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Medical Images and Physiological Signals

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Anatomy and Physiology of the Circulatory and Ventilatory Systems

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Abstract

Many visualization techniques are available to explore the cardiovascular system from usual ultrasound echography and velocimetry, multislice spiral computed tomography particularly for cardiac imaging, and magnetic resonance imaging for blood flow assessment, to magnetocardiography, diode laser, and optical coherence tomography. Functional magnetic resonance imaging is based on increased blood flow gushing in target regions that are responding to imposed stimuli. Ultrasound scattering from Rayleigh fractal aggregates is proposed for imaging flow dynamics of deformable or hardened red cell clusters in dense suspension.

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Notes

  1. 1.

    The wavelength is reduced in the human body according to the permittivity and conductivity of crossed tissues.

  2. 2.

    Diffusion of water within a tissue excited by a magnetic field gradient causes MRI signal attenuation. The eigenvectors and eigenvalues of the voxel-averaged diffusion tensor specify the principal directions and rates of water diffusion in each voxel of the tissue image. The eigenvector corresponding to the maximum eigenvalue of the diffusion tensor points in the direction of maximum rate of diffusion assumed to be the direction of the axis of a cylindrical fiber. The orientation of the eigenvectors can be defined by inclination and transverse angles. The inclination angle of the myofiber is the angle between: (1) the intersection line of the image plane and the plane parallel to the epicardial tangent plane at the corresponding azimuthal position (tangent plane); and (2) the projection of the eigenvector onto the tangent plane. The transverse angle is the angle between: (1) the intersection line, and (2) the projection of the eigenvector onto the image plane. The correlation has been checked by experiments performed in an excised portion of the right ventricle by comparison of DTMRI and histology myofiber angles [23, 24], but DTMRI time and space resolutions, especially in vivo, were too large to get an accurate map of myofiber angles. More recently, space resolution of 310 to 390 μm in the slice plane with a slice thickness of 0.8 to 1 mm has been obtained in isolated dog hearts [25]. These authors extract 2 local angles, the myofiber main axis angle and the cross-sheet (from endocardium to epicardium) angle. The myofiber angle is defined by the angle between the local circumferential tangent vector of the reconstructed mesh of the heart wall and projection of the primary eigenvector of the voxel-related water diffusion tensor onto the epicardial tangent plane. The cross-sheet angle is determined by the radial vector and the projection of the tertiary eigenvector of the diffusion tensor, which is parallel to the cardiac sheet normal, onto the plane defined by the radial and circumferential vectors. Images can be obtained using a slice-selection fast spin-echo diffusion-weighted technique coupled with gradient recalled acquisition in the steady-state (GRASS) imaging mode to define epicardial and endocardial surfaces [26].

  3. 3.

    The diffusivities along the 3 principal axes of the ellipsoid.

  4. 4.

    The displacement of the aortic valve has been estimated to be equal to 15–20 mm.

  5. 5.

    Comb excitation enables simultaneous tagging in multiple parallel planes during breathhold.

  6. 6.

    IVUS-based virtual histology results from signal processing by autoregressive spectral analysis of radiofrequency ultrasound backscatter signals to assess plaque composition that is not complex. However, necrotic cores that surround calcified zones can be artefacts. Wavelet analysis of radiofrequency US signals represents an alternative modality.

  7. 7.

    Displacement of the tissue between 2 images can be used to assess the bulk rheology of a region of interest of the explored tissue. Elastographic scanning maps strain magnitude (image brightness) and sign (color hue associated with compression or distention, for instance).

  8. 8.

    Broad bandwidth lights can be generated from superluminescent diodes or femtosecond laser pulses.

  9. 9.

    IVUS technique has a 100 μm axial resolution.

  10. 10.

    Elastin serves as the axial backbone of alveolar ducts and alveolar entrances. It also resides in the sheath of extraalveolar microvessels.

  11. 11.

    Vessel bore and wall smoothness depend on the threshold.

  12. 12.

    The snakes are dilated by external and internal forces using a finite element method to solve the minimization problem, only taking into account the suitable edge points that have been extracted by an edge detector.

  13. 13.

    The contour is then defined as the location of the maxima of the gradient of the image intensity in the gradient direction. Vascular modeling relies on the assumption of a Gaussian intensity profile with a first derivative maximal at the vessel wall and a second derivative maximal on the vessel axis, the vessel being supposed to have a circular cross section. When the vessel axis is determined and local radii are estimated, the vessel wall is reconstructed.

  14. 14.

    In straight pipes, the axial pressure difference, which varies either nonlinearly in the entry length or linearly when the flow is fully developed, is exhibited in any duct section that is not normal to the centerline.

  15. 15.

    The surface element size depends on the local surface curvature. The stronger the curvature, the smaller the size.

  16. 16.

    Quickly varying pressures must be measured by transducers, which convert pressures into electrical signals, able to accurately sense high frequencies. Sensitivity, linear output for the whole pressure range, suitable frequency response, and spatial resolution are the main features of transducers. In particular, the transducer size must be smaller than the distance over which exist spatial pressure variations.

  17. 17.

    The nonlinear soliton equation was developed by D.J. Korteweg and G. de Vries at the end of the nineteenth century. The nonlinear term balances the dispersion. The existence and uniqueness of solution to the Cauchy problem for the nonlinear Korteweg–de Vries equation and local controllability around the origin given by the nonlinear term has been proved [93]. Signal processing using progressive wave speed analysis is more appropriate than employing frequency analysis suitable for stationary waves.

  18. 18.

    The soliton is a wave that propagates without dispersion. Solitons interact without losing their identity, keeping shape and amplitude. An n-soliton solution refers to n components of different amplitude that interact. The propagation speed is proportional to wave amplitude. The higher the amplitude, the faster the propagation. Soliton solutions are used to model fast dynamics of pressure wave propagation and an associated windkessel model to take slow dynamics into account.

  19. 19.

    The second wave of the 2-soliton model is associated with the dicrotic wave due to the aortic valve closure. The 3-soliton model is used to fit bifid pressure waves. A bifid curve exhibits an incisure in the ascending systolic part near the peak value rather than an usual monotonic soaring aspect.

  20. 20.

    Blood resistivity depends on blood flow [109] and hematocrit [110].

  21. 21.

    The resistivity of the lungs is approximately 20 times that of the blood.

  22. 22.

    The resistivity of bones increases about a 100-fold with respect to blood.

  23. 23.

    Electric and magnetic leads are different. The signal-to-noise ratio for the electrical and magnetic recordings are affected by different factors. Although the electrical resistivity of the lung parenchyma is relatively high, the magnetic permeability of body tissues resembles that of a free space, allowing easy recordings from the posterior face of the thorax.

  24. 24.

    Magnetocardiographic signals have been computed using a model with a source represented by an uniform double layer and with a heterogeneous, multicompartmental model of the thorax, the geometry of which is derived from magnetic resonance imaging [124]. Computed and measured magnetic signals were in good agreement. The magnetocardiogram and electrocardiogram have a common basis.

  25. 25.

    The propagation speed of sound waves at 310 K is equal to 354, 357, and 352 m/s in partially humidified air, in air saturated with water vapor, and in exhaled air, respectively.

  26. 26.

    \(\upsigma _{t}^{2}\, \propto \,\overline{\mathcal{D}}_{\mathrm{app}}\bar{t}/V _{q}^{2}\), where \(\mathcal{D}_{\mathrm{app}}/\mathcal{D}\ =\ \kappa \mathrm{Pe}_{T}^{2}\) (Pe T : Péclet number in the trachea) varies according to literature data both at inspiration (1.1–1.5) and expiration (0.4–0.5) [132, 133].

  27. 27.

    The association speed of carbon monoxide on hemoglobin is slower than that of oxygen, but its dissociation rate is a thousand times slower than its association rate. Carbon monoxide is thus said to have a high affinity for hemoglobin.

  28. 28.

    The usual tracer is radiolabeled diethylenetriaminepentaacetic acid (DTPA).

  29. 29.

    The clearance \((dQ/dt)/cV\) (dimension: T −1) is the flux of tracer (dQ∕dt, Q: substance quantity) divided by the luminal tracer content, the latter being the product of tracer luminal concentration c by volume V of airway surface film, itself the product of the airway surface area (tracer uptake area) by the liquid film thickness. The uptake rate can also be evaluated from the decay rate constant, assuming a monoexponential relationship with time, although the clearance can follow a biexponential evolution. The clearance of DTPA from human lungs ranges 0.59–1.56.10−2/s, with a mean of about 10−2/s, varying with the aerosol size and the working group [142].

  30. 30.

    The population comprises 114 volunteers, 27 to 58-yr old, with 15 nonsmokers, and 43 ex-smokers. Smoking habits have been defined according to the amount (1 cigar being equivalent to 5 cigarettes, 1 cigarillo to 2 cigarettes, 1 g of tabacco to 1 cigarette), to the quality (with or without smoke inhalation), ex-smokers being subdivided into 2 groups whether they have stopped more than one month or more than one year. Slight smokers were defined by less than 5 cigarettes per day over any period of time or more than 5 cigarettes per day for less than one year. Smokers include 2 categories, according to the existence of respiratory symptoms.

  31. 31.

    Transit time moments are computed using the entire maneuver. They then depend on the effort performed at the end of the test. Forced expirations terminate more or less prematurely, at unrepeatable times in a given subject. A better repeatability is obtained using truncated spirograms. The values then strongly depend on the arbitrary chosen threshold.

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  1. Project-team INRIA-UPMC-CNRS REO Laboratoire Jacques-Louis Lions, CNRS UMR 7598, Université Pierre et Marie Curie, Place Jussieu 4, 75252, Paris Cedex 05, France

    Marc Thiriet

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Thiriet, M. (2014). Medical Images and Physiological Signals. In: Anatomy and Physiology of the Circulatory and Ventilatory Systems. Biomathematical and Biomechanical Modeling of the Circulatory and Ventilatory Systems, vol 6. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9469-0_5

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