Max A. Viergever

Medical image matching-a review with classification

A classification scheme for multimodal image matching is considered. The scope of the classification is restricted to methods that register data after acquisitions. The classification scheme may be used for any modality; not only for (2-D) projection images and (3-D) tomographic images, but also for other signal modalities that provide spatial insight into function or anatomy, e.g., EEG (electroencephalography) or MEG (magnetoencephalography) and for the real physical patient. The available literature on image matching is discussed and classified.<<ETX>>

Mechanics of Hearing

The performance of the external ear, when viewed as a diffuse-field receiver, is given in a simple expression containing two acoustic impedances. In this sense, the external ear has a high frequency performance quite close to the theoretical limit. Viewed as a directional antenna the external ear is an acoustical wave processor of considerable complexity. Approximately eight normal modes spread over nearly three octaves are required to account for its distinctive characteristics. At the highest frequencies, additional wave factors come into play near the eardrum. Network, concepts are well suited to the mechanics of the middle ear but require considerable development to allow for the complex motion of the eardrum which is the dominant factor at high frequencies. Considerable progress has been made with a two-piston model which gives reasonable eardrum impedance and middle ear transmission curves. This model shows that, at high frequencies, it is the internal resistance of the eardrum that absorbs most of the incident sound energy and controls middle ear transmission. A more sophisticated treatment of eardrum motion may soon be within reach. 1. RECEPTION IN A DIFFUSE SOUND FIELD The primary function of the external ear, the collection of acoustical energy, can be quantified in a precise manner by performing a mental experiment in which the ear is first a receiver and then a transmitter. Hence, by invoking the acoustical reciprocity theorem, it can be shown (Shaw 1979) that the power P, absorbed at the eardrum, when the ear is immersed in a a diffuse sound field of mean square pressure p 2 , is determined in essence by two impedances as follows: Pd = (X2/47r)|4nRaRd/ Za+Zd 2] pf2/pc (1) In this expression, Z is the acoustic impedance seen by the eardrum looking a outward through the external ear, Z, is the impedance presented to the d external ear by the middle ear system, R and R are the resistive parts of a d these impedances, and X is the wavelength of sound. When Z is the conjugate a of Z, and when the radiation efficiency n is 100% (no sound absorption d between the eardrum and the diffuse field), the power received at the eardrum has its greatest possible value P = ( X2/4tt) (pf2/pc). (2) This is the total power flowing through a transparent sphere of crosssectional area X2/4tt (radius X/2tt) when immersed in the same diffuse sound

Validity of the Liouville--Green (or WKB) method for cochlear mechanics.

This article presents a comparison of Liouville-Green (LG) calculations and exact solutions of 2- and 3-dimensional cochlea models. The agreement is in general quite good. For certain choices of the model parameters, however, the 2- and 3-dimensional LG solutions show appreciable errors in the region just beyond the location of maximum amplitude of the basilar membrane response. The origin of these errors appears to be the non-uniqueness of the (complex) LG wave number k(x) in 2- and 3-dimensional models: the eikonal equation from which k(x) has to be solved has multiple roots. To study this problem somewhat deeper, the properties of the locus of k=k(x) formed when x is varied, are investigated. Erratic behaviour of the LG solution is found to occur when this root locus approaches one of the saddle points of a complex function of k- called Q(k)- which plays the major role in the eikonal equation. Apart from this specific problem, the LG approximation is very well suited to unravel the mechanisms governing wave propagation and attenuation in the cochlea. The analysis shows clearly why and how the response of the basilar membrane builds up to a maximum and which factors cause a turnover and a rapid decrease to occur, in both the long-wave and the short-wave cases. A special discussion is dedicated to the relation between the LG approximation and the absence of wave reflection in cochlea models of the type studied.

Cochlear power flux as an indicator of mechanical activity

The question of whether one can conclude just from basilar membrane (BM) vibration data that the cochlea is an active mechanical system is addressed. To this end, a method is developed which computes the power flux through a channel cross section of a short-wave cochlear model from a given BM vibration pattern. The power flux is an important indicator of mechanical activity because a rise in this function corresponds to creation of mechanical energy. The power flux method is applied to BM velocity patterns as measured by Johnstone and Yates [J. Acoust. Soc. Am. 55, 584-587 (1974)] and by Sellick et al. [Hear. Res. 10, 101-108 (1983)] in the guinea pig and by Robles et al. [Peripheral Auditory Mechanisms, edited by J.B. Allen, J.L. Hall, A.E. Hubbard, S.T. Neely, and A. Tubis (Springer, New York, 1986a), pp. 121-128, and J. Acoust. Soc. Am. 80, 1364-1374 (1986b)] in the chinchilla. Before the calculations are performed, the BM data are interpolated and smoothed in order to avoid numerical errors as a result of too few and noisy data points. The choice of the smoothing method influences the computed power flux function considerably. Nevertheless, the calculations appear to make a clear distinction between the old data, showing broad BM tuning (Johnstone and Yates, 1974), and the new data, in which the response is much more peaked (Sellick et al., 1983; Robles et al., 1986a, b). The former do not give rise to a significant increase of the power flux; the latter do, although less convincingly for the Sellick et al. (1983) data than for the Robles et al. (1986a,b) data. It is thus concluded that the recently obtained, sharply tuned BM responses reflect the presence of mechanical activity in the cochlea.

Mutual information matching and interpolation artifacts

Registration algorithms often require the estimation of grey values at image locations that do not coincide with image grid points. Because of the intrinsic uncertainty, the estimation process will invariably be a source of error in the registration process. For measures based on entropy, such as mutual information, an interpolation method that changes the amount of dispersion in the probability distributions of the grey values of the images will influence the registration measure. With two images that have equal grid distances in one or more corresponding dimensions, a large number of grid points can be aligned for certain geometric transformations. As a result, the level of interpolation is dependent on the image transformation and hence, so is the interpolation-induced change in dispersion of the histograms. When an entropy based registration measure is plotted as a function of transformation, it will show sudden changes in value for the grid-aligning transformations. Such patterns of local extrema impede the optimization process. More importantly, they rule out subvoxel accuracy. Interpolation-induced artifacts are shown to occur in registration of clinical images, both for trilinear and partial volume interpolation. Furthermore, the results suggest that improved registration accuracy for scale-corrected MR images may be partly accounted for by the inequality of grid distances that is a result of scale correction.

Realistic mechanical tuning in a micromechanical cochlear model

Two assumptions were made in the formulation of a recent cochlear model [P.J. Kolston, J. Acoust. Soc. Am. 83, 1481-1487 (1988)]: (1) The basilar membrane has two radial modes of vibration, corresponding to division into its arcuate and pectinate zones; and (2) the impedance of the outer hair cells (OHCs) greatly modifies the mechanics of the arcuate zone. Both of these assumptions are strongly supported by cochlear anatomy. This paper presents a revised version of the outer hair cell, arcuate-pectinate (OHCAP) model, which is an improvement over the original model in two important ways: First, a model for the OHCs is included so that the OHC impedance is no longer prescribed functionally; and, second, the presence of the OHCs enhances the basilar membrane motion, so that the model is now consistent with observed response changes resulting from trauma. The OHCAP model utilizes the unusual spatial arrangement of the OHCs, the Deiters cells, their phalangeal processes, and the pillars of Corti. The OHCs do not add energy to the cochlear partition and hence the OHCAP model is passive. In spite of the absence of active processes, the model exhibits mechanical tuning very similar to those measured by Sellick et al. [Hear. Res. 10, 93-100 (1983)] in the guinea pig cochlea and by Robles et al. [J. Acoust. Soc. Am. 80, 1364-1374 (1986)] in the chinchilla cochlea. Therefore, it appears that mechanical response tuning and response changes resulting from trauma should not be used as justifications for the hypothesis of active processes in the real cochlea.

Nonlinear and active two‐dimensional cochlear models: Time‐domain solution

A numerical solution method for two-dimensional (2-D) cochlear models in the time domain is presented. The method has particularly been designed for models with a cochlear partition having nonlinear and active mechanical properties. The 2-D cochlear model equations are reformulated as an integral equation for the acceleration of the basilar membrane (BM). This integral equation is discretized with respect to the spatial variable to yield a system of ordinary differential equations in the time variable. To solve this system, the variable step-size, fourth-order Runge-Kutta method described in Diependaal et al. [J. Acoust. Soc. Am. 82, 1655-1666 (1987)] is used. This method is robust and computationally efficient. The incorporation of a simple middle-ear model can be handled by this method. The method can also be extended to models in which the cochlear partition at each point along its length is represented by more than one degree of freedom.

Wave propagation and dispersion in the cochlea

Insight into cochlear mechanics can be obtained from semi-analytical and asymptotic solution methods of which the Liouville -Green (LG) method - in another context known as the WKB method - is the most important one. This paper describes the dispersion properties of fluid waves in general terms and develops the LG formulation on that basis. The eikonal equation of the LG method is shown to be identical to the dispersion relation in dispersive-wave theory. Consideration of the group velocity then leads to the derivation of the central LG formula as it has been used in an earlier paper on the LG method ( Boer , E. and Viergever , M.A. (1982): Hearing Res. 8, 131-155). The formulation appears to apply as well to dissipative and active (i.e., energy-producing) systems. Of the many possible collateral subjects two are selected for a deeper discussion: amplification, concentration and expansion of energy, and the problem of reflection of cochlear waves. In the latter context, it is shown why - and under which conditions - cochlear waves are not reflected, despite the large degree of dispersion that they show. The analysis brings to light a fundamental asymmetry of the model regarding the direction of wave travel: waves travelling in the direction opposite to the normal one are likely to undergo reflection, while waves in the normal direction are not reflected.

What type of force does the cochlear amplifier produce

Recent experimental measurements suggest that the mechanical displacement of the basilar membrane (BM) near threshold in a viable mammalian cochlea is greater than 10(-8) cm, for a stimulus sound-pressure level at the eardrum of 20 microPa. The associated response peak is very sensitive to the physiological condition of the cochlea. In the formulation of all recent cochlear models, it has been explicitly assumed that this peak is produced by the cochlear amplifier injecting a large amount of energy into the cochlea, thereby altering the real component of the BM impedance. In this paper, a new cochlear model is described which produces a realistic response by assuming that the cochlear amplifier force acts at a phase such that the main effect is to reduce the imaginary component of the BM impedance. In this new model, the magnitude of the cochlear amplifier force required to produce a realistic response is much smaller than in the previous models. It is suggested that future experimental investigations should attempt to determine both the magnitude and the phase of the forces associated with the cochlear amplifier.

Marker-guided multimodality matching of the brain

applications there is a need for integration of the information obtained, as different modalities usually provide complementary information. Complete comprehension of a medical case in clinicians mind is facilitated by an integrated multimodal approach. Combining the diverse sources of information is difficult, not only because of the distinct physical reality represented by each technique, but especially because of the variations in patient positioning during the various studies and the use of different parameters for slice thickness, interslice gap, pixel size and angulation. This paper presents a patient-friendly matching method for brain studies of different modalities. The method, based on skin markers, supports CT, MRI, singlephoton emission CT (SPECT), electroencephalographic (EEG) and magnetoencephalographic (MEG) studies and requires no special patient positioning. The design of the marker allows high-accuracy matching even in images with large slice spacing. At the University Hospital Utrecht marker-guided matching is applied in clinical protocols concerning epilepsy surgery planning, brain ischaemia, and rolandic epilepsy in childhood. Some examples of these applications are presented to illustrate the feasibility of the matching method. Detailed results on those clinical studies will be described in future papers.