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Evolving Era of Multidimensional Medical Imaging

1999; Elsevier BV; Volume: 74; Issue: 4 Linguagem: Inglês

10.4065/74.4.399

1942-5546

James B. Seward, Marek Bělohlávek, T. M. Kinter, James F. Greenleaf,

Advanced MRI Techniques and Applications

Currently, computer-assisted imaging can visualize very fast or very slow nonvisible motion events. We can create measurable geometric representations of physiology, including transformation, blood flow velocity, perfusion, pressure, contractility, image features, electricity, metabolism, and a vast number of other constantly changing parameters. The greatest attribute is the ability to present physiologic phenomena as easily understood geometric images more suited to the human's four-dimensional comprehension of reality. The key research challenges are to discover new visual metaphors for representing information, understand the analysis tasks that they support, and associate relevant information to create new information. Currently, computer-assisted imaging can visualize very fast or very slow nonvisible motion events. We can create measurable geometric representations of physiology, including transformation, blood flow velocity, perfusion, pressure, contractility, image features, electricity, metabolism, and a vast number of other constantly changing parameters. The greatest attribute is the ability to present physiologic phenomena as easily understood geometric images more suited to the human's four-dimensional comprehension of reality. The key research challenges are to discover new visual metaphors for representing information, understand the analysis tasks that they support, and associate relevant information to create new information. Geometry is the purest visible expression of number and provides the bridge or ladder by which the mind can achieve its highest level in the realm of pure intelligence. -M. S. Schneider1Schneider MS A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art. and Science; A Voyage From 1 to 10. Harper Collins Publishers, New York1951Google Scholar Reality is what we take to be true. What we take to be true is what we believe. What we believe is based upon our perceptions. What we perceive depends upon what we look for. What we look for depends upon what we think. What we think depends upon what we perceive. What we perceive determines what we believe. What we believe determines what we take to be true. What we take to be true is our reality. -Gary Zukav2Zukav G The Dancing Wu Li Masters: An Overview of the New Physics. William Morrow, New York1979Google Scholar The future of medical imaging, particularly “three dimensional imaging,” lies in our ability to create new and useful information. A three-dimensional image is more realistic in appearance because it contains all three spatial dimensions and thus fosters greater ease of human understanding. The computer-generated three-dimensional organ can be stored, dissected, rearticulated, quantified, and physically replicated3Stewart JE Broaddus WC Johnson JM Rebuilding the visible man.in: Höhne KH Kikinis R Visualization in Biomédical Computing. Springer-Verlag, Berlin1996Google Scholar4MacLellan-Tobert SG Bulthieu J Beiohlavek M Behrenbeck T Greenleaf JF Edwards WD et al.Three dimensional imaging used for virtual dissection; image banking and physical replication of anatomy and physiology.Echocardiography. 1993; 15: 89-98Crossref Scopus (2) Google Scholar and can be viewed as a virtual substitute for the actual living4MacLellan-Tobert SG Bulthieu J Beiohlavek M Behrenbeck T Greenleaf JF Edwards WD et al.Three dimensional imaging used for virtual dissection; image banking and physical replication of anatomy and physiology.Echocardiography. 1993; 15: 89-98Crossref Scopus (2) Google Scholar or autopsied4MacLellan-Tobert SG Bulthieu J Beiohlavek M Behrenbeck T Greenleaf JF Edwards WD et al.Three dimensional imaging used for virtual dissection; image banking and physical replication of anatomy and physiology.Echocardiography. 1993; 15: 89-98Crossref Scopus (2) Google Scholar5Schiemann T Tlede V Hohne KH Segmentation of the visible human (or high-quality volume-based visualization, Med.Image Anal. 1996/1997; 1: 263-270Abstract Full Text Full Text PDF Scopus (60) Google Scholar tissues (Fig. 1 and 2). In comparison with current tomographic or projection imagery, volumetric three-dimensional images more closely replicate an object's actual morphology and contents.8Belohlavek M Foley DA Seward JB Greenleaf JF Diagnostic perfor-mance of two-dimensional versus three-dimensional transesophageal echocardiographic images of selected pathologies evaluated by receiver operating characteristic analysis.Echocardiography. 1994; 11: 635-645Crossref PubMed Scopus (12) Google Scholar9Belohiavek M Manduca A Bulthieu J Greenleaf JF Seward JB Extraction of endocardial boundary from echocardiographic images by means of the Kohonen Self-Organizing Map.Acoust Imaging. 1996; 22: 197-202Crossref Google Scholar The field of imagery has entered a new era made possible primarily by the advent of fast computers, sophisticated imaging software, and computer-generated higher order of information display, all driven by the need for human comprehension.2Zukav G The Dancing Wu Li Masters: An Overview of the New Physics. William Morrow, New York1979Google Scholar10Tufte ER Envisioning Information. Graphics press, Cheshire (CT)1990Google ScholarFig. 2Three-dimensional computed tomographic scans of corrected transposition of the great arteries6Khoury DS Berrier KL Badruddln SM Zoghbi WA Three-dimensional electrophysiological imaging of the intact canine (eft ventricle using a noncontact multielectrode cavity probe: study of sinus, paced, and spontaneous premature beats.Circulation. 1998; 97: 399-409Crossref PubMed Google Scholar in left frontal (left) and transverse sectional (right) views at the posteriorly located pulmonary artery (PA) bifurcation. The aorta (AO) arises anteriorly from the left-sided morphologically right ventricle. The PA arises from the right-sided morphologically left ventricle. Although of lower resolution than the component tomographic images, this three-dimensional anatomic presentation is very understandable by the three-dimensional perception of human vision. RA = right atrium; VER = vertebra. (From Furusho and associates.7Furusho H Hagai H Takamura M Shiraishi K Usuda K Nakamura Y et al.Three-dimensional computed tomography of corrected transposition of the great arteries.Circulation. 1997; 96: 4115PubMed Google Scholar By permission.)View Large Image Figure ViewerDownload (PPT) The prerequisites for state-of-the-art three-dimensional imaging are acquisition, reconstruction, segmentation, and display.11Greenleaf JF Belohlavek IM Gerber TC Foley DA Seward JB Multidimensional visualization in echocardiography: an introduction.Mayo Clin Proc. 1993; 68: 213-220Abstract Full Text Full Text PDF PubMed Scopus (40) Google Scholar, 12Belohlavek M Foley DA Gerber TC Kinter TM Greenleaf JF Seward JB Three-and four-dimensional cardiovascular ultrasound imaging: a new era for echocardiography.Mayo Clin Proc. 1993; 68: 221240Abstract Full Text Full Text PDF Scopus (130) Google Scholar, 13Nanda NC Rahman SMA Khatrt G Agrawal G El-Sayed AA Hassanian MAS et al.Incremental value of three-dimensional echocardiography over transesophageai multiplane two-dimensional echocardiography in qualitative and quantitative assessment of cardiac masses and defects.Echocardiography. 1995; 12: 619-629Crossref Scopus (46) Google Scholar, 14Rohling R Gee A Barman L Three-dimensional spatial compounding of ultrasound images.Med Image Anal 1996/. 1997; 1: 177-193Abstract Full Text Full Text PDF PubMed Scopus (100) Google Scholar Each of these components is in various stages of development; currently, however, in most circumstances, the necessary functions have not been interconnected in a manner conducive to easy or feasible clinical application.5Schiemann T Tlede V Hohne KH Segmentation of the visible human (or high-quality volume-based visualization, Med.Image Anal. 1996/1997; 1: 263-270Abstract Full Text Full Text PDF Scopus (60) Google Scholar In particular, motion (that is, a human perception of the fourth dimension) increases the computational demands of current computers to such an extent that any increase in temporal resolution (motion) greatly compromises spatial resolution (structure) of the reconstructed image. As such, dynamic spatial reconstruction15Robb RA Ritman EL Gilbert BK Kinsey JH Harri LD Wood EH The DSR: a high-speed three-dimensional x-ray computed tomography system for dynamic spatial reconstruction of the heart and circulation.IEEE Trans Nucl Sci. 1979; 26: 2713-2717Crossref Scopus (35) Google Scholar is an uncommon clinical reality at this time. In this new field of three-dimensional imagery, the three principal applications are anatomic (spatial, morphologic, and qualitative), quantitative (dimension, area, volume, and surface), and information display (comprehensible presentation of normally nonvisible motion information, such as electrical fields, blood flow, change, and pressure). Each application is separable yet intertwined with the others in perception and use. Because three-dimensional images are familiar to the human visual sense, structural or anatomic imagery has, to date, received the most attention in the form of artistic rendition and computer simulations of real objects (that is, virtual reality). In particular, high-resolution animation has received considerable emphasis in the entertainment and commercial fields. Conversely, medical three- and four-dimensional structural imagery is a more recent technology and, with few exceptions, is limited primarily by lower spatial resolution than that of the components from which the whole is constructed (Fig. 2).5Schiemann T Tlede V Hohne KH Segmentation of the visible human (or high-quality volume-based visualization, Med.Image Anal. 1996/1997; 1: 263-270Abstract Full Text Full Text PDF Scopus (60) Google Scholar7Furusho H Hagai H Takamura M Shiraishi K Usuda K Nakamura Y et al.Three-dimensional computed tomography of corrected transposition of the great arteries.Circulation. 1997; 96: 4115PubMed Google Scholar16Hong L Kaufman A Wei Y-C Viswambharan A Wax M Liang Z 30 virtual colonoscopy.IEEE Biomed Visualization Suppl. 1996; : 26-32Google Scholar Lower anatomic detail results because the component data from which the three-dimensional image is constructed are relatively dispersed in comparison with the actual anatomy (that is, data pixels or component images are separated by various distances that must be filled in by interpolation). To the less discriminating consumer (a medical or surgical clinician), however, three-dimensional images are often more visually appealing and comprehensible than the component data (Fig. 3). Quantitative imagery optimizes the added spatial information embedded in a volumetric presentation. Currently, volume and surface are usually estimated by geometric assumptions (for example, left ventricular volume is most often fit mathematically to a prolate ellipse solution). The three-dimensional object allows direct measurement of regularly and irregularly shaped geometry without geometric assumptions (that is, a nongeometric technique) (Jakrapanichakul D, Belohlavek M, Tanabe K, Bae RY, Greenleaf JF, Seward JB. Unpublished data). A threedimensional image contains quantifiable spatial information in excess of that conveyed by its components. Thus, volumetric images make quantification of curvilinear distance superior even when the amount of component data used to construct the three-dimensional object is comparatively low. The clinical example is comparison of singleplane, biplane, and octaplane volumetric calculations17Tanabe K Belohlavek M Jakrapanichakul D Bae RY Greenleaf JF Seward JB Three-dimensional echocardiography: precision and accuracy of left ventricular volume measurement using rotational geometry with variable numbers of slice resolution.Echocardiography. 1998; 15: 575-580Crossref PubMed Scopus (30) Google Scholar18Slu SC Rivera JM Handschumacker MD Weyman AE Levlne RA Picard MH Three-dimensional echocardiography: the influence of number of component images on accuracy of left ventricular volume quantitation.J Am Soc Echocardiogr. 1996; 9: 147-155Abstract Full Text PDF PubMed Scopus (33) Google Scholar (Fig. 4 and 5). The larger the number of planes, although substantially less than that needed for anatomic resolution, the closer one comes to calculating the true surface, volume, or shape of the object.21Kosko B Fuzzy Thinking: The New Science of Fuzzy Logic. Hyperion, New York1993Google Scholar Three-dimensional quantification is predicted to have a pronounced and early effect in comparison with current two-dimensional tomographic technology.Fig. 5Imaging electrical phenomena. Top Left, One-dimensional electrocardiogram. Top Right, Two-dimensional planar electrical distribution. (From Kamjoo and associates.19Kamjoo K Uchlda T Ikeda T Fishbein MC Garfinkel A Weise JN et al.Importance of location and timing of electrical stimuli in terminating sustained functional reentry in isolated swine ventricular tissues: evidence in support of a small reentrant circuit.Circulation. 1997; 96: 2048-2060Crossref PubMed Scopus (29) Google Scholar By permission.) Bottom Left, Two-dimensional tomographic echocardiographic Doppler display of local myocardial acceleration (that is, parametric image) coincident with stimulation of the left ventricular posterior wall (red-yellow area). (Photograph courtesy of Dr. Li-Zue Yin, Sichuan Province Hospital, Cheng du Sichuan, China.) Bottom Right, Three-dimensional electrical field in the human heart. The display of electrical physiology is easier to understand as the number of geometric dimensions of display increases. (From Durrer and associates.20Durrer D Van Dam RT Freud GE Janse MJ Meijier FL Anbaecher RC Total excitation of the isolated human heart.Circulation. 1970; 41: 899-912Crossref PubMed Scopus (1291) Google Scholar By permission.)View Large Image Figure ViewerDownload (PPT) Beyond the realism of four-dimensional imagery and the quantification afforded by a three-dimensional solution are yet other, more exciting data presentations that are referred to as information display.22Kaku M Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford University Press, New York1994Google Scholar A unique, clinically relevant image is the computer-assisted presentation of otherwise nonvisible phenomena that exist outside our visible four-dimensional spatiotemporal domain. A plethora of physiologic events are either so brief (for example, electrical depolarization) or so long (for example, aging) in duration that their progression (motion and distribution) cannot be perceived by the normal human senses. Our normal registration faculties perceive very rapid or very slow events (for example, color, electricity, temperature, smell, texture, remodeling, and aging) as continuous.1Schneider MS A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art. and Science; A Voyage From 1 to 10. Harper Collins Publishers, New York1951Google Scholar Information imagery takes maximum advantage of logical associations of multidimensional data in order to create unique images of otherwise nonvisible motion phenomena. These phenomena are most vividly understood through computer manipulation of data and presented as a multidimensional image (Fig. 6). Because multidimensional information is comprehensible in no other manner, very low resolution data can create meaningful depictions of dynamic information (Fig. 5). The distinctive features of the information image are (1) the processing of changing phenomena as time-lapse events with use of computers, (2) quantification of these events as individual quanta (for example, parameterized pixels) or static or changing volumetric distributions, and (3) comprehensible visualization of these otherwise nonvisible dynamic phenomena. This article focuses on the concept of information medical imaging as a most valuable and achievable approach to our visual comprehension of reality. Of most importance, this imaging solution adds new knowledge to our understanding of medical physiology. No more than three directions are needed to describe every permeation of physical space in our domain; hence, we call our space three-dimensional (Fig. 6). The three spatial dimensions of an object are height, length, and width. To these three dimensions, the dimension of time is added to complete the picture of our comprehensible space. In our reality, space and time cannot be disconnected and are presented to the human senses as a series of events.23Rucker RB The Fourth Dimension: A Guided Tour of the Higher. Universes, Boston; Houghon Mittlin1984Google Scholar To the human reality, the events of motion (space and time) are the best perception of the time domain (that is, space-time continuum).2Zukav G The Dancing Wu Li Masters: An Overview of the New Physics. William Morrow, New York1979Google Scholar Thus, imagery that creates our visual state of reality is referred to as “four-dimensional imaging.” Within our reality, an infinite number of temporal phenomena can be perceived and measured but not actually seen by our visual senses. These nonvisible phenomena are a part of our infinitely rich time domain. If time is the fourth dimension, how can these other events be described and appreciated? Motion is the visible extension of the fourth dimension, and nonvisible fourth-dimensional temporal events are referred to as “higher dimensional.”22Kaku M Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford University Press, New York1994Google Scholar This should not be confused with the theoretical existence of dimensions beyond the fourth dimension. All matter, including ourselves, is determined by “motion information,” and “events of this information motion” determine our perception of space and time.2Zukav G The Dancing Wu Li Masters: An Overview of the New Physics. William Morrow, New York1979Google Scholar23Rucker RB The Fourth Dimension: A Guided Tour of the Higher. Universes, Boston; Houghon Mittlin1984Google Scholar With use of increasingly sophisticated computers, the temporal domain can be altered, and these events can be displayed as cinematic geometric images. Because the components (pixels) and the geometry are numerically expressed (parameterized), these information images are eminently quantifiable. There is considerable interest in obtaining high-resolution three-dimensional virtual images. Because of the limitations of current computer technology, however, three-dimensional anatomic images are of relatively low resolution, particularly when applied to living organ systems or to the dynamic display of motion. Currently, medical use is confined to gross anatomic replication and virtual interaction with volume or surface renditions of organ systems.5Schiemann T Tlede V Hohne KH Segmentation of the visible human (or high-quality volume-based visualization, Med.Image Anal. 1996/1997; 1: 263-270Abstract Full Text Full Text PDF Scopus (60) Google Scholar24Kupferwasser I Mohr-Kahaly S Stahr P Rupprecht H-J Nlxdorff U Fenster M et al.Transthoracic three mensional echocardiographic volumetry of distorted left ventricles using rotational scanning.J Am Soc Echocardiogr. 1997; 10: 840-852Abstract Full Text Full Text PDF PubMed Google Scholar Usable three-dimensional quantification, however, can tolerate lower-resolution images while obtaining information superior to the component data set. As one goes from three-dimensional anatomy to quantification of objects, the resolution of the volumetric information can be lower (that is, lower spatial resolution).18Slu SC Rivera JM Handschumacker MD Weyman AE Levlne RA Picard MH Three-dimensional echocardiography: the influence of number of component images on accuracy of left ventricular volume quantitation.J Am Soc Echocardiogr. 1996; 9: 147-155Abstract Full Text PDF PubMed Scopus (33) Google Scholar25Gopal AS Schnellbaecher MJ Shen Z Akinboboye OO Sapin PM King DL Freehand three-dimensional echocardiography for measurement of left ventricular mass: in vivo anatomic validation using explanted human hearts.J Am Coll Cardiol. 1997; 30: 802-810Abstract Full Text Full Text PDF PubMed Scopus (86) Google Scholar, 26Leotta DF Munt B Bolson EL Kraft C Martin RW Otto CM et al.Quantitative three-dimensional echocardiography by rapid imaging from multiple transthoracic windows: in vitro validation and initial in vivo studies.J Am Soc Echocardiogr. 1997; 10: 830839Google Scholar, 27Nosir YF Fiorettl PM Vlerter WS Boerama E Salustri A Postma JT et al.Accurate measurement of left ventricular ejection fraction by three Dimensional echocardiography: a comparison with radionuclide angiography.Circulation. 1996; 94: 460-466Crossref PubMed Scopus (158) Google Scholar Consequently, acquisition of data can be faster (that is, higher temporal resolution).28Belohlavek M Seward JB Rapid image acquisition and automatad determination of left ventricular cavity boundary for precise and accurate volumetry by clinical three-dimensional echocardiography [abstract].J Am Coll Carüiol. 1997; 29: 57AGoogle Scholar The current state of the art is that fast-data-collection, low-resolution three- and four-dimensional imagery is feasible. In contrast, slow-acquisition, complex-processing, high-resolution imagery, although feasible, necessitates the greatest data density and complexity and is not currently available.3Stewart JE Broaddus WC Johnson JM Rebuilding the visible man.in: Höhne KH Kikinis R Visualization in Biomédical Computing. Springer-Verlag, Berlin1996Google Scholar17Tanabe K Belohlavek M Jakrapanichakul D Bae RY Greenleaf JF Seward JB Three-dimensional echocardiography: precision and accuracy of left ventricular volume measurement using rotational geometry with variable numbers of slice resolution.Echocardiography. 1998; 15: 575-580Crossref PubMed Scopus (30) Google Scholar With use of computer technology, displays of otherwise nonvisible motion information can also be brought into a more familiar four-dimensional presentation. These images tolerate very fast collection and low spatial resolution because the events are otherwise nonvisible. The most important effect of the initial application of advanced computer technology will be the generation of new knowledge through imagery of otherwise nonvisible motion phenomena. In medicine, this can be viewed as multidimensional physiology, mathematically displayed as two-, three-, or four-dimensional images.29Mor-Avi V Vlgnon P Koch R Weinert L Garcia MJ Spencer KT et al.Segmental analysis of color kinesis images: new method for quantification of the magnitude and timing of endocardial motion during left ventricular systole and diastole.Circulation. 1997; 95: 2062-2097Crossref Scopus (138) Google Scholar, 30Belohlavek M Foley DA Gerber TC Greenleaf JF Seward JB Three dimensional reconstruction of color Doppler jets in the human heart.J Am Soc Echocardiogr. 1994; 7: 553-560PubMed Scopus (54) Google Scholar, 31Bardinet E Cohen LO Ayache N Tracking and motion analysis of the left ventricle with deformable superquadrics.Med Image Anal. 1996; 1: 129-149Abstract Full Text Full Text PDF PubMed Scopus (125) Google Scholar, 32Ensing G Seward J Darragh R Caldwell R Feasibility of generating hemodynamic pressure curves from noninvasive Doppler echocardiographic Signals.J Am Coll Cardiol. 1994; 23: 434-442Abstract Full Text PDF PubMed Scopus (36) Google Scholar, 33Gorce J-M Friboulet D Magnln IE Estimation of three-dimensional cardiac velocity fields; assessment of a differential method and application to three-dimensional CT data.Med Image Anal. 1996/1997; 1: 245-261Abstract Full Text Full Text PDF Scopus (43) Google Scholar A mythical story written in 1884 by Edwin Abbott Abbott, a clergyman, describes Flatland, in which all inhabitants live in a two-dimensional world.34Abbott EA Flatland: A Romance of Many Dimensions. Dover Publications, New York1992Google Scholar The Flatlander lives as if on the surface of a piece of paper. When a line is encountered, the Flatlander must navigate around this barrier. A Spacelander, or Spherelander,35Burger D Sphereland: A Fantasy About Curved Spaces and an Expanding Universe. HarperPerennial, New York1994Google Scholar a three-dimensional being, looking at this situation immediately sees the solution and simply steps over the line. The Flatlander, however, has no concept of the third dimension and is eternally captured by simple lines. The Flatlander cannot see beyond two-dimensional reality and when confronted with this knowledge can only vaguely understand the higher dimension. Thus, higher-dimensional beings can easily visualize lower-dimensional objects, but lower-dimensional beings can visualize only sections or shadows of higher-dimensional objects.36Kaku M Thompson J Beyond Einstein: The Cosmic Quest for the Theory of the Universe. Doubleday, New York1987Google Scholar Just as two-dimensional beings can perceive only shadows of the nonvisible third spatial dimension, a three-dimensional being cannot see all forms of motion. The three-dimensional human can only imagine or produce visual “shadows” of these otherwise nonvisible phenomena. Comments by Banesh Hoffmann in the introduction to the Dover edition of Flatland latland show insight into the illusive dimension of time.34Abbott EA Flatland: A Romance of Many Dimensions. Dover Publications, New York1992Google Scholar The fourth [dimension] is temporal; and we are unable to move freely in time. We cannot return to days gone by, nor avoid the coming of tomorrow. We can neither hasten nor retard our journey into the future. We are like hapless passengers on a crowded escalator, carried relentlessly forward till our particular floor arrives and we step off into a place where there is no time, while the material composing our bodies continues its journey on the inexorable escalator-perhaps forever.… In Flatland we could escape from a two-dimensional prison by stepping momentarily into the third dimension and coming back on the other side of the prison wall. But that is because this third dimension is spatial. Our fourth dimension, time, true dimension though it be, does not permit us to escape from a three-dimensional prison. It does enable us to get out, for if we wait patiently for time to pass, our sentence will be served and we shall be set free. That is hardly an escape, however. To escape we must travel through time to some moment when the prison is wide open, or in ruins, or not yet built; and then, having stepped outside, we must reverse the direction of our time travel to return to the present. Neither we nor the inhabitants of Flatland can travel thus through time. The line has magnitude in one way, the plane in two ways, and the solid in three ways; beyond these, no other magnitude exists because these three are all that are needed. In AD 150, Ptolemy actually proved that it was impossible to visualize the fourth dimension with our three-dimensional brains, and for several thousand years, mathematicians repeated this simple but fatal mistake that the fourth dimension cannot exist because we cannot visually picture it in our minds. Thus, the dimensions of all things were described by height, width, and depth.22Kaku M Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford University Press, New York1994Google Scholar In 1854, the German mathematician Bernhard Riemann replaced Ptolemy's vision of the three-dimensional world. Riemann concluded that phenomena such as electricity, magnetism, and gravity were intertwined in our three-dimensional universe as an unseen fourth dimension. Riemann, however, did not specifically know the manner in which gravity or electricity and magnetism caused the warping of space.22Kaku M Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford University Press, New York1994Google Scholar It was not until 1905 that Einstein, at the age of 26 years, succeeded where Riemann had failed. Einstein introduced “relativity,” which referred to the elementary fact that the appearance of the world around us depends on our state of motion. Einstein first introduced the theory of special relativity, which joined the three physical dimensions with the fourth dimension of time. The fourth dimension, a temporal dimension, was the dimension beyond length, breadth, and width. In 1915, the theory of general relativity explained gravitation as the marriage of space-time and matter-energy. Bending of space was directly related to the amount of energy and matter within the space. These theories of the fourth dimension would forever change the course of human history. Today, only a few classic examples exist of static visual depictions of the fourth dimension (for example, Picasso's painting Portrait of Dora Maar; Salvador Dali's Christus Hypercubus; hypercube; and Klein bottle).22Kaku M Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford University Press, New York1994Google Scholar36Kaku M Thompson J Beyond Einstein: The Cosmic Quest for the Theory of the Universe. Doubleday, New York1987Google Scholar Tricks (for example, advanced image manipulation), however, can be used to visualize temporal dimension as geometric objects.23Rucker RB The Fourth Dimension: A Guided Tour of the Higher. Universes, Boston; H