Carotid function fractal

Author: m | 2025-04-25

The Carotid–Kundalini function is closely associated with Carotid-Kundalini fractals coined by popular science columnist Clifford A. Pickover and it is defined as follows. External links. Carotid–Kundalini function; Carotid-Kundalini fractal; Carotid-Kundalini Fractal Explorer; Carotid-Kundalini Fractals; References. ↑

Carotid Function Fractal - paulbourke.net

AbstractWe introduce a fractal operator on \(\mathcal {C}[0,1]\) which sends a function \(f \in \mathcal {C}(I)\) to fractal version of f where fractal version of f is a super fractal interpolation function corresponding to a countable data system. Furthermore, we study the continuous dependence of super fractal interpolation functions on the parameters used in the construction. We know that the invariant subspace problem and the existence of a Schauder basis gained lots of attention in the literature. Here, we also show the existence of non-trivial closed invariant subspace of the super fractal operator and the existence of fractal Schauder basis for \(\mathcal {C}(I)\). Moreover, we can see the effect of the composition of Riemann-Liouville integral operator and super fractal operator on the fractal dimension of continuous functions. We also mention some new problems for further investigation. Access this article Log in via an institution Subscribe and save Get 10 units per month Download Article/Chapter or eBook 1 Unit = 1 Article or 1 Chapter Cancel anytime Subscribe now Buy Now Price excludes VAT (USA) Tax calculation will be finalised during checkout. Instant access to the full article PDF. Similar content being viewed by others Data availabilityData sharing not applicable to this article as no data sets were generated or analyzed during the current study.ReferencesBarnsley, M.F.: Fractal functions and interpolation. Constr. Approx. 2, 303–329 (1986)Article MathSciNet MATH Google Scholar Barnsley, M.F.: Fractals Everywhere. Academic Press, Orlando (1988)MATH Google Scholar Barnsley, M.F., Harrington, A.N.: The calculus of fractal interpolation functions. J. Approx. Theory. 57(1), 14–34 (1989)Article MathSciNet MATH Google Scholar Barnsley, M.F.: Fractals Super. Cambridge University Press, Cambridge (2006) Google Scholar Beer, G.: Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance. Proc. Amer. Math. Soc. 95, 653–658 (1985)Article MathSciNet MATH Google Scholar Chandra, S., Abbas, S.: The calculus of bivariate fractal interpolation surfaces. Fractals 29(03), 2150066 (2021)Article MATH Google Scholar Chandra, S., Abbas, S.: Analysis of fractal dimension of mixed Riemann-Liouville integral, Numerical Algorithms. (2022)Falconer, K.J.: Fractal Geometry: Mathematical Foundations and Applications. John Wiley Sons Inc, New York (1990)MATH Google Scholar Gowrisankar, A., Uthayakumar, R.: Fractional calculus on fractal interpolation for a sequence of data with countable iterated function system. Mediterr J. Math. 13, 3887–3906 (2016)Article MathSciNet MATH Google Scholar Jachymski, J.: Continuous dependence of attractors of iterated function systems. J. Math. Anal. Appl. 198, 221–226 (1996)Article MathSciNet MATH Google Scholar Kapoor, G.P., Prasad, S.A.: Super fractal interpolation functions. Int. J. Nonlinear Sci. 19(1), 20–29 (2015)MathSciNet MATH Google Scholar Kapoor, G.P., Prasad, S.A.: Convergence of cubic spline super fractal interpolation functions. Fractals 22(1,2), 7 (2014)MATH Google Scholar Liang, Y.S.: Box dimensions of Riemann-Liouville fractional integrals of continuous functions of bounded variation. Nonlinear Anal. 72(11), 4304–4306 (2010)Article MathSciNet MATH

Carotid Function Fractal - paulbourke.org

Google Scholar Liang, Y.S.: Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions. Frac. Calc. Appl. Anal. 21(6), 1651–1658 (2019)Article MathSciNet MATH Google Scholar Limaye, B.V.: Linear Functional Analysis for Scientists and Engineers. Springer, Singapore (2016)Book MATH Google Scholar Mauldin, R.D., Urbański, M.: Dimensions and measures in infinite iterated function systems. Proc. London Math. Soc. 3(1), 105–154 (1996)Article MathSciNet MATH Google Scholar Nussbaum, R.D., Priyadarshi, A., Verduyn Lunel, S.: Positive operators and Hausdorff dimension of invariant sets. Trans. Amer. Math Soc. 364(2), 1029–1066 (2012)Article MathSciNet MATH Google Scholar Navascués, M.A.: Fractal polynomial interpolation. Z. Anal. Anwend. 25(2), 401–418 (2005)Article MathSciNet MATH Google Scholar Navascués, M.A.: Fractal approximation. Complex Anal. Oper. Theory 4(4), 953–974 (2010)Article MathSciNet MATH Google Scholar Navascués, M. A.: Affine fractal functions as bases of continuous functions, Quaest. Math. 1–20 (2014)Navascués, M.A.: New equilibria of non-autonomous discrete dynamical systems. Chaos Solitons Fractals 152, 111413 (2021)Article MathSciNet MATH Google Scholar Priyadarshi, A.: Lower bound on the Hausdorff dimension of a set of complex continued fractions. J. Math. Anal. Appl. 449(1), 91–95 (2017)Article MathSciNet MATH Google Scholar Read, C.J.: Quasinilpotent operators and the invariant subspace problem. J London Math. Soc. 56(3), 595–606 (1997)Article MathSciNet MATH Google Scholar Ri, S.I.: A new idea to construct the fractal interpolation function. Indag Math. 29(3), 962–971 (2018)Article MathSciNet MATH Google Scholar Ri, S.I.: Fractal functions on the Sierpinski gasket. Chaos, Solitons Fractals 138, 110142 (2020)Article MathSciNet MATH Google Scholar Ruan, H.J., Sub, W.-Y., Yao, K.: Box dimension and fractional integral of linear fractal interpolation functions. J Approx. Theory 161, 187–197 (2009)Article MathSciNet MATH Google Scholar Strotkin, G.: A modification of read’s transitive operator. J. Operator Theor. 55:1, 153–167 (2006)MathSciNet Google Scholar Schonefeld, S.: Schauder bases in spaces of differentiable functions. Bull. Amer. Math. Soc. 75, 586–590 (1969)Article MathSciNet MATH Google Scholar Secelean, N.A.: The fractal interpolation for countable systems of data, Beograd University Publikacije Electrotehn. Fak. Ser. Matematika 14, 11–19 (2003) Google Scholar Secelean, N.A.: Approximation of the attractor of a countable iterated function system. Gen. Math. 3, 221–231 (2009)MathSciNet MATH Google Scholar Secelean, N.A.: The existence of the attractor of countable iterated function systems. Mediterr. J. Math. 9, 61–79 (2012)Article MathSciNet MATH Google Scholar Vijender, N.: Bernstein fractal trigonometric approximation. Acta Appl. Math. 159, 11–27 (2019)Article MathSciNet MATH Google Scholar Vijender, N.: Bernstein fractal approximation and fractal full Müntz theorems. Electron. Trans. Numer. Anal. 51, 1–14 (2019)Article MathSciNet MATH Google Scholar Verma, S., Viswanathan, P.: A fractalization of rational trigonometric functions. Mediterr. J. Math. 17(3), 1–23 (2020)Article MathSciNet MATH Google Scholar Wang, H.Y., Yu, J.S.: Fractal interpolation functions with variable parameters and their analytical properties. J. Approx. Theory 175, 1–18 (2013)Article MathSciNet MATH Google Scholar Download referencesAcknowledgementsWe are thankful to the anonymous

Carotid Function Fractal( )V1.10 -

Schmaier et al. (2011) found that avian thrombocytes respond to many of the same activating stimuli as mammalian platelets (and so help stop blood loss from damaged vessels) but, unlike mammalian platelets, cannot form tighly adherent thrombi in arteries. Avian thrombocytes are larger than mammalian platelets and are less 'sticky' (because they release different chemicals) than mammalian platelets when exposed to collagen (connective tissue to which thrombocytes and platelets are exposed when there's a break in a blood vessel). When carotid arteries of mice are damaged, platelets form thrombi that can block blood flow (check this video showing the response of human platelets when exposed to a plate covered with collagen); similar damage to the carotid arteries of Budgerigars (similar in size and speed and pressure of blood flow to the carotid arteries of mice) did not cause the formation of thrombi (check this video showing the response of chicken thrombocytes when exposed to a plate covered with collagen). These results indicate that mammalian platelets, in contrast to avian thrombocytes, will form thrombi even in arteries where blood flow is rapid and under high pressure, an essential element in human cardiovascular diseases. Link:Heart disease linked to evolutionary changes that may have protected early mammals from trauma Brain size & immunity -- Parasitism can negativelyaffect learning and cognition. Greater susceptibility to parasitism bymales may impair cognitive ability, and greater male investment in immunitycould compensate for greater susceptibility, in particular when males havea relatively large brain. Why might males be more susceptible. The Carotid–Kundalini function is closely associated with Carotid-Kundalini fractals coined by popular science columnist Clifford A. Pickover and it is defined as follows. External links. Carotid–Kundalini function; Carotid-Kundalini fractal; Carotid-Kundalini Fractal Explorer; Carotid-Kundalini Fractals; References. ↑ Download Carotid Function Fractal latest version for Windows free. Carotid Function Fractal latest update: Aug

Carotid Function Fractal - Paul Bourke

We’re sorry, something doesn't seem to be working properly. Please try refreshing the page. If that doesn't work, please contact support so we can address the problem. AbstractFractal geometry has unique advantages for a broad class of modeling problems, including natural objects and patterns. This paper presents an approach to the construction of fractal surfaces by triangulation. After introducing the notion of iterated function systems (IFSs), we prove theoretically that the attractors of this construction are continuous fractal interpolation surfaces (FISs). Two fast, parallel, and iterative algorithms are also provided. Several experiments in natural phenomena simulation verify that this method is suitable for generating complex 3D shapes with self-similar patterns. Access this article Log in via an institution Subscribe and save Get 10 units per month Download Article/Chapter or eBook 1 Unit = 1 Article or 1 Chapter Cancel anytime Subscribe now Buy Now Price excludes VAT (USA) Tax calculation will be finalised during checkout. Instant access to the full article PDF. Similar content being viewed by others Explore related subjects Discover the latest articles, news and stories from top researchers in related subjects. ReferencesBarnsley MF (1986) Fractal function and interpolation. Constr Approx 2:303–329 Google Scholar Barnsley MF (1988) Fractals everywhere. Academic Press, New York Google Scholar Demko S, Hodges L. Naylor B (1985) Construction of fractal objects with iterated function systems. Comput Graph 19:271–278 Google Scholar Falconer K (1990) Fractal geometry, mathematical foundations and applications. Wiley, New York Google Scholar Fournier A, Fussell D, Carpenter L (1982) Computer rendering of stochastic models. Commun ACM 25:371–384 Google Scholar Geronimo JS, Hardin D (1993) Fractal interpolation surfaces and a related 2D nuetiresolution analysis. J Math Anal Appl 176:561–586 Google Scholar Hart JC, Lescinsky GW, Sandin DJ, DeFanti TA, Kauffman LH (1993) Scientific and artistic investigation of multidimensional fractals on the AT&T pixel machine. Visual Comput 9:346–355 Google Scholar Lewis JP (1987) Generalized stochastic subdivision. ACM Trans graph 6:167–190 Google Scholar Mandelbrot BB (1982) The fractal geometry of nature. Freeman, New York Google Scholar Massopust PR (1990) Fractal surfaces. J Math Anal Appl 151:275–290 Google Scholar Miyata K (1990) A method of generating stone wall patterns. Comput Graph 24:387–394 Google Scholar Nailiang Z, Yiwen J, Sijie L (1991) An approach to the synthesis of realistic terrain. In: Staudhammer J, Qunsheng P (ed) Proceedings of CAD/Graphics '91, International Academic Publishers, Beijing, pp 31–35 Google Scholar Oppenheimer PE (1986) Real-time design and animation of

PS (Carotid Function Fractal) v1.0

Best shows structures made of mainly fat (fluids are dark / black; fat is bright / white). T2w - T2 weighted image presents structures made of both water and fat (fat and fluids are bright). PD - Proton density is handy for examination of muscles and bones. FLAIR - Fluid-attenuated inversion recovery best shows the brain. It is useful for identifying central nervous system disease, such as cerebrovascular insults, multiple sclerosis and meningitis. DWI - Diffusion weighted imaging detects distribution of fluids (extra- and intra- cellular) within tissues. As the balance between fluid compartments is altered in some conditions (infarctions, tumors), DWI is useful for both structural and functional soft tissue assessment. Flow sensitive - examines the flow of body fluids but without using contrast agents. This method examines if everything is okay with the cerebrospinal fluid flow and blood flow through the vessels. MRI is mostly used for neuroimaging (NMRI), musculoskeletal, gastrointestinal and cardiovascular system assessments. Ultrasonography Ultrasonography uses high frequency sound waves emitted from a transducer through a person's skin. These sounds echo from the contours of the inner body structures bouncing back to the transducer, which then translates them into a pixelated image displayed on the connected monitor. The density of the tissues here defines how echogenic they are, meaning what amount of sound will they resonate back (echo) or pass through themselves. Very solid tissues (bones) are hyperechoic and are shown as white, loose structures are hypoechoic and shown gray, while fluid is anechoic and is shown as black. Ultrasound shows processes in real time, which is why it is useful for immediate assessment of certain structures. It has many applications, such as tracking pregnancy progress (obstetric ultrasound), pathology screening (e.g. breast cancer) and examining the content of hollow organs (e.g. gallbladder). Ultrasonography adjusted for examining blood flow through arteries and veins is called Doppler ultrasonography, of which transcranial ultrasonography and carotid ultrasonography are nice examples. The former examines brain blood flow and the latter examines flow through the carotid arteries. Nuclear medicine imaging Brain PET scan Nuclear medicine imaging is used to visualize the function rather than the structure of specific body parts. A radiopharmaceutical (radioactive pharmaceutical) is administered to the patient (intravenously) and images are created of the passage, accumulation or excretion of that product. This provides information on the function of the organ/s in question. One common nuclear medicine imaging technique is positron

Carotid Function Fractal - Fractal Curve Photoshop Plugin

Color as a point enclosed in a three-dimensional cube. However, the same point has cylindrical coordinates in HSB:Hue Saturation Brightness CylinderThe three HSB coordinates are:Hue: The angle measured counterclockwise between 0° and 360°Saturation: The radius of the cylinder between 0% and 100%Brightness: The height of the cylinder between 0% and 100%To use such coordinates in Pillow, you must translate them to a tuple of RGB values in the familiar range of 0 to 255:Pillow already provides the getrgb() helper function that you can delegate to, but it expects a specially formatted string with the encoded HSB coordinates. On the other hand, your wrapper function takes hue in degrees and both saturation and brightness as normalized floating-point values. That makes your function compatible with stability values between zero and one.There are a few ways in which you can associate stability with an HSB color. For example, you can use the entire spectrum of colors by scaling stability to 360° degrees, use the stability to modulate the saturation, and set the brightness to 100%, which is indicated by 1 below:To paint the interior black, you check that the stability of a pixel is exactly one and set all three color channels to zero. For stability values less than one, the exterior will have a saturation that fades with distance from the fractal and a hue that follows the HSB cylinder’s angular dimension:The Mandelbrot Set Visualized Using the HSB Color ModelThe angle increases as you get closer to the fractal, changing colors from yellow through green, cyan, blue, and magenta. You can’t see the red color because the fractal’s interior is always painted black, while the furthest part of the exterior has little saturation. Note that rotating the cylinder by 120° allows you to locate each of the three primary colors (red, green, and blue) on its base.Don’t hesitate to experiment with calculating the HSB coordinates in different ways and see what happens!ConclusionNow you know how to use Python to plot and draw the famous fractal discovered by Benoît Mandelbrot. You’ve learned various ways of visualizing it with colors as well as in grayscale and black and white. You’ve also seen a practical example illustrating how complex numbers can help elegantly express a mathematical formula in Python.In this tutorial, you learned how to:Apply complex numbers to a practical problemFind members of the Mandelbrot and Julia setsDraw these sets as fractals using Matplotlib and PillowMake a colorful artistic representation of the fractalsYou can download the complete source code used throughout this tutorial by clicking the link below:

Carotid Function Fractal for Windows - CNET Download

Calc FunctionDiagnosisRule OutPrognosisFormulaTreatmentAlgorithmOfficial guideline from the American College of Emergency Physicians.summary by Eric Steinberg, DO Diagnosis Clinical Decision RulesIn adult patients with suspected transient ischemic attack (TIA), do not rely on current existing risk stratification instruments (eg, age, blood pressure, clinical features, duration of transient ischemic attack and presence of diabetes [ABCD²] score) to identify transient ischemic attack patients who can be safely discharged from the emergency department (ED). ImagingThe safety of delaying neuroimaging from the initial emergency department (ED) workup is unknown. If noncontrast brain MRI is not readily available, it is reasonable for physicians to obtain a noncontrast head computerized tomography (CT) as part of the initial transient ischemic attack (TIA) workup to identify transient ischemic attack mimics (e.g. intracranial hemorrhage, mass lesion). However, noncontrast head computerized tomography should not be used to identify patients at high short-term risk for stroke.When feasible, physicians should obtain magnetic resonance imaging (MRI) with diffusion-weighted imaging (DWI) to identify patients at high short-term risk for stroke.When feasible, physicians should obtain cervical vascular imaging (e.g. carotid ultrasonography, computed tomography angiography [CTA], or magnetic resonance angiography [MRA]) to identify patients at high short-term risk for stroke.In adult patients with suspected transient ischemic attack (TIA), carotid ultrasonography may be used to exclude severe carotid stenosis because it has accuracy similar to that of magnetic resonance angiography (MRA) or computed tomography angiography (CTA). ProtocolsIn adult patients with suspected transient ischemic attack (TIA) without high-risk conditions, a rapid emergency department (ED)-based diagnostic protocol may be used to evaluate patients at short-term risk for stroke. High-risk conditions include abnormal initial head computerized tomography (CT) result (if obtained), suspected embolic source (presence of atrial fibrillation, cardiomyopathy, or valvulopathy), known carotid stenosis, previous large stroke, and crescendo transient ischemic attack.Literature Original/Primary Reference. The Carotid–Kundalini function is closely associated with Carotid-Kundalini fractals coined by popular science columnist Clifford A. Pickover and it is defined as follows. External links. Carotid–Kundalini function; Carotid-Kundalini fractal; Carotid-Kundalini Fractal Explorer; Carotid-Kundalini Fractals; References. ↑

Carotid Function Fractal for Windows - Free download and

Presented at MGUS-87, Redwood City, CA. Google Scholar Goodchild, M.F., 1980, Fractals and the accuracy of geographical measures: Math. Geol. 12, 85–98.Article Google Scholar Goodchild, M.F., 1982, The fractional Brownian process as a terrain simulation model: Model. Simulation 13, 1133–1137. Google Scholar Goodchild, M.F., and Mark, D.M., 1987, The fractal nature of geographic phenomena: Ann. AAG 77, 265–278. Google Scholar Goodchild, M.F., Klinkenberg, B., Glieca, M., and Hasan, M., 1985, Statistics of hydrologic networks on fractional Brownian surfaces: Model. Simulation 16, 317–323. Google Scholar Hakanson, L., 1978, The length of closed geomorphic lines: Math. Geol. 10, 141–167.Article Google Scholar Hobson, R.D., 1972, Surface roughness in topography: A quantitative approach: in Spatial Analysis in Geomorphology, R.J. Chorley, (Ed.): Methuen, London, pp. 221–245. Google Scholar Hunt, C.B., 1967, Physiography of the United States: Freeman, San Francisco. Google Scholar Kagan, Y.Y., and Knopoff, L., 1980, Spatial distribution of earthquakes: The two-point correlation function: Geophys. J. R. Astron. Soc. 62, 303–320. Google Scholar Kadanoff, L.P., 1986, Fractals, where’s the physics?: Phys. Today, February, 1986. Google Scholar Kennedy, S.K., and Lin, W.-H., 1986, Fract-A fortran subroutine to calculate the variables necessary to determine the fractal dimension of closed forms: Comput. Geosci. 12, 705–712.Article Google Scholar Kent, C., and Wong, J., 1982, An index of littoral zone complexity and its measurement: Can. J. Fish Aquatic Sci. 39, 847–853.Article Google Scholar Klinkenberg, B., 1988, Tests of a fractal model of topography: Ph.D. thesis, University of Western Ontario. Google Scholar Lovejoy, S., 1982, Area-perimeter relation for rain and cloud areas: Science 216, 185–187.Article Google Scholar Lovejoy, S., and Mandelbrot, B.B., 1985, Fractal properties of rain, and a fractal model: Tellus 37 (A), 209–232. Google Scholar Lovejoy, S., and Schertzer, D., 1985, Generalized scale invariance in the atmosphere and fractal models of rain: Water Resources Res. 21(8), 1233–1250.Article Google Scholar Lovejoy, S., and Schertzer, D., 1986, Scale invariance, symmetries, fractals, and stochastic simulations of atmospheric phenomena: Bull. Am. Meteorol. Soc. 67, 21–32.2.0.CO;2" data-track-item_id="10.1175/1520-0477(1986)0672.0.CO;2" data-track-action="Article reference" data-track-value="Article reference" href=" aria-label="Article reference 32" data-doi="10.1175/1520-0477(1986)0672.0.CO;2">Article Google Scholar Lovejoy, S., and Schertzer, D., 1988, Extreme variability, scaling and fractals in remote sensing: analysis

Carotid-Kundalini Fractal - mathhand.com

Hand, you must scale it and clamp it before using it as an integer index in the palette.Pillow only understands integers in the range of 0 through 255 for the color channels. However, working with normalized fractional values between 0 and 1 often prevents straining your brain. You may define another function that’ll reverse the normalization process to make the Pillow library happy:This function scales fractional color values to integer ones. For example, it’ll convert a tuple with numbers like (0.13, 0.08, 0.21) to another tuple comprised of the following channel intensities: (45, 20, 53).Coincidentally, the Matplotlib library includes several colormaps with such normalized color channels. Some colormaps are fixed lists of colors, while others are able to interpolate values given as a parameter. You can apply one of them to your Mandelbrot set visualization right now:The twilight colormap is a list of 510 colors. After calling denormalize() on it, you’ll get a color palette suitable for your painting function. Before invoking it, you need to define a few more variables:This will produce the same spiral as before but with a much more attractive appearance:A Spiral Visualized Using the Twilight Color PaletteFeel free to try other color palettes included in Matplotlib or one of the third-party libraries that they mention in the documentation. Additionally, Matplotlib lets you reverse the color order by appending the _r suffix to a colormap’s name. You can also create a color palette from scratch, as shown below.Suppose you wanted to emphasize the fractal’s edge. In such a case, you can divide the fractal into three parts and assign different colors to each:Choosing a round number for your palette, such as 100 colors, will simplify the formulas. Then, you can split the colors so that 50% goes to the exterior, 5% to the interior, and the remaining 45% to the gray area in between. You want both the exterior and interior to remain white by setting their RGB channels to fully saturated. However, the middle ground should gradually fade from white to black.Don’t forget to set the viewport’s center point at -0.75 and its width to 3.5 units to cover the entire fractal. At this zoom level, you’ll also need to drop the number of iterations:When you call paint() and show the image again, then you’ll see a clear boundary of the Mandelbrot set:A Custom Color Palette To Bring Out The Edge Of The FractalThe continuous transition from white to black and then a sudden jump to pure white creates a shadowy embossing effect that brings out the edges of the fractal. Your color palette combines a few fixed colors with a smooth color progression known as a color gradient, which you’ll explore next.Color GradientYou may. The Carotid–Kundalini function is closely associated with Carotid-Kundalini fractals coined by popular science columnist Clifford A. Pickover and it is defined as follows. External links. Carotid–Kundalini function; Carotid-Kundalini fractal; Carotid-Kundalini Fractal Explorer; Carotid-Kundalini Fractals; References. ↑ Download Carotid Function Fractal latest version for Windows free. Carotid Function Fractal latest update: Aug

Carotid-Kundalini Fractal - from Wolfram

Changes in patients with cognitive impairment and is detailed in [6]. Briefly, all images were obtained on a GE 3 T HDXT MR scanner with a standard eight-channel array head coil. Anatomical coronal spin echo T2-weighted scans were first obtained through the hippocampi (TR/TE 1550/97.15 ms, NEX = 1, slice thickness 5 mm with no gap, FOV = 188 x 180 mm, matrix size = 384 x 384). Baseline coronal T1-weighted maps were then acquired using a T1-weighted 3D spoiled gradient echo (SPGR) pulse sequence and variable flip angle method using flip angles of 2°, 5° and 10°. (TR/TE = 8.29/3.08 ms, NEX = 1, slice thickness 5 mm with no gap, FOV 188 x 180 mm, matrix size 160 x 160). Coronal DCE MRI covering the hippocampi and temporal lobes were acquired using a T1-weighted 3D SPGR pulse sequence (FA = 15°, TR/TE = 8.29/3.09 ms, NEX = 1, slice thickness 5 mm with no gap, FOV 188 x 180 mm, matrix size 160 x 160, voxel size was 0.625 x 0.625 x 5 mm3). This sequence was repeated for a total of 16 min with an approximate time resolution of 15.4 s. Gadobenate dimegulumine (MultiHance®, Braaco, Milan, Italy) (0.05 mmol/kg), a gadolinium-based CA, was administered intravenously into the antecubital vein using a power injector, at a rate of 3 mL/s followed by a 25 mL saline flush, 30 s into the DCE scan. Imaging data were processed by ROCKETSHIP. The AIF, which was extracted from an ROI positioned at the internal carotid artery, was fitted with a bi-exponential function prior to fitting analysis with 2CXM.Parametric maps and associated concentration vs. time curves are shown in Fig. 7. Compared to the murine tumor that contains leaky vasculature [41], Ktrans values for the human brain are lower, as expected given the intact blood brain barrier in normal human subjects [6]. As shown in Fig. 7e, the bi-exponential function estimated the AIF well and allowed for a good fit of concentration time curves within the brain parenchyma (Fig. 7f).Fig. 72CXM fitting of a normal human brain. Parameters for Ktrans (a), ve (b), vp (c) and Fp (d) are shown. e shows the AIF used (taken from internal carotid artery). The AIF was fitted with a bi-exponential curve (blue) prior to tissue fitting. f shows a sample time curve from the brain parenchyma (denoted by arrow) with corresponding fit (blue denotes the fit, red lines denote the 95 % prediction bounds for the fitted curve). Fold over artifact is seen on the lateral brain edges due to truncation by the field of view bounding boxFull size imageDiscussionDevelopment and adoption of DCE-MRI by clinicians and researchers requires the availability of analysis software that not only has sufficient functionality for the novice end-user, but also the flexibility and extensibility capability for more complicated analyses. Using its default settings, users can follow ROCKETSHIP’s pipeline to generate parametric maps of common kinetic models. Its modular design allows other models to be incorporated in a straightforward manner.