A semi-automated approach towards generating three-dimensional mesh of the heart using a hybrid MRI/histology database

Both the forward and inverse problems of electrocardiography rely on the precise modelling of the anatomic and electrical properties of the thoracic tissues. This, in turn, requires good knowledge of the electrical anisotropy as well as conductivity inhomogeneity of the heart, lungs and the rest of the thorax. Cardiac electrical anisotropy is related to its microstructure (fibre length, density and orientation). We hereby present detailed three-dimensional (3D) meshes of the thorax and heart, using image data from contiguous 2D magnetic resonance (MR) imaging slices as well as a realistic 3D cardiac fibre orientation model that derives its data from high-resolution ex vivo human heart MR images and from histology specimens of heart tissue. Using specific software, we integrated the 3D thorax and heart meshes in one that addresses the related modelling requirements for the solution of the forward and inverse problems of electrocardiography.     

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes.

The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation.

In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola–Kirchhoff active stress tensor.

As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.     

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria - the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.     

A finite element model of the human left ventricular systole

Local wall stress is the pivotal determinant of the heart muscle's systolic function. Under in vivo conditions, however, such stresses cannot be measured systematically and quantitatively. In contrast, imaging techniques based on magnetic resonance (MR) allow the determination of the deformation pattern of the left ventricle (LV) in vivo with high accuracy. The question arises to what extent deformation measurements are significant and might provide a possibility for future diagnostic purposes. The contractile forces cause deformation of LV myocardial tissue in terms of wall thickening, longitudinal shortening, twisting rotation and radial constriction. The myocardium is thereby understood to act as a densely interlaced mesh. Yet, whole cycle image sequences display a distribution of wall strains as function of space and time heralding a significant amount of inhomogeneity even under healthy conditions. We made similar observations previously by direct measurement of local contractile activity. The major reasons for these inhomogeneities derive from regional deviations of the ventricular walls from an ideal spheroidal shape along with marked disparities in focal fibre orientation. In response to a lack of diagnostic tools able to measure wall stress in clinical routine, this communication is aimed at an analysis and functional interpretation of the deformation pattern of an exemplary human heart at end-systole. To this end, the finite element (FE) method was used to simulate the three-dimensional deformations of the left ventricular myocardium due to contractile fibre forces at end-systole. The anisotropy associated with the fibre structure of the myocardial tissue was included in the form of a fibre orientation vector field which was reconstructed from the measured fibre trajectories in a post mortem human heart. Contraction was modelled by an additive second Piola-Kirchhoff active stress tensor. As a first conclusion, it became evident that longitudinal fibre forces, cross-fibre forces and shear along with systolic fibre rearrangement have to be taken into account for a useful modelling of systolic deformation. Second, a realistic geometry and fibre architecture lead to typical and substantially inhomogeneous deformation patterns as they are recorded in real hearts. We therefore, expect that the measurement of systolic deformation might provide useful diagnostic information.     

A computational method for developing hierarchical large deformation viscoelastic models of the contracting heart

In this study, a new computational method for modelling the contracting heart is described. Using this method, the cardiac wall is constructed from basic, repeating contractile units that represent individual myocardial units and collagen, each with its own set of parameters, including orientation, passive and active behaviour and stimulation propagation. The method allows individual control of each structural unit (e.g. at the level of a single myocardial unit). Feasibility of modelling dynamic heart contraction using this method is demonstrated using 2D cross-sections and simplified 3D geometries. Effects of non-contractile scar and myopathic tissue were also tested in these geometrical configurations. Results from the 2D and 3D simulations were, overall, in agreement with well-established physiological data. The present method holds promise for modelling complex heart pathologies, abnormal mechanical properties (e.g. myocardial infarcts) and electrical conduction properties (branch blocks), and their spatial distributions across the myocardial tissues.     

Adaptive local regularization methods for the inverse ECG problem

One of the fundamental problems in theoretical electrocardiography can be characterized by an inverse problem. We present new methods for achieving better estimates of heart surface potential distributions in terms of torso potentials through an inverse procedure. First, we outline an automatic adaptive refinement algorithm that minimizes the spatial discretization error in the transfer matrix, increasing the accuracy of the inverse solution. Second, we introduce a new local regularization procedure, which works by partitioning the global transfer matrix into sub-matrices, allowing for varying amounts of smoothing. Each submatrix represents a region within the underlying geometric model in which regularization can be specifically ‘tuned’ using an a priori scheme based on the L-curve method. This local regularization method can provide a substantial increase in accuracy compared to global regularization schemes. Within this context of local regularization, we show that a generalized version of the singular value decomposition (GSVD) can further improve the accuracy of ECG inverse solutions compared to standard SVD and Tikhonov approaches. We conclude with specific examples of these techniques using geometric models of the human thorax derived from MRI data.     

Longitudinal arrhythmogenic remodelling in a mouse model of longstanding pressure overload

Introduction. Sudden arrhythmogenic cardiac death is a major cause of mortality in patients with congestive heart failure due to adverse electrical remodelling. To establish whether abnormal conduction is responsible for arrhythmogenic remodelling in progressed stages of heart failure, we have monitored functional, structural and electrical remodelling in a murine model of heart failure, induced by longstanding pressure overload. Methods. Mice were subjected to transverse aortic constriction (TAC; n=18) or sham operated (n=19) and monitored biweekly by echocardiography and electrocardiography. At the 16-week endpoint, electrical mapping was performed to measure epicardial conduction velocity and susceptibility to arrhythmias. Finally, tissue sections were stained for Cx43 and fibrosis. Results. In TAC mice, fractional shortening decreased gradually and was significantly lower compared with sham at 16 weeks. Left ventricular hypertrophy was significant after six weeks. TAC mice developed PQ prolongation after 12 weeks, QT prolongation after 16 weeks and QRS prolongation after two weeks. Right ventricular conduction velocity was slowed parallel to fibre orientation. In 8/18 TAC hearts, polymorphic ventricular tachyarrhythmias were provoked and none in sham hearts. TAC mice had more interstitial fibrosis than sham. Immunohistology showed that Cx43 levels were similar but highly heterogeneous in TAC mice. All parameters were comparable in TAC mice with and without arrhythmias, except for Cx43 heterogeneity, which was significantly higher in arrhythmogenic TAC mice. Conclusion. Chronic pressure overload resulted in rapid structural and electrical remodelling. Arrhythmias were related to heterogeneous expression of Cx43. This may lead to functional block and unstable reentry, giving rise to polymorphic ventricular tachyarrhythmias. (Neth Heart J 2010;18:509-15.)     

Saccadic head and thorax movements in freely walking blowflies

Visual information processing is adapted to the statistics of natural visual stimuli, and these statistics depend to a large extent on the movements of an animal itself. To investigate such movements in freely walking blowflies, we measured the orientation and position of their head and thorax, with high spatial and temporal accuracy. Experiments were performed on Calliphora vicina, Lucilia cuprina and L. caesar. We found that thorax and head orientation of walking flies is typically different from the direction of walking, with differences of 45° common. During walking, the head and the thorax turn abruptly, with a frequency of 5–10 Hz and angular velocities in the order of 1,000°/s. These saccades are stereotyped: head and thorax start simultaneously, with the head turning faster, and finishing its turn before the thorax. The changes in position during walking are saccade-like as well, occurring synchronously, but on average slightly after the orientation saccades. Between orientation saccades the angular velocities are low and the head is held more stable than the thorax. We argue that the strategy of turning by saccades improves the performance of the visual system of blowflies.     

Three-dimensional kinematic analysis of the pectoral girdle during upside-down locomotion of two-toed sloths (Choloepus didactylus, Linné 1758)

Background

Theria (marsupials and placental mammals) are characterized by a highly mobile pectoral girdle in which the scapula has been shown to be an important propulsive element during locomotion. Shoulder function and kinematics are highly conservative during locomotion within quadrupedal therian mammals. In order to gain insight into the functional morphology and evolution of the pectoral girdle of the two-toed sloth we here analyze the anatomy and the three-dimensional (3D) pattern of shoulder kinematics during quadrupedal suspensory ('upside-down') locomotion.

Methods

We use scientific rotoscoping, a new, non-invasive, markerless approach for x-ray reconstruction of moving morphology (XROMM), to quantify in vivo the 3D movements of all constituent skeletal elements of the shoulder girdle. Additionally we use histologic staining to analyze the configuration of the sterno-clavicular articulation (SCA).

Results

Despite the inverse orientation of the body towards gravity, sloths display a 3D kinematic pattern and an orientation of the scapula relative to the thorax similar to pronograde claviculate mammalian species that differs from that of aclaviculate as well as brachiating mammals. Reduction of the relative length of the scapula alters its displacing effect on limb excursions. The configuration of the SCA maximizes mobility at this joint and demonstrates a tensile loading regime between thorax and limbs.

Conclusions

The morphological characteristics of the scapula and the SCA allow maximal mobility of the forelimb to facilitate effective locomotion within a discontinuous habitat. These evolutionary changes associated with the adoption of the suspensory posture emphasized humeral influence on forelimb motion, but allowed the retention of the plesiomorphic 3D kinematic pattern.     

Genetic variation and plasticity of thorax length and wing length in Drosophila aldrichi and D. buzzatii

Reaction norms across three temperatures of development were measured for thorax length, wing length and wing length/thorax length ratio for ten isofemale lines from each of two populations of Drosophila aldrichi and D. buzzatii. Means for thorax and wing length in both species were larger at 24 °C than at either 18 °C or 31 °C, with the reduction in size at 18 °C most likely due to a nutritional constraint. Although females were larger than males, the sexes were not different for wing length/thorax length ratio. The plasticity of the traits differed between species and between populations of each species, with genetic variation in plasticity similar for the two species from one locality, but much higher for D. aldrichi from the other. Estimates of heritabilities for D. aldrichi generally were higher at 18 °C and 24 °C than at 31 °C, but for D. buzzatii they were highest at 31 °C, although heritabilities were not significantly different between species at any temperature. Additive genetic variances for D. aldrichi showed trends similar to that for heritability, being highest at 18 °C and decreasing as temperature increased. For D. buzzatii, however, additive genetic variances were lowest at 24 °C. These results are suggestive that genetic variation for body size characters is increased in more stressful environments. Thorax and wing lengths showed significant genetic correlations that were not different between the species, but the genetic correlations between each of these traits and their ratio were significantly different. For D. aldrichi, genetic variation in the wing length/thorax length ratio was due primarily to variation in thorax length, while for D. buzzatii, it was due primarily to variation in wing length. The wing length/thorax length ratio, which is the inverse of wing loading, decreased linearly as temperature increased, and it is suggested that this ratio may be of greater adaptive significance than either of its components.     

3D Finite Element Electrical Model of Larval Zebrafish ECG Signals

Assessment of heart function in zebrafish larvae using electrocardiography (ECG) is a potentially useful tool in developing cardiac treatments and the assessment of drug therapies. In order to better understand how a measured ECG waveform is related to the structure of the heart, its position within the larva and the position of the electrodes, a 3D model of a 3 days post fertilisation (dpf) larval zebrafish was developed to simulate cardiac electrical activity and investigate the voltage distribution throughout the body. The geometry consisted of two main components; the zebrafish body was modelled as a homogeneous volume, while the heart was split into five distinct regions (sinoatrial region, atrial wall, atrioventricular band, ventricular wall and heart chambers). Similarly, the electrical model consisted of two parts with the body described by Laplace’s equation and the heart using a bidomain ionic model based upon the Fitzhugh-Nagumo equations. Each region of the heart was differentiated by action potential (AP) parameters and activation wave conduction velocities, which were fitted and scaled based on previously published experimental results. ECG measurements in vivo at different electrode recording positions were then compared to the model results. The model was able to simulate action potentials, wave propagation and all the major features (P wave, R wave, T wave) of the ECG, as well as polarity of the peaks observed at each position. This model was based upon our current understanding of the structure of the normal zebrafish larval heart. Further development would enable us to incorporate features associated with the diseased heart and hence assist in the interpretation of larval zebrafish ECGs in these conditions.     

Adaptive generation of multimaterial grids from imaging data for biomedical Lagrangian fluid–structure simulations

Spatial discretization of complex imaging- derived fluid–solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where the fluid and solid phases share a common interface geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to have a matching surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid–solid mesh of the mouse heart. An MRI dataset of a perfusion-fixed mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue, and background. Subsequently a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid–structure interaction computations will tend to have relative error equilibrated over the whole mesh.     

Generating fibre orientation maps in human heart models using Poisson interpolation

Smoothly varying muscle fibre orientations in the heart are critical to its electrical and mechanical function. From detailed histological studies and diffusion tensor imaging, we now know that fibre orientations in humans vary gradually from approximately ? 70° in the outer wall to +80° in the inner wall. However, the creation of fibre orientation maps for computational analyses remains one of the most challenging problems in cardiac electrophysiology and cardiac mechanics. Here, we show that Poisson interpolation generates smoothly varying vector fields that satisfy a set of user-defined constraints in arbitrary domains. Specifically, we enforce the Poisson interpolation in the weak sense using a standard linear finite element algorithm for scalar-valued second-order boundary value problems and introduce the feature to be interpolated as a global unknown. User-defined constraints are then simply enforced in the strong sense as Dirichlet boundary conditions. We demonstrate that the proposed concept is capable of generating smoothly varying fibre orientations, quickly, efficiently and robustly, both in a generic bi-ventricular model and in a patient-specific human heart. Sensitivity analyses demonstrate that the underlying algorithm is conceptually able to handle both arbitrarily and uniformly distributed user-defined constraints; however, the quality of the interpolation is best for uniformly distributed constraints. We anticipate our algorithm to be immediately transformative to experimental and clinical settings, in which it will allow us to quickly and reliably create smooth interpolations of arbitrary fields from data-sets, which are sparse but uniformly distributed.     

Biophysical models of the heart electrical activity

Based on the fundamental knowledge of the space-temporal organization of extracellular electrical fields of the myocardium, a system for 3-D computer modeling of the cardiac electrical activity at different structural levels of the object is being developed at the Institute of Theoretical and Experimental Biophysics. The system is based on the earlier proposed and modified biophysical model of the electrocardiosignal genesis represented by a double electrical layer along the surface of the electrically active myocardium. The system combines the model for activation and repolarization of the heart ventricles; the advanced model for the evaluation of parameters of the cardiac electric field, which makes it possible to derive model electrocardiosignals both in the direct regime of calculation of the potentials and in the regime of calculation of electrocardiosignals from preliminarily determined components of the multipole equivalent electrical heart generator; a database for the model parameters and their combinations in the form of cards of simulated "patients", and a database of modeled electrocardiosignals. In the present paper (first from three within the framework of the problem), simulation methods in electrocardiology are briefly described and a biophysical model of the heart electrical activity is presented, which has made up the basis of the system for computer modeling of forward and inverse problems of the cardiac electric field. The parameters of the model are electrophysiological, anatomical, and biophysical characteristics of the heart.     

A computational model of in vitro angiogenesis based on extracellular matrix fibre orientation

Recent interest in the process of vascularisation within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remains poorly understood. In vitro methods for studying angiogenesis exist; however, measurements available using such techniques often suffer from limited spatial and temporal resolutions. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This paper outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching and orientation morphometrics collected from vascularised tissue constructs. Microvessels were represented as a series of connected line segments. The morphology of the vessels was determined by a linear combination of the collagen fibre orientation, the vessel density gradient and a random walk component. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modelling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.     

REACTION NORMS OF MORPHOLOGICAL TRAITS IN DROSOPHILA: ADAPTIVE SHAPE CHANGES IN A STENOTHERM CIRCUMTROPICAL SPECIES?

Reaction norms of wing length, thorax length, and ovariole number were studied according to growth temperature in the circumtropical Drosophila ananassae, and compared to similar data from the cosmopolitan D. melanogaster. In the two species convex reaction norms were observed, but they were not parallel and sometimes exhibited intersections either at high (wing) or at low (thorax) temperature. On average, D. ananassae may be considered as a species with a bigger thorax but shorter wings than D. melanogaster. The shapes of reaction norms were analyzed and compared after quadratic polynomial adjustments. Significant differences were observed, in several cases between polynomial parameters, and in all cases between characteristic points that is, Maximum Value (MV) and Temperature of Maximum Value (TMV). The wing/thorax ratio may also be considered as a specific trait related to wing loading. Major differences were observed between the two species for the mean value and the shape of the response curves of this trait. The main observation of this work was however a shift of TMVs for wing and thorax length and ovariole number in D. ananassae toward higher temperatures. These variations in the reaction norms corresponded to a shift in the species thermal range, suggesting that temperature adaptation was accompanied by a modification of the shape of the response curves.     

Validation of q-ball imaging with a diffusion fibre-crossing phantom on a clinical scanner

Magnetic resonance (MR) diffusion imaging provides a valuable tool used for inferring structural anisotropy of brain white matter connectivity from diffusion tensor imaging. Recently, several high angular resolution diffusion models were introduced in order to overcome the inadequacy of the tensor model for describing fibre crossing within a single voxel. Among them, q-ball imaging (QBI), inherited from the q-space method, relies on a spherical Radon transform providing a direct relationship between the diffusion-weighted MR signal and the orientation distribution function (ODF). Experimental validation of these methods in a model system is necessary to determine the accuracy of the methods and to optimize them. A diffusion phantom made up of two textile rayon fibre (comparable in diameter to axons) bundles, crossing at 90 degrees , was designed and dedicated to ex vivo q-ball validation on a clinical scanner. Normalized ODFs were calculated inside regions of interest corresponding to monomodal and bimodal configurations of underlying structures. Three-dimensional renderings of ODFs revealed monomodal shapes for voxels containing single-fibre population and bimodal patterns for voxels located within the crossing area. Principal orientations were estimated from ODFs and were compared with a priori structural fibre directions, validating efficiency of QBI for depicting fibre crossing. In the homogeneous regions, QBI detected the fibre angle with an accuracy of 19 degrees and in the fibre-crossing region with an accuracy of 30 degrees .     

The modelling of fibre reorientation in soft tissue

In this paper, a hyperelastic and thermodynamically consistent model for soft tissue is developed that is able to describe the change of the initial orientation of the collagen fibres. Full numerical implementation is considered as well. The collagen architecture is assumed to reorient driven by a specific thermodynamical force. The anisotropy is described by a strain energy function, which is decomposed into a part related to the matrix and a part related to the fibres. The initial fibre orientation is defined by a structural tensor, while the current orientation is described by a time-dependent structural tensor, which results from the initial one by a rotational transformation. The rotation tensor is obtained via an integration process of a rate tensor, which depends on an adequately defined thermodynamical force. The integration is achieved via an exponential map algorithm, where it is shown that the rotation is necessarily a two-parametric one. Efficiency of the proposed formulation is demonstrated using some numerical examples.     

Recording of data and immediate interpretation of myoelectric activity of the stomach--electrogastrography]

Unlike other electrophysiological measurements such as electrocardiography (ECG) and electroencephalography (EEG), the cutaneous measurement of the electrical activity of the stomach (electrogastrography, EGG) is not an established clinical diagnostic procedure. To overcome common problems in acquiring very-low-frequency signals in the presence of large and unstable voltages we developed a real time data acquisition and analysis system based on linear-phase digital signal processing instead of analog filtering. FFT's computed on line from highly overlapping time sets are displayed as pseudo-3D or grey-scale graphic plots.     

Ultrastructure of the flagellar apparatus in the green flagellateSpermatozopsis similis

The ultrastructure of the flagellar apparatus of the naked, biflagellate green algaSpermatozopsis similis Preisig & Melkonian has been studied in detail using an absolute configuration analysis. The two basal bodies are displaced by 350 nm in the 1/7 o'clock direction and do not overlap proximally. They are interconnected by a principal distal connecting fibre consisting of a bundle of 5–8 nm filaments and possibly two proximal striated connecting fibres. The flagellar root system is cruciate (5-2-5-2 or 4-2-4-2 system) and contains a prominent continuous system I fibre overlying the two opposite two-stranded roots. A system II fibre is absent. Pronounced structural differences have been observed in the flagellar apparatus ultrastructure at two types of flagella orientation: During backward swimming basal bodies are parallel, the distal connecting fibre is extremely contracted; during forward swimming basal bodies assume various angles (from 20° to 180°) and the connecting fibre is about five times longer compared to the contracted state. The function of the connecting fibre as a contractile organelle and the mechanism of its contraction are discussed. On the basis of the flagellar apparatus ultrastructure,Spermatozopsis similis is related toChlamydomonas-type green algae.