothesis stated, through statistics, many of the curves can can be differentiated.

Figure #6: Relative System Response of samples cooked 1-16 min.

Figure #7: Normalized System Response Vs. Cooking Time

        Figure #8 shows a side view of this plot, where the shape of individual curves are more readily noticable.

Figure #8: Side View of Normalized LUT

        Looking at Figure #8, one can notice the unique curves of many of the carrot textures. Also evident, as exemplified by the upper right section, is the fact that a handful of the response curves have very similar corresponding sections. An important issue is whether the similar response curves are too similar in their entirety.

      The purpose of the last experiment, the imaging of unknown samples, was to test the robustness of the above LUT. If indeed different texture response curves are too similar, then using this table to identify an unknown sample would yield error prone, or ambiguous results.

   Part VI: Unknown Sample

   Using the 'Unknown Dataset' option from the carrot ultrasound analysis program, the cooking times of the 10 unknown carrots were predicted. Below is an overview of the analysis of 5 of the samples:

Figure #9: Unknown Sample Analysis

        Overall, the program correctly matched 4 of the 10 unknown sample. Among the samples that weren't correctly matched, there was a standard deviation of 1.8 minutes. The average variance of unknown samples from their LUT response was 28%.

        As shown in figure #2, there was a 6% average variation of the transducer response. I am uncertain as to the standard amount of variation that is expected from ultrasound transducers of this quality. When properly accounted for, it seems that variation would be a limited source of error when characterizing carrots.

        Ideally, when the same sample is imaged numerous times, the same response would be measured each time. As exemplified in figure #3, there is an average 20% variation between replications. All things being equal, looking at the transducer variation above, one would expect the variation here to be 6%. But in this case, we see an extra 14% variation. This may have been caused by different couplings of the samples between the transducers, transducer misalignment, or variation of pressure applied to the samples. During the measurement process, it is assumed that that carrot was in a constant state. Realistically, it is reasonable to suggest that slight changes could have occurred within the carrot. For instance, the sample imaged near the end of the trial was in the jar setup substantially longer than the sample imaged near the beginning. This gives the last sample more of an opportunity to absorb the water around it. What this means that the frequency response of a sample could vary to some degree with time. This research data was not analyzed in this respect, so this factor is not accounted for. Needless to say, the majority of the variation was likely due to problems with transducer alignment and coupling.

        As figure #4 shows, the frequency response of a sample varies along the length of the carrot. Magnitudes can vary by as much as 45% after only a few centimeters of distance. This is due the dense xylem that comprises the core of carrots. As this core increases in diameter, it attenuates more and more ultrasound. With large xylem diameters, a substantial portion of the input signal can be lost. This especially poses a problem when imaging a sample near the top of the carrot. As noted, when these responses are normalized, the average variation drops to 15%. As earlier, different transducer coupling is also likely to be a strong factor in this. This 15% value suggests that there is slightly less variation in imaging different segments than in repeatedly imaging the same sample. This may seem somewhat surprising at first, but can be accounted for. Namely, all the samples in this trial remained in the setup for the same length of time. This means that they all had the opportunity to absorb equal amounts of water, thus their response variation with respect to time is not a factor here. This realization implies that in the previous trial, variation with respect to time is on the order of 5%. Overall, results from this trial suggest that as xylem size increases, the response magnitude decreases equally across the total frequency response of the sample. It is this acessment that allows for the normalized response similarity among the different segments. Further testing needs to be conducted in order to evaluate whether this hypothesis holds true for xylem diameters larger than 0.4 cm.

        As Figure #5 accentuates, there is a substantial amount of variation among the response of different carrots. Even normalized, this variation averages at 36%. As explained above, problems with transducer coupling and alignment contribute to this number. Although there is a degree of biological commonality among carrots, no two carrots can be exactly the same. When imaging them, variations in cell biology among different carrots contribute to frequency response variation. This varied biology can be due to a number of factors. Perhaps the carrots were exposed to different pesticides. Maybe they were grown in different parts of the world, absorbed different minerals from the soil, or received different amounts of sunlight. Overall, many environmental factors could contribute to a carrot variation. In the course of this experiment, we attempted to limit these possible biological variations by choosing samples from similar sized carrots from the same harvest. As seen, this was still not completely effective in eliminating variation. Another source of variation difficult to control is the cooking. Non-uniform cooking of the samples can also lead to some degree of variation in the texture of the carrot, and thus the variation in the propagation characteristics of the sample.

        Figure #6 displays the relative changes in frequency magnitude for carrot samples cooked up to 16 minutes. For simplicity, only 1 minute cooking intervals are shown here; responses were actually measured in 30 second intervals. By examining how the carrot cell biology changes as a result of cooking, the observed response shifts can be explained. The compactness characterized with raw carrot tissue allows the passage of very little signal at all. In the first 3 minutes of cooking, there is denaturing of the cell membranes and changes in the turgor pressure of the sample. This causes the amount of attenuation to decrease substantially. After about 3 minutes, studies have noted that heat induces the cells into irregular shapes, and the development of intercellular cavities between cells. Because the wavelength of the high frequency ultrasound is so small, these small spaces have a higher propensity to scatter it. This increases the observed attenuation. With additional cooking, these spaces grow in number and size. Eventually, there is a breakdown of the cell membranes. This allows the cytoplasm to flow freely into the air cavities. In addition, outside water is increasingly being absorbed into the carrot sample. These contribute toward making the carrot more uniformly homogenous, thus decreasing the overall attenuation. This point could correspond to the peak seen in the figure at about 12 minutes. With prolonged cooking, large cracks develop in the carrot cell structure. These can highly serve as scatterers; this could account for the degradation of signal seen near the 14 minute cooking mark. The further destruction of the cell structure, shown at 16 minutes cooking interval, is characterized by a substantial increase in the amount of signal passed. A more thorough correlation between frequency response and biology can be established by examining the cellular cross-sections of each sample at each cooking time. Due to time constraints, this was not attempted.

        For the last part, ten unknown samples were used to do preliminary tests on the response curve look up table shown in Figure #7. Of these 10 samples, four were correctly identified. In these cases, the error was on the amount of variation was on the same order as the previous tests. The results shows that this process has the potential of making positive matches, but a more in depth investigation needs to be conducted.

        A different response matching routine could likely yield better results. The program efficiency might benefit from applying a low pass filter to the data and data LUT before analysis. Another analysis approach would to choose one unique valued common point (or series of points) from all the normalized LUT cooking times, and associate that parameter with carrot’s cooking time. This would be based on the hypothesis that there are particular frequencies that all the samples attenuate to a unique degree.

        Overall, initial results prove promising, but not completely perfect. As shown above, there are many different sources of variation in imaging a carrot sample. When creating the LUT, there is likely on the order of 20-30% error introduced to the measurements. In addition, when an unknown sample is measured, another 20-30% error could be introduced here. The compilation of all these errors has the potential of causing similarities among different response curves, and thus a mismatch. It would be interesting to combine this frequency response analysis approach with previous studies about velocity and attenuation. This would yield three variable with which to identify a sample. This would likely yield a much more accurate and robust texture identification model.

        As shown, there is the potential for a high degree of variation when imaging a carrot sample. Sources of frequency response error include: variation in the transducer response, variation in same sample readings, variation along the length of a sample, and variation among the biology of different carrots. All these factors ass add to identification inaccuracy. By simply relying on a closest fit match, my program currently can only predict cooking times in intervals that were mentioned. To predict a time outside of these intervals would be highly speculative, and error prone. In addition, although many of the cooking response curves are unique, some of them are very similar. This adds increased uncertainty in correctly identifying a carrot’s texture. At present, only a few unknown samples have been examined. The program needs to be further tested to evaluate its full potential and efficiency.

        In this research, it has been shown that changes in the carrot can be associated with corresponding frequency response changes. To a limited degree, it has been shown that high frequency ultrasound can be used to identify the cell texture of some carrots. Combining frequency information with velocity and attenuation information would likely provide a firmer foundation for identification. With further study and analysis, a similar procedure might prove useful for studying other tissues.

Table of Contents