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Luzi F, Fenn M, Christ J, Kennedy Z, Varga T, Hughes MS, Ortiz-Marrero C. Application of entropy and signal energy for ultrasound-based classification of three-dimensional printed polyetherketoneketone components. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2020; 148:292. [PMID: 32752739 DOI: 10.1121/10.0001581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/29/2020] [Accepted: 06/28/2020] [Indexed: 06/11/2023]
Abstract
This paper describes a preliminary method for the classification of annealed and unannealed polyetherketoneketone (PEKK) components manufactured using a material extrusion three-dimensional (3D) printing process. PEKK is representative of a class of high-performance thermoplastics that are increasingly employed as feedstocks for use in 3D printing. PEKK components may be used continuously at elevated temperatures, are chemically resistant, and able to withstand large mechanical loads. These properties render PEKK suitable as a metal component replacement in aerospace applications, high-temperature industrial applications, and surgical implants. The structure of PEKK is semi-crystalline with the specific crystallinity correlating to the final properties during application, making determination of this property crucial. This study compares three different signal processing techniques intended to distinguish annealed (high crystallinity) from unannealed (low crystallinity) components using backscattered ultrasound. The first is energy-based and is unable to detect annealing. The second two are based on different entropies of the backscattered signal: a limiting form of Renyi's entropy and a limiting form of joint entropy. The joint entropy values for the annealed and unannealed specimens fall into two non-overlapping intervals and have a statistical separation of two standard deviations.
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Affiliation(s)
- Francesco Luzi
- Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, USA
| | - Michelle Fenn
- Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, USA
| | - Josef Christ
- Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, USA
| | - Zachary Kennedy
- Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, USA
| | - Tamas Varga
- Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, USA
| | - Michael S Hughes
- Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, USA
| | - Carlos Ortiz-Marrero
- Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99354, USA
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Marsh JN, Korenblat KM, Liu TC, McCarthy JE, Wickline SA. Resolution of Murine Toxic Hepatic Injury Quantified With Ultrasound Entropy Metrics. ULTRASOUND IN MEDICINE & BIOLOGY 2019; 45:2777-2786. [PMID: 31320149 PMCID: PMC6718339 DOI: 10.1016/j.ultrasmedbio.2019.06.412] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Revised: 06/19/2019] [Accepted: 06/21/2019] [Indexed: 06/10/2023]
Abstract
Image-based classification of liver disease generally lacks specificity for distinguishing between acute, resolvable injury and chronic irreversible injury. We propose that ultrasound radiofrequency data acquired in vivo from livers subjected to toxic drug injury can be analyzed with information theoretic detectors to derive entropy metrics, which classify a statistical distribution of pathologic scatterers that dissipate over time as livers heal. Here we exposed 38 C57BL/6 mice to carbon tetrachloride to cause liver damage, and imaged livers in vivo 1, 4, 8, 12 and 18 d after exposure with a broadband 15-MHz probe. Selected entropy metrics manifested monotonic recovery to normal values over time as livers healed, and were correlated directly with progressive restoration of liver architecture by histologic assessment (r2 ≥ 0.95, p < 0.004). Thus, recovery of normal liver microarchitecture after toxic exposure can be delineated sensitively with entropy metrics.
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Affiliation(s)
- Jon N Marsh
- Department of Immunology & Pathology, Washington University School of Medicine, St. Louis, Missouri, USA
| | - Kevin M Korenblat
- Department of Internal Medicine-Gastroenterology, Washington University School of Medicine, St. Louis, Missouri, USA
| | - Ta-Chiang Liu
- Department of Anatomic & Molecular Pathology, Washington University School of Medicine, St. Louis, Missouri, USA
| | - John E McCarthy
- Department of Mathematics and Statistics, Washington University, St. Louis, Missouri, USA
| | - Samuel A Wickline
- University of South Florida Health Heart Institute, Morsani School of Medicine, Tampa, Florida, USA.
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Hughes MS, McCarthy JE, Bruillard PJ, Marsh JN, Wickline SA. Entropy vs. Energy Waveform Processing: A Comparison Based on the Heat Equation. ENTROPY 2016; 17:3518-3551. [PMID: 27110093 PMCID: PMC4838411 DOI: 10.3390/e17063518] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an “energy” picture. However, waves also carry “information”, as quantified by some form of entropy, and this may also be used to produce an “information” image. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be defined as the mean variation (i.e., observed change) divided by mean variance (i.e., noise). Wiener integration permits computation of the required mean values and variances as solutions to the heat equation, permitting estimation of their relative magnitudes. There always exists a reference, such that joint entropy has larger variation and smaller variance than the corresponding quantities for signal energy, matching observations of several studies. Moreover, a general prescription for finding an “optimal” reference for the joint entropy emerges, which also has been validated in several studies.
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Affiliation(s)
- Michael S. Hughes
- Pacific Northwest National Laboratory, 902 Battelle Blvd., Richland, WA 99354, USA
- Author to whom correspondence should be addressed; ; Tel.: +1-509-375-2507; Fax: +1-505-375-6497
| | - John E. McCarthy
- Department of Mathematics, Washington University in St. Louis, 1 Brookings Dr., St Louis, MO 63130, USA
| | - Paul J. Bruillard
- Pacific Northwest National Laboratory, 902 Battelle Blvd., Richland, WA 99354, USA
| | - Jon N. Marsh
- School of Medicine, Washington University in St. Louis, 660 S. Euclid Ave, St Louis, MO 63110, USA
| | - Samuel A. Wickline
- School of Medicine, Washington University in St. Louis, 660 S. Euclid Ave, St Louis, MO 63110, USA
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Chen J, Pan H, Lanza GM, Wickline SA. Perfluorocarbon nanoparticles for physiological and molecular imaging and therapy. Adv Chronic Kidney Dis 2013; 20:466-78. [PMID: 24206599 DOI: 10.1053/j.ackd.2013.08.004] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2013] [Revised: 08/20/2013] [Accepted: 08/20/2013] [Indexed: 11/11/2022]
Abstract
Herein, we review the use of non-nephrotoxic perfluorocarbon nanoparticles (PFC NPs) for noninvasive detection and therapy of kidney diseases, and we provide a synopsis of other related literature pertinent to their anticipated clinical application. Recent reports indicate that PFC NPs allow for quantitative mapping of kidney perfusion and oxygenation after ischemia-reperfusion injury with the use of a novel multinuclear (1)H/(19)F magnetic resonance imaging approach. Furthermore, when conjugated with targeting ligands, the functionalized PFC NPs offer unique and quantitative capabilities for imaging inflammation in the kidney of atherosclerotic ApoE-null mice. In addition, PFC NPs can facilitate drug delivery for treatment of inflammation, thrombosis, and angiogenesis in selected conditions that are comorbidities for kidney failure. The excellent safety profile of PFC NPs with respect to kidney injury positions these nanomedicine approaches as promising diagnostic and therapeutic candidates for treating and following acute and chronic kidney diseases.
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Hughes MS, McCarthy JE, Marsh JN, Wickline SA. Joint entropy of continuously differentiable ultrasonic waveforms. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2013; 133:283-300. [PMID: 23297902 PMCID: PMC3548839 DOI: 10.1121/1.4770245] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2012] [Revised: 10/17/2012] [Accepted: 11/19/2012] [Indexed: 06/01/2023]
Abstract
This study is based on an extension of the concept of joint entropy of two random variables to continuous functions, such as backscattered ultrasound. For two continuous random variables, X and Y, the joint probability density p(x,y) is ordinarily a continuous function of x and y that takes on values in a two dimensional region of the real plane. However, in the case where X=f(t) and Y=g(t) are both continuously differentiable functions, X and Y are concentrated exclusively on a curve, γ(t)=(f(t),g(t)), in the x,y plane. This concentration can only be represented using a mathematically "singular" object such as a (Schwartz) distribution. Its use for imaging requires a coarse-graining operation, which is described in this study. Subsequently, removal of the coarse-graining parameter is accomplished using the ergodic theorem. The resulting expression for joint entropy is applied to several data sets, showing the utility of the concept for both materials characterization and detection of targeted liquid nanoparticle ultrasonic contrast agents. In all cases, the sensitivity of these techniques matches or exceeds, sometimes by a factor of two, that demonstrated in previous studies that employed signal energy or alternate entropic quantities.
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Affiliation(s)
- M S Hughes
- Department of Medicine/Cardiology Division, Campus Box 8215, Washington University School of Medicine, 660 South Euclid Avenue, St. Louis, Missouri 63110-1093, USA.
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Hughes MS, Marsh JN, Agyem KF, McCarthy JE, Maurizi BN, Wickerhauser MV, Wallace KD, Lanza GM, Wickline SA. Use of smoothing splines for analysis of backscattered ultrasonic waveforms: application to monitoring of steroid treatment of dystrophic mice. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2011; 58:2361-2369. [PMID: 22083769 PMCID: PMC4281034 DOI: 10.1109/tuffc.2011.2093] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Duchenne muscular dystrophy (DMD) is an X-linked genetic disease characterized by progressive weakness and wasting of skeletal and cardiac muscle; boys present with weakness by the age of 5 years and, if left untreated, are unable to walk without assistance by the age of 10 years. Therapy for DMD has been primarily palliative, with oral steroids emerging as a first-line approach even though this treatment has serious side-effects. Consequently, low-cost imaging technology suitable for improved diagnosis and treatment monitoring of DMD would be of great value, especially in remote and underserved areas. Previously, we reported use of the logarithm of the signal energy, log [E(f)], and a new method for ultrasound signal characterization using entropy, H(f), to monitor prednisolone treatment of skeletal muscle in a dystrophin-deficient mouse model. Three groups were studied: mdx mice treated with prednisolone, a control group of mdx mice treated with saline, and a control group of wild-type mice treated with saline. It was found that both log [E(f)] and H(f) were required to statistically differentiate the three groups. In the current study, we show that preprocessing of the raw ultrasound using optimal smoothing splines before computation of either log [E(f)] or a rapidly computable variant of Hf, denoted I(f,∞), permits delineation of all three groups by either metric alone. This opens the way to the ultimate goal of this study, which is identification and implementation of new diagnostically sensitive algorithms on the new generation of low-cost hand-held clinical ultrasonic imaging systems.
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Affiliation(s)
- M. S. Hughes
- School of Medicine, Department of Internal Medicine/Cardiology, Washington University in St. Louis, St. Louis, MO
| | - J. N. Marsh
- School of Medicine, Department of Internal Medicine/Cardiology, Washington University in St. Louis, St. Louis, MO
| | - K. F. Agyem
- School of Medicine, Department of Internal Medicine/Cardiology, Washington University in St. Louis, St. Louis, MO
| | - J. E. McCarthy
- Department of Mathematics, Washington University in St. Louis, St. Louis, MO
| | - B. N. Maurizi
- School of Medicine, Department of Internal Medicine/Cardiology, Washington University in St. Louis, St. Louis, MO
| | - M. V. Wickerhauser
- Department of Mathematics, Washington University in St. Louis, St. Louis, MO
| | - K. D. Wallace
- General Electric’s Global Research Center in Niskayuna, NY
| | - G. M. Lanza
- School of Medicine, Department of Internal Medicine/Cardiology, Washington University in St. Louis, St. Louis, MO
| | - S. A. Wickline
- School of Medicine, Department of Internal Medicine/Cardiology, Washington University in St. Louis, St. Louis, MO
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Hughes M, Marsh J, Lanza G, Wickline S, McCarthy J, Wickerhauser V, Maurizi B, Wallace K. Improved signal processing to detect cancer by ultrasonic molecular imaging of targeted nanoparticles. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2011; 129:3756-3767. [PMID: 21682399 PMCID: PMC3143678 DOI: 10.1121/1.3578459] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2010] [Revised: 03/24/2011] [Accepted: 03/25/2011] [Indexed: 05/30/2023]
Abstract
In several investigations of molecular imaging of angiogenic neovasculature using a targeted contrast agent, Renyi entropy [I(f)(r)] and a limiting form of Renyi entropy (I(f,∞)) exhibited significantly more sensitivity to subtle changes in scattering architecture than energy-based methods. Many of these studies required the fitting of a cubic spline to backscattered waveforms prior to calculation of entropy [either I(f)(r) or I(f,∞)]. In this study, it is shown that the robustness of I(f,∞) may be improved by using a smoothing spline. Results are presented showing the impact of different smoothing parameters. In addition, if smoothing is preceded by low-pass filtering of the waveforms, further improvements may be obtained.
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Affiliation(s)
- Michael Hughes
- Cardiovascular Division, Washington University School of Medicine, Campus Box 8215, 4320 Forest Park Avenue, St. Louis, Missouri 63108, USA.
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Marsh JN, Wallace KD, McCarthy JE, Wickerhauser MV, Maurizi BN, Lanza GM, Wickline SA, Hughes MS. Application of a real-time, calculable limiting form of the Renyi entropy for molecular imaging of tumors. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2010; 57:1890-1895. [PMID: 20679020 PMCID: PMC3086696 DOI: 10.1109/tuffc.2010.1630] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Previously, we reported new methods for ultrasound signal characterization using entropy, H(f); a generalized entropy, the Renyi entropy, I(f)(r); and a limiting form of Renyi entropy suitable for real-time calculation, I(f),(infinity). All of these quantities demonstrated significantly more sensitivity to subtle changes in scattering architecture than energy-based methods in certain settings. In this study, the real-time calculable limit of the Renyi entropy, I(f),(infinity), is applied for the imaging of angiogenic murine neovasculature in a breast cancer xenograft using a targeted contrast agent. It is shown that this approach may be used to reliably detect the accumulation of targeted nanoparticles at five minutes post-injection in this in vivo model.
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Affiliation(s)
- J. N. Marsh
- School of Medicine at Washington University in St. Louis
| | - K. D. Wallace
- School of Medicine at Washington University in St. Louis
| | - J. E. McCarthy
- Department of Mathematics at Washington University in St. Louis
| | | | | | - G. M. Lanza
- School of Medicine at Washington University in St. Louis
| | - S. A. Wickline
- School of Medicine at Washington University in St. Louis
| | - M. S. Hughes
- School of Medicine at Washington University in St. Louis
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