Comparison of both PET and CT raw and reconstructed file sizes
\r\n\tIn the book the theory and practice of microwave heating are discussed. The intended scope covers the results of recent research related to the generation, transmission and reception of microwave energy, its application in the field of organic and inorganic chemistry, physics of plasma processes, industrial microwave drying and sintering, as well as in medicine for therapeutic effects on internal organs and tissues of the human body and microbiology. Both theoretical and experimental studies are anticipated.
\r\n\r\n\tThe book aims to be of interest not only for specialists in the field of theory and practice of microwave heating but also for readers of non-specialists in the field of microwave technology and those who want to study in general terms the problem of interaction of the electromagnetic field with objects of living and nonliving nature.
",isbn:"978-1-83968-227-8",printIsbn:"978-1-83968-226-1",pdfIsbn:"978-1-83968-228-5",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"8f6a41e4f5ce0e9c48628516d7c92050",bookSignature:"Prof. Gennadiy Churyumov",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10089.jpg",keywords:"Electromagnetic Wave, Microwave Energy Application, Electromagnetic Energy Generation, Intelligent Microwave Heating, Microwave Organic Chemistry, Microwave Reactor, Microwave Discharge, Microwave Plasma, Microwave Drying System, Tissue Microwave Heating, Measurement Automation, Industrial Microwave Process",numberOfDownloads:224,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"July 3rd 2020",dateEndSecondStepPublish:"July 24th 2020",dateEndThirdStepPublish:"September 22nd 2020",dateEndFourthStepPublish:"December 11th 2020",dateEndFifthStepPublish:"February 9th 2021",remainingDaysToSecondStep:"7 months",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:"Prof. Gennadiy I. Churyumov is a professor at two universities: Kharkiv National University of Radio Electronics, and Harbin Institute of Technology and a senior IEEE member.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"216155",title:"Prof.",name:"Gennadiy",middleName:null,surname:"Churyumov",slug:"gennadiy-churyumov",fullName:"Gennadiy Churyumov",profilePictureURL:"https://mts.intechopen.com/storage/users/216155/images/system/216155.jfif",biography:"Gennadiy I. Churyumov (M’96–SM’00) received the Dipl.-Ing. degree in Electronics Engineering and his Ph.D. degree from the Kharkiv Institute of Radio Electronics, Kharkiv, Ukraine, in 1974 and 1981, respectively, as well as the D.Sc. degree from the Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine, in 1997. \n\nHe is a professor at two universities: Kharkiv National University of Radio Electronics, and Harbin Institute of Technology. \n\nHe is currently the Head of a Microwave & Optoelectronics Lab at the Department of Electronics Engineering at the Kharkiv National University of Radio Electronics. \n\nHis general research interests lie in the area of 2-D and 3-D computer modeling of electron-wave processes in vacuum tubes (magnetrons and TWTs), simulation techniques of electromagnetic problems and nonlinear phenomena, as well as high-power microwaves, including electromagnetic compatibility and survivability. \n\nHis current activity concentrates on the practical aspects of the application of microwave technologies.",institutionString:"Kharkiv National University of Radio Electronics (NURE)",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"0",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"24",title:"Technology",slug:"technology"}],chapters:[{id:"74623",title:"Influence of the Microwaves on the Sol-Gel Syntheses and on the Properties of the Resulting Oxide Nanostructures",slug:"influence-of-the-microwaves-on-the-sol-gel-syntheses-and-on-the-properties-of-the-resulting-oxide-na",totalDownloads:94,totalCrossrefCites:0,authors:[null]},{id:"75284",title:"Microwave-Assisted Extraction of Bioactive Compounds (Review)",slug:"microwave-assisted-extraction-of-bioactive-compounds-review",totalDownloads:12,totalCrossrefCites:0,authors:[null]},{id:"75087",title:"Experimental Investigation on the Effect of Microwave Heating on Rock Cracking and Their Mechanical Properties",slug:"experimental-investigation-on-the-effect-of-microwave-heating-on-rock-cracking-and-their-mechanical-",totalDownloads:28,totalCrossrefCites:0,authors:[null]},{id:"74338",title:"Microwave Synthesized Functional Dyes",slug:"microwave-synthesized-functional-dyes",totalDownloads:21,totalCrossrefCites:0,authors:[null]},{id:"74744",title:"Doping of Semiconductors at Nanoscale with Microwave Heating (Overview)",slug:"doping-of-semiconductors-at-nanoscale-with-microwave-heating-overview",totalDownloads:45,totalCrossrefCites:0,authors:[null]},{id:"74664",title:"Microwave-Assisted Solid Extraction from Natural Matrices",slug:"microwave-assisted-solid-extraction-from-natural-matrices",totalDownloads:25,totalCrossrefCites:0,authors:[null]}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"252211",firstName:"Sara",lastName:"Debeuc",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/252211/images/7239_n.png",email:"sara.d@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"45883",title:"Positron Emission Tomography-Computed Tomography Data Acquisition and Image Management",doi:"10.5772/57119",slug:"positron-emission-tomography-computed-tomography-data-acquisition-and-image-management",body:'Combined and optimized Positron Emission Tomography and Computed Tomography (PET-CT) exams are among the more complex of the radiographic modalities utilized in both body oncology and neurology settings. A distinct and targeted workflow is essential to successful data acquisition, processing, and related image management and reporting [1, 2]. This chapter will review the primary considerations involved in acquisition, processing, and archiving of PET-CT raw data and image data in a clinical PET-CT environment primarily centered on oncology and neurology.
The method utilized for the creation of PET images is steeped in proprietary acquisition techniques available from a very limited number of PET-CT scanner manufacturers. Regardless of the manufacturer, successful PET-CT acquisition depends on a consistent quality assurance and quality control program as well as an attentive technologist staff and supportive physicist. Routine and careful quality control at daily intervals is at the center of any high performing PET-CT department. The pinnacle of PET quality control is the acquisition and evaluation of PET sinograms that comprise the raw data. PET-CT raw data consists of gigabyte sinogram data sets that are used to generate image sets consisting of transverse slices. Each transverse slice maps to a sine wave frequency. These frequencies on the sinogram can be practically visualized as displacements or rows on the x axis and an angle on the y-axis which represent a projection through the object being imaged. At the smallest level, each pixel in the sinogram corresponds to specific line-of-response (LOR) based on the byproducts of a positron annihilation event detected in the scanner PET crystals. The resulting pixel rendering is considered image data. Additional or revised reconstructions of different slice thickness or overlap can only be rendered from raw data. Image data slice thickness cannot be changed once rendered. Figure 1 illustrates a sinogram rendered from daily quality control procedures.
Normal PET sinogram
The PET sinogram will reveal excessive and non-uniform fluctuations occurring in the gantry crystal detector architecture. Any significant change in the detector crystals will be manifest as a “stripe” of non-uniformity. In most cases, this stripe indicates a detector block failure. The presence of a failed detector block will require a repeat of the quality control to attempt to verify scanner malfunction. Block failure is a serious malfunction that in most cases requires the intervention of a PET service engineer. The block will either need to have the corresponding electronics tuned or the block will require replacement in order to continue with scanning. Figure 2 depicts a PET sinogram with a failed block artifact.
PET sinogram with failed block (“stripes” with no activity)
PET scintillation crystals are especially susceptible to failure due to environmental conditions such as dramatic alterations in ambient temperature, humidity, or cooling infrastructure. As a result, the technologist should intermittently but frequently review a gantry interface that provides a continuous report of gantry status and conditions. In particular, the technologist should be mindful of alterations in gantry temperature or dew point as well as substantial changes in the voltage of the detector electronics. Maintaining vigilance in monitoring gantry conditions can be an important part of early troubleshooting to minimize delays and eventual downtime. Figure 3 demonstrates a typical positron emission tomography acquisition interface.
PET acquisition interface. In addition to critical benchmarks such as gantry temperature and dew point, the technologist may also view PET prompt information such as random, true, and single events.
Once an appropriate sinogram data set has been acquired and confirmed as meeting the manufacturer and site-specific quality control requirements, reconstruction of slices from the data can be commenced. Common and clinically useful reconstructions include filtered back projection corrected and uncorrected images as well as iterative reconstructions. With iterative reconstructions, manufacturers are also bringing to bear time of flight capabilities made possible as a result of the very latest and most progressive reconstruction algorithms. Regardless of the vendor or reconstruction methodology employed, any actions necessary to correct for random events, scatter, decay, normalization, and dead time will be applied.
Two dimensional (2D) versus three dimensional (3D)acquisitions continue to play a role in image reconstruction management with 3D gaining primacy and near routine usage for all PET reconstructions [3]. In the earlier days of PET, 2D imaging was the most desirable and feasible means of imaging. This was true because, too many events would be detected within the PET crystal array with excessive dead time and image degradation in adjacent PET detector rings. This was overcome by placing septa comprised of tungsten or lead in between the detector rings. Along with these septa, the scanner electronics were configured to only detect coincidence events from within a limited plane to exclude non-collinear events. This also reduced the sensitivity of coincidence detection and corresponding image resolution. With improvements in crystal technology and detector electronics, it became possible to remove the septa that separated PET rings and detect collinear events in the adjacent PET rings. This could occur without concomitant dead time affects and allowed for a nearly quadruple increase in sensitivity. Figure 4 depicts 2D mode imaging (left) and 3D mode (right):
PET detection modes
Attenuation corrections methods must also be implemented routinely or the PET axial images will have a muted or dim appearance for those structures that are more towards the center and deeper aspects of the patient’s anatomy. The most simple attenuation correction method is that of filtered back projection whereby the body is assumed to be an ellipse of relatively uniform density. This “Chang technique” works well in uniformly dense anatomic structures but is woefully slow and inadequate in portions of the anatomy that contains variable density structures. Therefore, for both speed and accuracy, measured attenuation is preferable via the use a of a CT source. The historical arc of PET-CT attenuation projection has progressed from usage of an external transmission rod source to “modern” CT scanners that are now commercially available and integrated with PET-CT. CT detector architecture utilizing upwards of 128 rows can now be found on commercially available PET-CT scanners [4]. In the earlier days of PET, Ge-68 or Cs-137 rod sources were used to generate a transmission scan through each slice of the patient’s body resulting in a measurement of attenuation correction for each pixel. Typically, the rod source was maintained within a shielded portion of the gantry. Upon the issuing of a transmission command from the scanner operating software, the shielded rod would be extended and rotated about the patient for a predefined time per bed position, usually 3-4 minutes per bed. This was a lengthy process that commonly took upwards of 30 minutes to complete. Modern PET scanners no longer utilize transmission rod sources and PET scanners containing CT infrastructure are the norm due to the dramatically increased speed of acquisition and resulting attenuation correction map [5]. Figure 5 depicts transmission scan created with a rotating radioactive rod source assembly.
PET rod transmission source scan: Contemporary PET scanners no longer make use of rod-based transmission because CT has become the sole source of transmission-based attenuation correction.
The advantage of the traditional transmission rod source was that the patient received much less radiation dose with a transmission rod source compared to modern CT transmission methods [6]. Additionally, the transmission data were acquired in the native 511 keV energy obviating the need for segmentation that is required for CT. Segmentation involves smoothing the transaxial CT images to approximate the spatial resolution of the PET scanner. This segmentation is necessary because the energy settings of 80-140 keV inherent to CT are much lower than the 511 keV energies common to PET. The pixel values of these regions are altered and replaced with the known linear attenuation coefficient for the imaged tissue or other internal materials such as a prosthetic (joint replacement, pacemaker etc.). The process of replacing the pixel values eliminates a considerable amount of noise inherent in the “raw” image. The segmented CT attenuation map is scaled to the 511 keV and applied as attenuation correction to the PET images.
As mentioned previously, the PET-CT scanning acquisition results in the creation of raw projection data. This raw projection data is processed and rendered into reconstructed image sets. It is common practice at most clinical imaging institutions to retain the CT raw projection data for a limited number of days. This permits sufficient time to elapse such that the corresponding reconstructed images can be reviewed by the interpreting physician. It is particularly important to retain the raw data for those limited but important circumstances that the interpreting physician requests an additional reconstruction for better elucidation of a particular abnormality prior to generating the final scan interpretation. Reconstructed axial images may also be utilized to create additional projections including coronal and sagittal image sets. If the images are to be used outside of the oncology realm that PET-CT has principally been concerned with, the image data will be rendered into vertical and horizontal long axis images to accompany the usual transverse/transaxial image sets. However, certain institutions due to internal protocols or to adhere to specific research protocols must retain the raw data indefinitely. In this case, a reliable and timely means of archiving of all of the raw data generated by a scan will be necessary. There are myriad options available for archiving of said data. Reliable and timely archiving and retrievabililty will figure prominently in deciding which type of archiving solution is appropriate. Despite the increasing availability of robust and inexpensive computer memory, these data sets quickly deplete available hard drive space and create a pressing need for removal. This is because the CT raw data sets are much larger when compared to a corresponding PET acquisition of the same axial coverage. Archival and retrieval methods and strategies will be covered later in this chapter.
The amount of raw image data space required for each PET-CT examination depends on both the particular scanner configuration as well as the scan protocols in general usage by a facility. Each PET bed will require fewer than 10 megabytes (MB) of storage for lower matrix acquisitions. Lower matrices are usually those that are lower than 256. A lower matrix would be commonly used for axial coverage necessary for torso-based oncology such as breast, colorectal, and lymphoma staging and restaging. Higher matrices, such as those used for head & neck oncology or neurology imaging on the very latest and modern PET-CT scanners, are as high as 512. These high, fine matrices will require in excess of 70 MB for a single PET bed position. Figure 6 shows lower and higher matrix image examples.
PET low (128 matrix) PET high (400 matrix)
CT raw data requires substantially more space, with modern 64-row scanner used in PET-CT generating upwards of 70 MB of projection data per second. As a result, the typical whole torso PET-CT examination can readily require in excess of 2 gigabytes (GB) of hard drive storage space for the raw data alone when there is a single CT acquisition created for the entire torso axial coverage (Table 1). With the addition of other CT acquisitions which may include lung breath hold, multiple contrast phases or longer axial coverage, the raw data space consumed increases accordingly to 4 GB and greater. The reconstructed images consume considerably less hard drive space; an entire image set, including different PET and CT image reconstructions occupy less than 500 MB. Common PET image reconstructions include attenuation corrected iterative and non-attenuation corrected filtered back projection. Figure 7 depicts the transaxial PET reconstructions commonly used in body oncology imaging.
Typical transaxial PET-CT image reconstructions. Note CT was acquired with both arterial and equilibrium contrast phases and rendered in multiple kernels and windows
In a very active practice in which 10 or more patients are imaged per scanner, several GB of hard drive space can be easily filled in the course of a day [1]. If the PET-CT technologist does not routinely transfer raw data sets and reconstructed image sets to other storage sites or delete them from the hard drive space on a routine basis, system functionality can be severely hampered. In some cases, intensive hard drive utilization may cause database corruption resulting in significant interruptions and possibly downtime. Table 1 depicts a comparison of both PET and CT raw and reconstructed file sizes.
# of PET beds | \n\t\t\tCT scanning time in seconds | \n\t\t\tPET raw data set size in MB | \n\t\t\tCT raw data set size in MB | \n\t\t\tTotal PET-CT file size in MB | \n\t\t
1 | \n\t\t\t3 | \n\t\t\t70 | \n\t\t\t210 | \n\t\t\t280 | \n\t\t
2 | \n\t\t\t6 | \n\t\t\t140 | \n\t\t\t420 | \n\t\t\t560 | \n\t\t
3 | \n\t\t\t9 | \n\t\t\t210 | \n\t\t\t630 | \n\t\t\t840 | \n\t\t
4 | \n\t\t\t12 | \n\t\t\t280 | \n\t\t\t840 | \n\t\t\t1120 | \n\t\t
5 | \n\t\t\t15 | \n\t\t\t350 | \n\t\t\t1050 | \n\t\t\t1400 | \n\t\t
\n\t\t\t\t*6\n\t\t\t | \n\t\t\t\n\t\t\t\t18\n\t\t\t | \n\t\t\t\n\t\t\t\t420\n\t\t\t | \n\t\t\t\n\t\t\t\t1260\n\t\t\t | \n\t\t\t\n\t\t\t\t1680\n\t\t\t | \n\t\t
7 | \n\t\t\t21 | \n\t\t\t490 | \n\t\t\t1470 | \n\t\t\t1960 | \n\t\t
8 | \n\t\t\t24 | \n\t\t\t560 | \n\t\t\t1680 | \n\t\t\t2240 | \n\t\t
9 | \n\t\t\t27 | \n\t\t\t630 | \n\t\t\t1890 | \n\t\t\t2520 | \n\t\t
10 | \n\t\t\t30 | \n\t\t\t700 | \n\t\t\t2100 | \n\t\t\t2800 | \n\t\t
11 | \n\t\t\t33 | \n\t\t\t770 | \n\t\t\t2310 | \n\t\t\t3080 | \n\t\t
12 | \n\t\t\t36 | \n\t\t\t840 | \n\t\t\t2520 | \n\t\t\t3360 | \n\t\t
13 | \n\t\t\t39 | \n\t\t\t910 | \n\t\t\t2730 | \n\t\t\t3640 | \n\t\t
14 | \n\t\t\t42 | \n\t\t\t980 | \n\t\t\t2940 | \n\t\t\t3920 | \n\t\t
15 | \n\t\t\t45 | \n\t\t\t1050 | \n\t\t\t3150 | \n\t\t\t4200 | \n\t\t
File size assumptions: A PET bed occupying approximately 10 cm of axial coverage requires 70 MB. A CT of the corresponding PET axial coverage is 3 times as large or ~ 210 MB. *The typical PET-CT would be of the torso ("skull base to thighs") and would be approximately 5-6 bed positions. Depending on the axial field of view, wholebody (skull vertex to toes) imaging may require as many as 15 or more bed positions to provide sufficient axial coverage. | \n\t\t
Comparison of both PET and CT raw and reconstructed file sizes
Common and scalable raw and image data archiving strategies and solutions will be discussed later in this chapter.
The PET scanner crystals remain the primary limiting factor in both image resolution and speed of acquisition capabilities [7]. The development and implementation of Time-of-Flight (ToF) technology has been the primary strategy targeted at improving image resolution and acquisition speed [8, 9]. The concept of time of flight dates back many years and was utilized for limited applications employing very fast and expensive crystal arrays [8, 9]. The economics of crystal manufacture combined with more affordable and rapid computer processors and memory have made ToF feasible to deploy among virtually all of the mainstream PET-CT manufacturers. The crystal standard for many years in PET technology was the bismuth germinate crystal. It had the advantage of having good 511 keV stopping power, universal availability and was well-tested within PET gantry design. However, it lacked the fast scintillation capabilities that are essential to ToF PET. Lutetium oxyorthosilicate (LSO) or cerium-doped lutetium yttrium orthosilicate (LYSO) have emerged as the industry standard capable of the rapid scintillation times necessary to support ToF [10].
The principle advantage of ToF is the ability to dramatically improve the positioning of annihilation events that occur outside of the line of response (LOR). This is accomplished by locating the annihilation photon energy deposition on the opposing sides of the ring of crystals in the PET gantry and determining the difference in arrival times of those events.
It is important to understand that ToF allows for better lesion detectability not because of improvement in resolution but as a result of improved signal-to-noise definition inherent in improved timing resolution. For this to occur in contemporary PET scanners, the coincidence timing window must be configured to be very short (4-6 nanoseconds) to improve the fraction of randoms detected and resultant improvement in image contrast.
Provided accurate attenuation correction is performed, PET scanners provide the opportunity to generate semi-quantitative measurements of tumor metabolism. These measurements, known as standardized uptake values (SUVs) continue to be the primary and most universally accepted method for generating semi-quantitative measurements that depict tumor metabolism [11]. The default unit of measurement in all PET scanners is kilobecuerels per milliliter. This unit of measurement together with the quantity of injected radioactivity, patient weight, and decay time is used to compute the SUV. Considerable error inherent to all of the aforementioned criteria can result in badly flawed measurements and ultimately, false tumor metabolism quantification. In order to reduce the likelihood of introducing error in SUVs, at a minimum, the following must be evaluated and effectively implemented in the SUV calculation [11]:
Scanner cross-calibration: procedure performed to ensure that dose calibrator dose assays match the radioactivity measured by the PET scanner.
Measurement of residual syringe activity: This occurs immediately subsequent to administering the dose to the patient. The residual syringe activity is subtracted and the total quantity administered is recorded in the radiopharmaceutical administration record. This same resulting quantity is used for all SUV calculations.
Synchronization of all clocks utilized in reporting injection time
Assurance of proper infusion of radiopharmaceutical (no dose extravasation)
Accurate patient weight
Accurate patient dose
The equation for SUV calculation is as follows:
SUV= Region of interest of radiopharmaceutical concentration
(Tracer dose/patient weight)
Because radiopharmaceutical dose and patient weight are in the denominator, these are among the 2 most important values to optimize to reduce the magnitude of error inherent to the calculation.
Prior to 1998 and the prototype development of the PET-CT at the University of Pittsburgh, PET-only systems had primacy given that those systems were the only offering available [3]. The genesis of PET combined with CT derived from the suggestion of a Swiss oncology surgeon. During the development of the PET-CT, the oncologist opined that a CT scanner in the voids between the banks of the PET detectors might provide useful anatomical information familiar to oncology surgeons. This suggestion was a catalyst to the advent of the modern-day PET-CT. Dr. David Townsend and Ron Nutt began creating a prototype PET-CT in 1991 but it would not be a viable device for use clinically until 1998 [3].
Since that time, the practice of PET-CT could be considered more largely to be PET-ct in which the CT portion of the scan is used primarily for attenuation correction and anatomic localization. However, the original intent of Townsend and colleagues was to generate clinical CT and clinical PET scans in the course of a single scanning session using a single machine. Moreover, the desired purpose of the CT was to provide clinical patient information rather than only attenuation correction and anatomic localization. Indeed, CT for attenuation correction was a secondary to the main purpose of developing a clinical PET-CT scanner [3]. High-quality, optimized CT was possible routinely even on 2 row CT units that were commonly available and interfaced with the PET gantry at that time [3].
There has been considerable divergence over the routine integration of optimized, contrast enhanced CT with PET. However, over the course of the past decade, the literature has repeatedly borne out the superior quality and efficacy of optimized CT used in conjunction with PET [12, 13]. The most strident objection to performing optimized, contrast-enhanced CT with PET is that the oral and/or intravenous contrasts utilized on the CT creates artifacts in the PET images. More specifically, it was proposed that the intravenous contrast or oral barium sulfate attenuation correction artifacts diminished the readability of the PET [14, 15]. While there are limited examples of attenuation correction artifacts from oral or intravenous contrast, experienced PET-CT readers have learned to utilize filtered back projection uncorrected images to differentiate artifacts versus clinically relevant findings [16]. The emergence of routinely used dual syringe intravenous contrast injectors that permit the injection of a normal saline “chaser” after the initial intravenous contrast have virtually eliminated intravenous contrast artifacts on the attenuation corrected images [17].
There are substantial requirements and preparations necessary to incorporating optimized CT into PET-CT practice [2]. The most ideal approach has been to have truly-dually trained and boarded radiologists and technologists working together to produce the PET-CT images. Regrettably, this situation is rarely achievable given the time investment necessary to garner nuclear medicine physician and radiologist credentials or for similar circumstances to be available to nuclear medicine technologists. Nevertheless, it is possible to routinely incorporate optimized CT into the PET-CT practice provided there can be collaboration between nuclear medicine and CT departments.
Critical considerations for optimizing CT acquired along with PET include configuring scanner parameters for the best quality image while dosing the patient safely. Technologist staff should become knowledgeable regarding basic CT principles such as pitch and slice overlap, CT dose index (mGy and mAs or mA), slice thickness and noise inter-relationship, and x-ray penetration characteristics (keV setting). Intravenous contrast administration requires careful screening of each patient both at the time the patient’s appointment is scheduled as well as during the actual appointment. Internal protocols should be developed to optimize the patient’s ingestion of oral contrast, administration of intravenous contrast for optimized bolus timing, as well as persistent awareness of the potential for contrast reactions. Figure 8 illustrates a protocol for PET-CT incorporating optimized CT:
Optimized CT-PET protocol
A final consideration for performing optimized CT is patient safety given clinically significant findings. In the course of performing optimized CT, it is not uncommon to encounter a large pleural effusion (fluid in the lungs) or a pneumothorax (collapsed region of lung) or similar life-threatening circumstance. PET-CT technologists must be vigilant and trained to routinely evaluate the CT images for obvious significant findings and report these findings to a radiologist for appropriate follow up. Figure 9a illustrates a pleural effusion and Figure 9b shows a pneumothorax:
(a.) Bilateral pleural effusions encountered during viewing of CT images; (b.) Pneumothorax. Note that this clinically-significant finding is only fully revealed upon application of a CT kernel and appropriate windowing.
On rare occasions, pulmonary emboli are also encountered and must be reported but these findings are often extremely subtle even to the experienced imager.
Along with noticing clinically significant findings during and subsequent to the scan, it is vital that the technologist provide the utmost in safety while administering intravenous contrast. The threat of intravenous contrast extravasation, allergic reactions, or renal compromise are the foremost dangers for the patient. It has been well-documented that intravenous contrast extravasations of 100 milliliters or greater almost always require a plastic surgery consult as localized tissue necrosis may occur [18]. This is because the osmolality of commonly used non-ionic intravenous contrast (~650 mOsm/kg) is often vastly different from osmolality of blood (~285 mOsm/kg) creating conditions for unfavorable osmotic gradients to occur [19]. The majority of intravenous contrast extravasations can be avoided entirely by verifying venous patency prior to and during the administration of contrast [1]. Figure 10 demonstrates a graphical depiction of the venous patency both before (10a) and during (10b) contrast administration. Figure 10c reveals an example of a steeply sloped, worrisome curve that may indicate an extravasation event will occur.
a. Saline test bolus phase, b. Intravenous contrast bolus phase, c. Non-patent I.V.: Administering intravenous contrast when the test bolus has a rapidly increasing slope that does not level off is an imminent indicator of extravasation Venous patency tracing viewed both during test bolus of saline (a), injection of intravenous contrast (b) and non-patent IV (c). For maximum safety, the technologist should actually palpate the injection site during an initial bolus of normal saline while also reviewing the time versus pressure tracing.
Additionally, though uncommon, allergic reactions to intravenous contrast range from localized mild urticaria to anaphylactic shock [20]. Also, patients at risk for renal insufficiency such as those who have diabetes, hypertension, solitary kidney, or any combination of the aforementioned are at substantial risk for developing contrast induced nephropathy (CIN) [21]. Therefore, all patients must be carefully screened prior to receiving contrast. This will include a thorough review of the patient’s medical history as well as assessment of creatinine and estimated glomerular filtration rate ideally within 30 days of administering intravenous contrast [22].
Prior to the introduction and routine utilization of modern PET-CT scanners, the technologist or similar staff used third party programs in post-processing attempts targeted at aligning PET and CT or PET and MR image sets that had been acquired on different scanners. In addition, the radiologist was also tasked with customary mental alignment of image metabolism structures, so called “mental fusion” [23]. The fully integrated and combined PET-CT has allowed for practical and real-time image fusion that is considered commonplace in contemporary imaging [24]. Unfortunately, this has not obviated the need for third party image fusion systems because fusion of IR, MR or other modality fusion is now considered standard-of-care. This is increasingly becoming the case in multidisciplinary oncology environments as well as neurology subspecialty environments that include an epileptologist as part of a multidisciplinary epilepsy team. Until recently, rigid fusion was the only possible fusion option. Rigid fusion involves image landmark matching to achieve the closest best fit among anatomic structures and metabolic activity. This is achievable by using software to co-register multiple image volumes against a reference volume. However, due to myriad alterations in patient position between scanners, patient weight changes, and surgical variants rigid fusion frequently reveals undesirable matches between image sets. In contrast, deformable fusion has emerged and permits more favorable metabolic and structural alignment by incorporating virtual stretch algorithms. This involves mutual information algorithms that function at the pixel and/or voxel level to “warp” the image data [25].
Figure 11 demonstrates a post-processed PET-CT fusion image while Figure 12 illustrates a post-processed PET-MR deformably fused image.
PET-CT fusion images: Images were acquired during co-registered acquisition and fused during post-processing
PET-MR fusion images-the PET and MR were acquired separately and fused utilizing deformable fusion post-process application software.
Provided the processed image matrices are similar, deformable fusion is routinely achievable and permits for favorable and clinically useful alignment of morphological and metabolic image sets across multiple cross-sectional modalities [26].
If PET-CT experienced a “golden age” it was immediately following more widespread adoption of PET-CT in the early 2000s. Numerous PET-CT facilities had business models based upon as few as 3 patients per day due to robust reimbursement that prevailed up until 2005. This was an ephemeral but important time of prosperity, growth, and development for PET-CT. At that time, the per scan fee provided by the Centers for Medicare and Medicaid Services (CMS) was at an all time high. This period was destined for an eventual phase out but was hastened by the implementation and enforcement of the Deficit Reduction Act (DRA) [26, 27, 28, 29].The DRA of 2005 (signed into law February of 2006) was implemented as part of a broader strategy targeted at limiting the unnecessary expenditure of funds thought to be redundant in patients’ care [26]. The ultimate result of this policy was that reimbursement for PET-CT was reduced by nearly one half in the non-hospital, free-standing imaging environment [26]. Many independent imaging centers that once prospered by only performing 3 or 4 patients per day no longer could achieve a margin to sustain a solvent business model. In the ensuing aftermath of full phase in of DRA policy, many of these facilities were either assimilated by larger institutions or simply became insolvent and bankrupt.
In addition to the DRA of 2005, a second blow to PET-CT arrived in the form of the major economic downturn and crisis of 2008. This dramatically reduced the borrowing power of institutions as well as the number of patients with healthcare insurance who could afford to have PET-CTs. What emerged was a new paradigm of very efficient, higher volume imaging workflows in PET-CT in both public and private hospital industry. Institutions with targeted and efficient workflows have been able to weather the continued acrimonious economic conditions as funds for both full time equivalents (FTEs) and capital infrastructures such as scanners continues to diminish. PET-CT has continued to grow although the percentage increase has tended to decrease each year since 2005 [30]. This environment is indeed the new normal and will likely persist for several years to come.
Pediatric PET-CT acquisition requires all of the same precautions as those that accompany adult PET-CT plus specific considerations for PET emission times, matrix, and minimization of movement artifacts. Despite the fact that pediatric patients tend to be shorter and have much lower body mass than adult patients, acquisition paradoxically takes longer. This is because ideally, a higher and finer matrix will be used to image the smaller bodies of pediatric patients. As a general guideline, if the matrix size is doubled there should be concomitant quadrupling of acquisition time in order to achieve appropriate imaging statistics and image quality. Given these considerations, achieving high-quality, motion-free images may require coordination of sedation services, immobilization devices and/or considerable psychosocial support from the PET-CT staff as well as accompanying patient guardian(s) [31]. Within a conventional scheduling paradigm, high quality pediatric scanning invariably requires more planning and imaging time. These needs cannot be underestimated and should be an integral part of the pediatric PET-CT scheduling process.
In any pediatric PET-CT imaging environment, there should be age and weight-specific criteria for dosing the patient with radiopharmaceuticals. One method that can be used is to standardize the pediatric dose to the “standard man” of 70 kilograms while also setting absolute low and high dose limits. As an example, an institution might designate 74 MBq (2 mCi) as the minimum dose and 370 MBq (10 mCi) as the maximum dose. The dose would then be computed with the following equation:
Pediatric radiopharmaceutical dose=370 MBq x child’s weight in kg/150 kg
It is helpful to use any number of commercially available spreadsheet programs to extrapolate all values of radiopharmaceutical dosing based on this equation for ease of reference.
Pediatric PET-CT will also require careful consideration of radiation dose delivered in the CT portion of the exam. This is of the utmost importance if the institution has incorporated optimized or diagnostic CT parameters because dose from CT will be nearly twice the radiation dose from the 511 keV emitting radiopharmaceutical such as fluorine-18 2-deoxy-2-fluoro-D-glucose (18FDG) [32]. There are now well-established “Image Gently” protocols available from the American College of Radiology that can assist any facility in creating protocols that provide age-appropriate CT dosing. In recent years, these protocols have become increasingly common in many pediatric-based radiology departments although the adoption of optimized or diagnostic CT parameters in PET-CT has been slower to emerge [33]. Integrated applications to reduce CT dose should be routinely incorporated into the imaging of pediatric patients to maintain their dose as low as reasonably achievable (ALARA). Low dose pediatric CT is generally accepted to be 5 mSv or below for the typical torso axial coverage [34]. This is easily achievable in younger and smaller pediatric patients who possess a lower body mass index (BMI) but becomes considerably more difficult in imaging older and higher BMI pediatric patients. An ongoing and continuing dialogue with a health physicist and radiologist is essential to providing safe and lower dose CT in the pediatric PET-CT environment [35].
Similar to pediatric PET-CT, radiation therapy (RT) planning may be a very small portion of image volume but requires considerable additional time and attention to execute properly. PET-CT has been playing an increasingly important role in the radiation therapy process, especially in multidisciplinary oncology centers [36, 38]. One of the essential advantages that PET-CT offers over CT alone is the detection of smaller lymph nodes that would not likely be considered positive on CT by size criteria [36]. Additionally, there is now ample evidence that PET-CT consistently locates unsuspected distant metastatic disease that is not visible on CT alone [36]. There are several possible approaches to incorporating radiation therapy planning into the PET-CT environment but 2 primary methods have emerged in more routine PET-CT clinical practice. The simplest method is to complete the PET-CT on a flat RT therapy planning pallet with the patient positioned in a manner approximating the positioning established or anticipated in the patient’s RT planning [36-39]. Figure 13 depicts a PET-CT scanner equipped with the RT pallet.
PET-CT equipped with RT pallet. Note radiation therapy planning laser adjacent to scanner (left) that will be used in aligning patient.
This approach requires no additional preparation other than the PET-CT staff receiving notification in advance to place the patient on the RT pallet. A more complex method is to position the patient in the same RT apparatus as created for the patient’s original simulation. In this case, the patient is instructed to bring their simulation position device with them to their PET-CT appointment.
The primary limiting factor for this approach is usually the bore of the PET-CT gantry [36, 40]. Most manufacturers now offer RT-sized PET-CT gantries because of the emerging complementary nature of RT and PET-CT [36]. This approach permits the most accurate but also most complex and time-intensive approach with the simulation and PET-CT occurring all in one session. In this environment, the dosimetrist or radiation therapist will position the patient in their custom radiation therapy body cradle, thermoplastic mask, or similar radiation therapy simulation apparatus [36-38]. Figure 13 a and b depict a patient who has been fitted with the same thermoplastic mask as used in the patient’s actual radiation therapy. Figure 14 shows the fiducials together with RT planning “B pillar” viewed on the reconstructed images. The PET-CT image sets are then migrated to the radiation therapy planning software and used by the radiation oncologist and dosmetrist for the patient’s radiation therapy sessions. The advantage of this approach is that the PET-CT images acquired are the actual simulation or planning images and PET with respect to a simulation CT will contain no error [36]. The disadvantage is that the additional time required to perform a full PET-CT simulation of this type can be upwards of 30 minutes. Moreover, the radiation exposure the dosimetrist and technologist receive while setting the patient up can be significant and unacceptable if performed routinely. Additionally, scanner time is expensive and in a busy institution, the additional time necessary for true PET-CT RT may create significant scheduling backlogs or patient scanning delays. For this approach to be practical, the PET-CT scanner may even be sited in the RT department.
a: Patient positioned for RT planning on RT pallet with simulation position device. Note that external RT planning laser array has been aligned to patient’s fiducials. b: Additional view of patient positioned for RT planning on RT pallet with simulation position device. Note patient has been fitted with thermoplastic mask that will be utilized for each RT treatment event. Intravenous contrast dual injector has also been positioned and is ready to use for optimized CT. Fiducials visualized on axial reconstructed images
A final but important consideration for PET-CT acquisition is the additional maneuvers required for inpatient scanning. Inpatients will almost always require more time to ambulate, transition, and position in the PET-CT scanner. A corresponding increase in staff time must be planned for given the higher level of acuity inherent to inpatient scanning. A variety of imaging workflows and paradigms exist for incorporating inpatients into a busy imaging practice. One approach is to have an inpatient-only scanner dedicated exclusively to performing inpatient requests. This approach is more readily integrated in a large academic institution that has the resources for multiple scanners allocated for specific purposes. It is not well-suited to the typical, smaller imaging environment that relies on higher volume and more closely sequenced outpatients. Nevertheless, as the result of diminishing funds and resources, it has become increasingly common to perform inpatient studies in the outpatient setting. In any case, many institutions have found that a radiology RN is vital link in the preparation necessary to create a high-quality PET-CT scan. The RN should be available to perform a true peer-to-peer interaction with the patient’s RN prior to the patient’s actual arrival. This helps to insure the patient can be transported and maintained in the PET-CT department safely. Primary considerations include but are not limited to the following:
Ambulation and falls: Minimizing falls is at the center of patient safety in any clinical service and becomes especially important when caring for inpatients. The public health and hospital safety literature have repeatedly reported the poor outcomes and compromised care that falls cause in the hospital setting [41-43]. The prevention of falls has arisen to such a level that it has garnered the attention of the Joint Commission as a National Patient Safety Goal [44]. Preventing falls for inpatients undergoing PET-CT will require a peer-to-peer RN interaction whenever possible to reduce the likelihood of the patient falling upon transition to the PET-CT environment.
Diabetes: In an oncology setting, diabetes can be the single most challenging inpatient management regimen as the patient’s medication schedule and diet must be carefully controlled to achieve a euglycemic state compatible with high quality 18FDG PET-CT imaging. If blood glucose levels exceed 200 mg/dL, the PET imaging cannot be undertaken [45]. This is true because image quality will be suboptimal as endogenous glucose competes with the same binding sites as exogenous 18FDG [45].
Medications: Many inpatients receive intravenous medications in an excipient such as dextrose that will make the PET-CT impossible to perform due to glucose receptor saturation. There are also numerous medications that create difficult circumstances for blood sugar control and achieving the desired serum glucose level prior to the PET-CT. These include but are not limited to corticosteroids, chemotherapy infusions, and insulin [45].
Telemetry: Contemporary higher acuity inpatient practice has incorporated routine usage of telemetry as a proactive means of discovering and treating cardiac events. In the peer-to-peer interaction, a plan must be formulated either for safely and temporarily discontinuing the telemetry or sending a specialized individual with the patient to monitor for cardiac events.
Patient line status: Inpatients will have a variety of ostomies, surgical drains, catheters and the like that will require maintenance and specialized positioning within the scanner. Because these devices will contain patient secretions that may be radioactive, additional caution to minimize the likelihood of contamination in the scanner will be required.
Isolation: In an era of increasingly resistant microorganisms, more and more inpatients will be discovered to be colonized with bacteria that cannot be treated with conventional antibiotics. The vast majority of hospital infection control protocols require that once a patient has been characterized as having a resistant microorganism, the patient must be isolated from other patients and staff. The more common resistant bacteria include methicillin resistant staph aureus (MRSA) and vancomycin resistant enterococcus (VRE) [46-48]. Clostridium difficile (C. diff.) isolation also has become problematic in these same hospital scenarios [49]. Since many hospital organizations cannot afford multiple PET-CT scanners, the prospect of needing to scan isolation patients in the midst of a busy outpatient workflow is not uncommon. Internal protocols that uphold cleaning the patient’s uptake room, PET-CT scan room, and scanner itself must be consistently applied to reduce the likelihood that immuno-compromised outpatients do not contract a resistant bacterial strain from a scheduled inpatient.
Attire: Inpatients will typically be attired in standard hospital gowns which may contain metal snaps that can result in beam hardening and scatter on the CT phase of the imaging. This same metal can also introduce artifacts into the attenuation corrected PET-CT images. Therefore, it is beneficial to proactively remove said gowns or provide alternative attire such as scrubs prior to the scanning event.
Pain management: Given the higher acuity of inpatients as compared to outpatients, it is not surprising that a greater degree of patient pain management may be required. It is helpful to identify additional pain management needs in a peer-to-peer interaction prior to the inpatient’s arrival. This will be paramount to maximizing patient comfort such that motion is minimized and a successful PET-CT scanning event will occur. Along with the pain evaluation, the RN can ascertain the patient’s need for anxiolytics targeted at minimizing claustrophobia-related distress. To standardize the care of inpatients and enhance a safe time for the patient in PET-CT, it is highly desirable to collect, review, and access all of the aforementioned information prior to the patient’s arrival. Figure 15 shows an example of an inpatient criteria sheet that assists the PET-CT staff with determining if an inpatient can safely be transported and scanned:
Inpatient criteria sheet example
Once the PET-CT image data has been acquired and processed, a convenient, rapid, and reliable system must exist to archive the image data. The historical arc of image archiving has spanned from hard-copy radiographic film systems to present day systems that permit viewing digital soft-copies of PET-CT images in Picture Archiving and Communication Systems (PACS). In most radiology and medical imaging settings, PACS has emerged as the preferred archival strategy although there continues to be a diversity of images rendered in the varied hospital and imaging center environments across the United States and globally.
PACS has been configured to support the extensive tomographic image production which is the result of torso axial coverage in the typical PET-CT. This has been especially important as multi-detector CT associated with PET has advanced and resulted in thinner and increased number of slices. It is not unusual for the combined PET-CT image set to contain in excess of 2000 image slices that require rapid transfer to the PACS server and corresponding distribution to image review workstations. Image transfer rates and efficiency will be a function of the bandwidth available throughout the hospital or imaging system network. Rate of image transfer is central to availability of image data on centralized and remote workstations. System slow-downs will also impact the performance of the PET-CT acquisitions if the processed data cannot be rapidly transferred to the PACS. This phenomenon is both vendor and system topology dependant but best practices require that an entire study be transmitted in under 5 minutes for a busy PET-CT imaging center. Figure 16 graphically depicts the relationship between image data transfer rate and transfer time. There is a clear exponential relationship which is quickly realized within the imaging workflow because transfer rate and time delays can cause backlogs and impair overall PET-CT system performance.
Relationship between rate of image transfer and archival time:
Given the opportunity, PET-CT, medical informatics professions, and information technology professionals should begin to collaborate early in the process of configuring PET-CT operations. This working relationship has become an imperative as image acquisition and corresponding PET-CT report turn-around-time have become an important metric in quantifying standard-of-care. The shape and layout of the network and nodes (topology) should be considered both before and during the establishing of the PET-CT infrastructure. For large hospital systems with multiple sites and remote viewing requirements, having a scalable network with very high bandwidth and redundancies will be paramount. This becomes a complicated and expensive undertaking as network cabling, switches, servers, and all manner of information technology infrastructure will need to be considered, purchased, deployed, and maintained over the course of many years. Figure17 illustrates an example of the configuration of a typical PET-CT system topology and interconnectivity. A clear understanding of the connectivity, dependence, and relationship of both hardware and software items is vital to initial troubleshooting during system failure. Many issues such as physical disconnection between devices due to lose cabling or locating of devices requiring a reboot can be identified simply by knowing the system topology and understanding the interrelationship of system components.
Example PET-CT system topology
A consistent, reproducible, and accessible PACS workflow should be conceived and followed by the PET-CT staff who generate the images. In particular, it will be important to consider ancillary information that the radiologist requires to read the images and the accessibility of said materials [1, 38]. The PET-CT images are certainly the centerpiece of the exam but additional information such as pathology reports, consults, and imaging reports augment the interpretation process. There are three approaches to incorporating this information into the PACS workflow effectively. The first option will be to simply printout and provide the radiologist with any ancillary clinical information that will be used to render the report. This is the least desirable method because it involves a substantial shuffling of paper and usage of printer resources. However, many institutions still use the standard paper method because of the imaging culture of the institution. The 2nd option will be to forego any printing of documents and deliver these to the radiologist in a purely “paperless” or soft format. This will require a favorable and convenient adjacency of the Health Information System/Radiology Information System (HIS/RIS) to the PACS workstation. It also requires support staff to scan in any documents that are not native to the hospital or imaging center. The third option that occurs in highly integrated healthcare environments is a merger of PACS, HIS, & RIS all within the PACS environment. This requires maximum collaboration and cooperation of Radiology and Medical Informatics as well as appropriately planned monitor and screen real estate. In a well-planned and executed fully integrated PACS/HIS/RIS, the radiologist can readily navigate and among the aforementioned applications with minimal paper waste and stream lined workflow. Figure 18 shows a fully functional PACS/HIS/RIS configuration.
Fully-integrated PACS together with HIS & RIS. Note that full voice recognition transcription functionality has also been incorporated into the process for the most optimized report turn-around-time.
In addition to PACS-based image viewing systems, it is inevitably necessary to view PET-CT images in other venues where PACS may not be available. Given that all data is DICOM-based, the best solution is to obtain the images on a solid-state media such as compact disk (CD) or digital video disk (DVD) and upload the data to PACS for viewing. This option also has the advantage of being executed on the user’s computer regardless of bandwidth limitations.
Hospital or imaging centers with virtual private networking (VPN) capability may use file transfer protocol (FTP) as a means of securely and reliably transferring image data. With contemporary firewall systems, this often becomes a challenging undertaking fraught with information technology issues that will require an advanced user with administrative system access capabilities. Invariably, however, many institutions lack a full PACS or means of securely transmitting image data via ftp. This includes many surgical suites outside of the hospital or imaging center where the PET-CT originated, as well as community-based oncology groups, and virtually any location beyond the reach of native PACS. For such situations, the next best option for viewing images will be client-server based viewing capabilities. This will involve providing the remote user with a username and password to authenticate with the PACS server and then streaming data to the remote user’s monitor. The distinct disadvantage of this method is that almost no PC-based client server monitors possess the appropriate resolution inherent to a PACS monitor that has true DICOM gray scale standard rendering [50, 51].
There are instances in which PACS does not provide a desirable location for storage. This is particularly true in instances whereby raw data sets such as PET or CT sinograms must be stored. This situation will commonly occur and be an imperative for research protocols that require the original raw data to be available in perpetuity. Sending the PET and/or CT sinograms across the network from the modality to PACS invariably results in raw data corruption resulting either in transmission failure or unusable data. Offline storage devices such as Redundant Arrays of Independent Disks (RAID) or terabyte hard drives are viable solutions in these cases. The compatibility of these options must first be vetted with the PET-CT scanner vendor to ensure long-term stability and recoverability of the raw data. These systems do have the advantage of being scalable as additional disk space can be added both to RAID and other types of offline hard drive systems [1, 38, 40].
From PET’s primary research-oriented imaging in the 1970s and 1980s to contemporary PET-CT routinely used for oncology and neurology, PET continues to play an important role in the management of and characterization of a wide variety of disease processes. PET-CT as practiced today remains one of the most challenging and complex type of imaging studies performed in most hospital or imaging center environment. This derives largely from the integration of 2 somewhat divergent modalities along with the multifaceted diagnostic requirements of patients in oncology and neurology. An understanding of the acquisition, processing, and archiving of PET-CT data is central to sustaining a safe, patient-centered and high-quality PET-CT image product.
The author wishes to thank Dr. Paul Shreve and the staff of the Spectrum Health Lemmen Holton PET-CT Cancer Pavilion for their insight and support in writing this chapter.
Digitization is occurring in many industries in many different forms; however, regardless of the application, a common set of enablers are employed. As the proliferation of digital transformation continues, decision makers will need to distinguish between reliability and resiliency in the planning, design, and operation of these subsystems. Tightly coupled common hardware and software platforms potentially increase the breadth of accidental failures as well as the impact of intentional sabotage. Beyond end use applications is an overall reliance on electricity which these digital subsystems require to function. Hardware, software, and electricity form the foundation upon which digitalization rest. The increased interdependence and interconnection can lead to common failure modes of previously isolated subsystems, resulting in increased probability of high impact events. Interconnection results in the establishment of a singular system with all other structures existing as subsystems. Evaluation of subsystems will need to include internally and externally initiated disruptive events. Highly impactful events, sometimes termed black swans, cannot only disrupt subsystems but fundamentally change their structure. Impactful as they are, rarity can make these events prone to underinvestment due to heuristics and biases, most prominently the availability heuristic. A quantifiable metric can aid in our ability to appropriately allocate resources to study, adapt, and mitigate these high impact, low probability events before they unexpectedly fracture the established subsystems we rely on. The avoidance of fracture is central to the application of the modulus of resilience in critical subsystems. The chapter will review the differences between the reliability and resiliency as well as the importance of distinguishing between the concepts. Additionally, ideals related to resilience are identified and expressed in a concise operational definition. The research utilized the progression shown in Figure 1 for the investigation.
\nResearch phases.
Representative plot of event type distribution.
Borrowing concepts from materials science allows for an isomorphic application where analogous structures are leveraged to represent HILP event scenarios. In this chapter, the isomorphic application is presented to provide a method of quantifying resiliency or its absence based on the intended aim of the subsystem. This concept is consistent with select portions of previous literature, but divergent in others. Following a review of previous research, a gap analysis was completed to identify opportunities for new considerations in quantifying resiliency. Lastly, an example in applying the modulus of resilience for critical subsystems is provided to demonstrate the computational process.
\nReliability and resiliency are sometimes discussed in a similar context with respect to subsystem performance; however, they differ conceptually in both the events they measure and the characteristics they quantify. The measures which define reliability provide insights as to the context of the metrics use. Many of the most common reliability metrics utilize mean-based calculations from reoccurring failures over time. These metrics include mean time between failure (MTBF), mean time to failure (MTTF), and mean time to repair (MTTR). These metrics require successive failures in order to quantify subsystem performance. Mean time between failure (MTBF) is used in reliability to provide the number of failures per million hours for a subsystem. Mean time to repair (MTTR) is the time needed to repair a failed subsystem. Mean time to failure (MTTF) measures reliability for a subsystem which cannot be repaired. It is the mean time expected until the first failure of a subsystem. MTTF is a statistical value and represents the mean over a long period of time and a large number of operations. The reliability metrics can effectively represent common cause events which produce reoccurring failures; however, these calculations are less applicable to low probability special cause events. A special cause is something special, not part of the system of common causes. It is detected by a point that falls outside the control limits [1]. Often, subsystems have an allowable level of tolerance to minor disruption preventing sustained impairment in accomplishing the aim of the subsystem. Plotting the number of events by type versus percent of subsystem output disrupted graphically displays the relationship between common cause and special cause events. The allocation of events is closely represented by a pareto distribution Figure 2.
\nResiliency events reside at the tail of the distribution as rare events resulting from extraordinary scenarios. Such events have been produced by multiple failures within a single subsystem as discussed in the book Normal Accidents by Charles Perrow. His work examined failures in highly complex operating environments. The increasing interdependence results in an interconnected ecosystem where a failure in a single subsystem can create failures in multiple subsystems. When interactive complexity is joined with tight coupling, the risk of a system accident is considerably increased. Interconnectedness and complexity among contemporary subsystems is increasing at a rapid pace as technologies develop faster than assessments can be made regarding their risks. As we move away from individual events and account for the larger system, we find the “eco-system accident,” an interaction of systems that were thought to be independent but are not because of the larger ecology [2]. As systems grow in size and in the number of diverse functions they serve, and are built to function in ever more hostile environments, increasing their ties to other subsystems, they experience more and more incomprehensible or unexpected interactions [2]. Common mode failures, first included in analytical models in 1967, can contribute to unexpected actions from complex systems. In addition to common mode failures, proximity and indirect information sources are two additional indications of interconnectedness. Ultimately, the probability of a subsystem being subjected to significant disruption is dependent on the cumulative probability of both internal and external risks. Inevitably, the probability of significant disruption will increase as interdependence increases. While increases in events causing significant disruption are expected, their count is not expected to be significant enough for the application of mean-based reliability metrics. Therefore, resiliency-based metrics are needed which match the periodicity and scale of high impact, low probability events.
\nHILP events require a subsystem to bounce back to normalcy following major disruption. The goal is to regain pre-disruption levels of output as quickly as possible; however, recovery time is not the only metric of importance. The shape of the recovery curve is also of significance. Resiliency aids in defining a disaster response paradigm which differs from previous approaches such as resistance and sustainability by emphasizing return to normal. Nonetheless, the literature frequently uses the concept of resilience to imply the ability to recover or bounce back to normalcy after a disaster occurs [3]. Review of scholarly work related to the resiliency concept identified three main ideals: no assumption that disaster prevention is always possible, recognition of the need to include social variables, and the necessity to include disciplines outside the physical sciences and engineering. The term resiliency has increased in usage over the past decades. A multitude of definitions have been proposed whose interpretations can align with either resistance or sustainability. Although the resilience construct offered advantages in many areas relative to competing paradigms, the ambiguity associated with its meaning and scope hindered consensus. The multiplicity of definitions is a reflection of the philosophical and methodological diversities that have emerged from disaster scholarship and research [4].
\nResilience first came to prominence in the English language in the early 19th century when Tredgold used the term to describe a property of timber [5]. In his essay “On the transverse strength and resilience of timber,” Tredgold tested the properties of timber to be used in ship making. Tredgold cites resilience as the power of resisting a body in motion [5]. The statement is foundational in establishing the concept of resilience as more than recovery but instead as an ability to first withstand an applied force. Furthermore, Tredgold varied the weight and height of objects dropped on the test samples and recorded the effects to different forces on various wood pieces. These effects ranged from no effect, broke to curved. A second reference to the consideration of force can be found in the 1858 work, “On the Physical Conditions Involved in the Construction of Artillery, and on Some Hitherto Unexplained Causes of the Destruction of Cannon in Service,” by Robert Mallet. He states the modulus of resilience of other writers, referred to hereafter, depends, is much greater for gunmetal, and hence a given force produces a greater proportional distortion of form [6]. The modulus of resilience was further formalized by materials science using stress/strain testing.
\nThe range of methods for defining resilience include qualitative, quantitative and probabilistic. A quantitative method can be used to compare outcomes using data from different actual events. A number of researchers have explored quantifying resilience to move beyond qualitative representations. Henry and Ramirez-Marquez [7] proposed a quantitative approach for system resilience as a function of time. The formulation was a ratio of the recovery and losses using a figure-of-merit function. A disruptive event (ej) at time, te, impacts the system until time, td.
\nAs shown, the numerator relates to the recovery until time t and the denominator represents the total loss due to disruption. Hosseini et al. [8] reviewed definitions and measures of system resilience. Their literature review was based on multiple domains including organizational, social, economic, and engineering using papers published between 2000 and April 2015. The major categories of assessment approaches are qualitative and quantitative with quantitative measures further defined as either probabilistic or deterministic.
\nThe intent to analyze protracted subsystem disruptions leads to a focus on quantitative deterministic methods of calculating resiliency. The literature review by Hosseini et al. [8] included 11 deterministic methods of quantification. Bruneau et al. [9] utilized a method of integration based on the degradation in quality of infrastructure during recovery period of Eq. (5). Larger RL values indicate lower resilience while smaller RL imply higher resilience. Hosseini et al. [8] RL is calculated based on the formulation in Eq. (2).
\nZobel [10] proposed a method based on the total possible loss over some suitably long-time interval (T*), percentage of functionality lost after disruption (X), and time required for full recovery (T). An effort was made to analyze different combinations of X and T which result in the same level of resilience as shown in Eq. (3).
\nThis metric is based on a linear recovery making it unrealistic for some scenarios.
\nAlternative methods were proposed by Cox et al. [11] based on economic resilience using the difference in disruption (%∆DYmax) between the expected disruption (%∆Y) and maximum potential disruption (%∆Ymax). Therefore, an estimate of performance degradation is required. Such an estimation may be a challenge to precisely develop; however, the formulation is shown in Eq. (4).
\nAlternatively, Rose [12] considered time effects using a concept of dynamic resilience. The quantification of dynamic resilience is the difference in system recovery with hastened system recovery (SOHR) and without hastened system recovery (SOWR). This calculation is utilized over the total number of time steps (N) considered. The dynamic resilience calculation is shown in Eq. (5).
\nWang et al. [13] explored resilience in information systems based on the number of operations in the enterprise information system (m). The ratio of the demand time (di) and completion time of operation (ci) are weighted by the importance of operation (zi).
\nThe larger the value of the metric the more resilient the system is determined to be. The calculation requires the assignment of a weight and assumes the number of operations is known. When attempting to quantify unknown events the number of operations can be difficult to estimate.
\nChen and Miller-Hooks [14] quantifies the “post-disruption expected fraction of demand that, for a given network, can be satisfied within pre-determined recovery budgets” (Hosseini et al.). The measure was based on transportation networks and compares the maximum demand that can be satisfied before disruption (Dw) and after disruption (dw) for pair (w).
\nOrwin and Wardle [15] considered the instantaneous and maximum disturbance in the quantification of resilience. The maximum absorbable force without upsetting system function (Emax) and effect of the disturbance on safety (Ej) at a given time (Tj) are used to define resilience.
\nFrameworks for local and global resilience were introduced by Enjalbert et al. [16] for modeling system safety in public transportation systems. A safety indication function (S(t)) is used to calculate resilience either instantaneously or over time, representing local and global, respectively. Global resilience is calculated from the time of disturbance (tb) to the end of the disturbance (te). The calculations are as follows:
\nFrancis and Bekera [17] introduced a metric for dynamic resilience. The calculation uses the speed of recovery (Sp), original performance level (Fo), performance level at new stable level (Fr\n) and performance level immediately after disruption (Fd). The speed of recovery variable assumes exponential growth for a maximum acceptable recovery time (tδ), total recovery time (tr) to a new equilibrium state, time to complete initial recovery (\n
Otherwise,
\nCimellaro et al. [18] utilized quality of service to represent resilience. The method uses before disruption quality of service (Q1(t)), post disruption quality of service (Q2(t)), a control time (TLC) and a weighting factor (α) in developing a healthcare resilience metric.
\nAside from the works investigated by Hosseini et al. [8], Dessavre et al., [19] introduced a new model and visual tools adding a stress dimension representing the force and stress of disruptive events. Defining the stress of the events is not a trivial task and completely domain dependent [19].
\nA review of the concepts found in literature was completed for elements consistent with the modulus of resilience. Methods were limited to quantitative approaches which could be utilized with empirical data sets. Although the use of scaling factors was identified in literature [13, 18], such methods are not desired in the development of subsystem-based methods due to the subjectivity associated with them. A ratio-based approach has merit in its ability to normalize event effects and resulting recovery. Area-based calculations using integration are preferred to point calculations based on their ability to compensate for nonlinear restoration curves; however, complexity beyond the resilience triangle [9] would be necessary to capture differences in event magnitude and restoration response in disparate events.
\nThe concept of a yield point was not identified in existing literature. A return to normal operation was typically used to identify the end of the restoration time period; however, this approach does not set the time based on the aim of the subsystem. Evaluations of subsystems beyond a critical point with respect to use of the subsystem output could lead to poor decision-making. One of the main weaknesses of the current resilience metric is that they do not relate the effects of a disruptive event to any of the event characteristics, unlike materials science [19]. Materials science utilizes a change in length for evaluation of stress and strain; however, the difference in recovery response to a common cause and special cause event was not found in the literature review. These distinctions serve to highlight the differences between reliability for normally occurring events and resiliency to low frequency events. Additionally, the need for utilizing subjective variables [10, 11, 12, 14, 15] does not lend well to empirical study.
\nThe ability to normalize responses to different events is beneficial for evaluating the resiliency of different subsystems or different events on the same subsystem. The literature reviewed began analysis of the event from the start of restoration [7] or by treating the entire curve from time of event to the completed restoration as a single integral [16]. This approach can confuse the quantities of force, stress and strain. An equal force can result in different stress and strain based on the subsystem being reviewed. As a result, the descending slope and associated area prior to the start of recovery may prove informative of stress. Strain is more associated with the total area under the curve. The review of literature did not identify a bifurcation of the curve to delineate stress (prior to start of recovery) and strain (total area). Therefore, the assumption of instantaneous loss and exponential recovery [17] are not representative of many empirical cases.
\nIn reviewing the concepts of resilience, a force is applied to a subsystem, the subsystem absorbs a portion of the force, experiences stress, and adapts to recover to a pre-disruption state. These references highlight an importance of considering the stress on the subsystem in determining the resiliency of a subsystem. Three primary points of measure for use in quantifying resiliency were identified including: stress, total area of event and change in length. Stress is a foundational variable of resiliency, as the term resiliency implies a response to a significant disruption. Therefore, only events of significance from a subsystem level are commonly referred to in terms of resilience. Additionally, the ability to compare resiliency events needs some level of normalization based on the associated stress for each event. Force continues to be applied until the subsystem decay ceases, allowing for subsystem assessment and initiation of recovery. The rate of subsystem decay influences the stress applied to the subsystem and the subsystem ability to bounce back. This connection exists due to the role of adaptation in the resiliency process. A slow evolving scenario (i.e., slow subsystem decay) presents the subsystem opportunity to adapt, resist, and recover in ways an acute decay will not. Therefore, when considering the normalization process of resiliency both the decay (i.e., stress proxy) and recovery portion of the resiliency curve must be independently considered. The delayed decay provides an opportunity for improved response from the subsystem.
\nTotal area of recovery best quantifies recovery and resiliency by compensating for the nonlinearity in the response function. As the subsystem attempts to recover, disruptions in the recovery process may cause discontinuities not captured by linear slope calculations. Similarly, time to recovery (i.e., 3 days to recovery) calculations may fail to represent intermediate progress in recovery.
\nConsideration of a failure point based on the aim of the subsystem aids in representing real-world scenarios. Recovery which occurs after a critical point of the subsystem would indicate a lack of resiliency. As an example, if a water subsystem requires 10 days to restore operation post contingency but the consumers of the water can only survive 4 days without water; the subsystem lacks resiliency. Attempts to quantify the subsystem’s resilience should stop at 4 days. Calculations beyond the 4-day time period no longer support the aim of the subsystem or the practical operation of the subsystem.
\nLastly, change in length was included in the materials science calculation of the modulus of resilience. The change in length from the original length to the length under stress could be translated to a subsystem resilience construct to allow consideration of how subsystem recovery under lower stress common cause events and high stress special cause events are related. The consideration of a change in length may aid in joining concepts associated with reliability in the quantification of resilience.
\nComparing these constructs with the reviewed literature results in the identification of conceptual gaps. The resulting resiliency values should reflect the subsystem performance for practical cases. Units are required based on subsystem parameters. The x-axis utilizes units of time, while the y-axis measures the units associated with the aim of the subsystem.
\nThe methods of quantification reviewed begin the process of quantification at the point of recovery or assume no time delta between the initiating event and start of recovery. To support the incorporation of stress in the quantification of resilience, a bifurcation of the event curve is used as shown in Figure 3.
\nBifurcation of event curve.
The use of ratio methods may provide consistency in scenarios of similar characteristics. When disparate characteristics are present, computed values may prove inconsistent with event outcomes. Depending on the event characteristics, either ratio methods or area-based methods may identify a less resilient subsystem response as more resilient. Figure 4 depicts the concept of less recovery time for less disruption. The scenario of Figure 4 is representative of a minor difference in subsystem response and would provide consistent rankings for resilience outcomes in many cases, where less area is representative of increased resilience.
\nRecovery curves with similar characteristics.
Conversely, cases may exist where a longer recovery results from a less impactful initial event. The delayed recovery to a less impactful event could result from many factors including a lack of preparedness, inability to adapt, etc. In such cases, observation would assume that the subsystem which took longer to recover from a less impactful event is less resilient. However, present formulations may suggest the opposite. Figure 5 illustrates this scenario, where the smaller area is not representative of the more resilient outcome.
\nRecovery curves with dissimilar characteristics.
The fracture point should be set based on the aim of the subsystem. For example, if a drinking water subsystem failure requires a 7-day restoration period but 4 days is the survival period without water; the calculation of subsystem resiliency should be limited to a 4-day period. In some cases, the acknowledgement of a fracture point will result in the calculation of resiliency stopping prior to the subsystem returning to pre-disruption output levels. Figure 6 represents a case where the subsystem recovery takes longer than the subsystem failure point.
\nRepresentation of failure point.
Calculations to quantify resiliency which consider values beyond the failure point are theoretical as opposed to practical in nature. The failure point should be given priority in quantifying resiliency.
\nAn operational definition is derived from the combination of literature review and isomorphic adaptation of the modulus of resilience. Hence, resiliency is defined as the ability to limit proportional stain from abnormal stress to less than the subsystem yield point, through the achievement of recovery in less than the subsystem critical timeframes. This definition allows the use of quantitative measures in the calculation of resilience in a deterministic and normalized approach based on concepts from materials science.
\nAn evaluation between two groups can result in an isomorphic application of findings from one structure to another. This mapping between groups can yield opportunities to apply known methodologies in an inter-disciplinary manner. The process of verifying an isomorphism requires the identification of elements in each structure and evaluating their equivalence. If equivalence is identified an opportunity for applying the computational framework may exist. The quantification of subsystem resilience was compared to resiliency as used in materials science. Materials science’s definition of resiliency includes the concepts of per unit volume, maximum energy, and integration from zero to the elastic limit. The modulus of resilience (Ur) is found from the stress-strain curve measured during the tensile test. Stress (σ) in the stress-strain curve is “the applied force per unit original undeformed cross-sectional area of the specimen” [20] as delineated in Eq. (15).
\nwhere F = force; A0 = cross sectional area.
\nYoung’s modulus (E) serves as a measure of stiffness for a solid material. “Because of the difficulty in determining the elastic limit, it is commonly replaced by the proportional limit, which is the stress at which the stress-strain curve is out of linearity” [20].
\nAnd,
\nwhere F = force; A = actual cross-sectional area; ∆L = amount of change in length; L0 = original length of the object.
\n“The modulus of resilience is the strain energy per unit volume absorbed up to the elastic limit for a tensile test and equals the area under the elastic part of the stress-strain curve” [20].
\n“This quantity indicates how much energy a material can absorb without deforming plastically” [20]. Plastic deformation occurs when a material undergoes non-reversible changes in response to applied forces. The use of the stress-strain curve from materials testing is similar to conditions faced by disrupted subsystems regardless of type. Stress is the impact to the material under test, while strain is the resulting effects of the stress.
\nBased on the desire of applying a consistent methodology to quantify resilience regardless of disruption magnitude or subsystem size, the percentage of subsystem disrupted is proposed to achieve a per unit value. The area under the curve will then be integrated from the beginning to end of the disruptive event. Calculus to determine area under the curve is shown in Eq. (19).
\nwhere Ei = Event initial; Er = Event restored.
\nThe area under the curve will then be applied to the maximum percentage of subsystem disrupted.
\nwhere SD = % of subsystem disrupted; Anl = Area under the curve to nonlinearity; At = Total area under the curve; Da = Duration of average disruption; De = Duration of event disruption.
\nProtracted subsystem disruptions create stress and strain due to an inability to complete the subsystem aim. The similarities between tensile strength test used in materials science and the need to measure stress and strain subsystems create an isomorphic relationship. Table 1 shows the parallels between materials science and protracted subsystem disruptions.
\nMaterials science. | \nProtracted subsystem disruption | \nComparisons | \n
---|---|---|
Stress applied | \nPeak percent of subsystem out of service | \nPercent out of service is equivalent to stress | \n
Cross-sectional area | \nArea under curve from the origin to peak subsystem out of service | \nArea from zero to peak subsystem out of service is point where curve loses linearity | \n
Actual cross-sectional area | \nArea under curve for entire disruptive event | \nRepresents total strain experienced by subsystem | \n
Change in length | \nDelta between subsystem’s average duration of disruptions and event disruption duration | \nUse of change in duration accounts for the change in length between average and protracted event | \n
Original length | \nSystem’s average duration of disruptions | \nAccounts for average non-protracted disruptions events | \n
Parallels between materials science test and protracted subsystem disruptions.
The application of the modulus of resilience to a specific subsystem requires the identification of an aim the subsystem exist to accomplish. “Without an aim, there is no system” [21]. The aim should be quantifiable with metrics available for analysis. The data must be accessible in order to serve as the basis for the resilience calculations and will vary based on the subsystem under study. Examples include percentage of successful operations or percentage of end users receiving service. The next section provides an empirical example in applying the modulus of resilience.
\nThe power industry was selected to provide an example for applying the modulus of resiliency using empirical data. The aim of the electric subsystem is to deliver electricity to all end use customers; therefore, data regarding the number of customers out of service can be used to quantify subsystem performance. The use of customers out of service in quantifying subsystem performance was supported by a review of regulatory reliability metrics used by Public Utility Commissions. For major electric utility disruptions, DOE situation reports provide customer outage information for and are publicly available from the DOE website. One of the most prominent events to challenge utilities is hurricane, and as a result, multiple hurricane events have data on the DOE website. Following data collection, plots can be constructed of the electric utility response in restoring customers. The inflection points were identified, and a yield point designated by reviewing disaster preparedness data from the Capital Region Study [22]. The study indicated that 73% of survey respondents had less than 10 days of food stored. Therefore, an event lasting greater than 10 days would most likely result in scarcity from food spoilage and diminished retail capabilities. With a known bifurcation and yield point, analysis can be completed.
\nHurricanes Wilma and Irma presented an opportunity to compare resiliency of separate events in the same region. Following Wilma, the ability of several infrastructures to recover from severe events was reviewed in the Florida region. “[M]ore than $141.5 million has been obligated by FEMA for 119 Hazard Mitigation Grant Program projects to build stronger, safer more resilient communities in Florida” [23]. Florida was once again subjected to a hurricane when Irma came ashore 12 years later. More than six million customers lost power as a result of Irma; compared to 4 million from Wilma. Although more than a decade apart, these two storms provide an opportunity to compare the recoveries following significant investment in resiliency. The comparison of the two resiliency indices can present an opportunity to calculate a cost per unit of resiliency and explore concepts such as diminishing returns or optimization from multi-hazard investment. Multi-hazard resiliency actions would provide an ability to address multiple HILP scenarios with a single investment. A resiliency index for each of the scenarios would be computed in order to create a composite change in resiliency for a given investment. The goal of this composite approach is to provide a means for justifying highly adaptable subsystem structures based on resiliency benefits.
\nThe example demonstrates the process of calculating the resiliency index for a power utility scenario and comparing the response before and after the investment in resiliency. The values shown in Table 2 were extracted from United States Energy Information Administration (EIA) data. The additional data points associated with 0.5 and 1.5 days were included due to nonlinearities in customer outages associated with Hurricanes Wilma and Irma, respectively. Similarly, day 9 for Hurricane Wilma was approximated for the purpose of this analysis. The data required to calculate the change in length was available by collecting System Average Interruption Duration Index (SAIDI) data. SAIDI data provides a basis for the average duration a customer faces and can be compared to the protracted system disruption as a change in length.
\nDay. | \n% Out of service (Hurricane Wilma 2005) | \n% Out of service (Hurricane Irma 2017) | \n
---|---|---|
0 | \n0 | \n0 | \n
0.5 | \n34 | \n20 | \n
1 | \n35 | \n40 | \n
1.5 | \n34 | \n64 | \n
2 | \n31 | \n56 | \n
3 | \n28 | \n40 | \n
4 | \n21 | \n31 | \n
5 | \n18 | \n20 | \n
6 | \n12 | \n11 | \n
7 | \n10 | \n7 | \n
8 | \n9 | \n4 | \n
9 | \n6 | \n1 | \n
Outages for Hurricanes Wilma and Irma.
Following the collection of empirical data, the total area under the curve was calculated by dividing the outage curve into time steps and summing the areas of each time step as shown in Figures 7 and 8, respectively.
\nHurricane Wilma restoration plot.
Hurricane Irma restoration plot.
The study region had a SAIDI of 60 minutes and a protracted outage duration of 12,960 minutes. Therefore, the resiliency index (RI) for Hurricane Wilma is determined as shown in Eq. (7).
\nThe study region had a SAIDI of 57 minutes and a protracted outage duration of 12,960 minutes. Therefore, the resiliency index (RI) for Hurricane Irma is determined as shown in Eq. (22) based on EIA data [24] (Tables 3 and 4).
\nDay. | \n% Out of service (Hurricane Wilma 2005) | \nArea | \n
---|---|---|
0 | \n0 | \n0.085 | \n
0.5 | \n0.34 | \n0.173 | \n
1 | \n0.35 | \n0.173 | \n
1.5 | \n0.34 | \n0.163 | \n
2 | \n0.31 | \n0.295 | \n
3 | \n0.28 | \n0.245 | \n
4 | \n0.21 | \n0.195 | \n
5 | \n0.18 | \n0.150 | \n
6 | \n0.12 | \n0.110 | \n
7 | \n0.10 | \n0.095 | \n
8 | \n0.09 | \n0.075 | \n
9 | \n0.06 | \n\n |
\n | Total area under curve | \n1.758 | \n
\n | Area under curve to nonlinearity | \n0.258 | \n
\n | Maximum % of customers out | \n0.350 | \n
Resiliency index calculation for Hurricane Wilma.
Day. | \n% Out of service (Hurricane Irma 2017) | \nArea | \n
---|---|---|
0 | \n0 | \n0.050 | \n
0.5 | \n0.20 | \n0.150 | \n
1 | \n0.40 | \n0.260 | \n
1.5 | \n0.64 | \n0.300 | \n
2 | \n0.56 | \n0.480 | \n
3 | \n0.40 | \n0.355 | \n
4 | \n0.31 | \n0.255 | \n
5 | \n0.20 | \n0.155 | \n
6 | \n0.11 | \n0.090 | \n
7 | \n0.07 | \n0.055 | \n
8 | \n0.04 | \n0.025 | \n
9 | \n0.01 | \n\n |
\n | Total area under curve | \n2.175 | \n
\n | Area under curve to nonlinearity | \n0.560 | \n
\n | Maximum % of customers out | \n0.640 | \n
Resiliency index calculation for Hurricane Irma.
Change in resiliency is found by Eq. (3).
\nThe determination of a change in resiliency allows for a quantitative measurement related subsystem response. The use of resiliency indices can aid in quantifying the efficacy of resiliency investment.
\nIn this chapter, a comparison to mean-based reliability was contrasted with the use of resiliency calculations for HILP events. Resiliency calculations are required, given the infrequent nature of protracted subsystem disturbances. Following a review of resiliency computations, a gap analysis was used to identify the opportunities for ensuring a resiliency calculation can capture the nonlinearities observed in empirical data. Parallels are provided between the modulus of resilience construct from materials science and an isomorphic application defined. In conclusion, an example is presented for the power utility sector demonstrating the methods of collecting the inputs and completing the computations. These inputs include defining the aim of the system and failure point, data collection, determination of bifurcation point, and the use of reliability data for calculating a change in length.
\nThe ability to calculate resiliency regardless of the subsystem or scenario can assist in the evaluation of resiliency actions already taken or planning for new investment. The ability to compute resiliency on a common base may also offer opportunities to optimize investment based on interconnectedness to the subsystems which yield the greatest improvement. A more integrated approach may lead to increased systemic resiliency as opposed to more common heuristics-based subsystem specific approaches. The proposed method more closely adheres to the ontological and conceptual frameworks associated with initial references of resiliency. Furthermore, subjective inputs are avoided increasing the replicability and repeatability of associated research. By acknowledging a yield point specific to the aim of the subsystem, results from the resiliency index better represent the outcomes of real-world subsystems. Lastly, bifurcating the event curve allows the onset characteristics of the disruptive event to normalize the resiliency performance metric.
\nFurther research on the distribution of events by type will be conducted to validate the anecdotal evidence regarding common cause and special cause events. This additional data will assist in the development of statistics for assessing the correlation between increasing interdependence and HILP events for critical subsystems. In order to test a wider array of empirical data sets, resiliency indexes will be calculated using both historical and future HILP event data. The results of these analyses will be used to continually evaluate the efficacy of the metrics and identify opportunities for enhancements.
\nhigh impact, low probability
\nmean time between failure
\nmean time to failure
\nmean time to repair
\ndepartment of energy
\nFederal Emergency Management Agency
\nenergy information administration
\nsystem average interruption duration index
\nresiliency index
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