Exploring New Electroencephalogram Parameters in Electroconvulsive Therapy.

OBJECTIVE: This pilot study aims to evaluate a novel metric based on the power spectrum of the EEG recordings from ECT-induced seizures-its association to volume changes in the hippocampus after ECT and improvement in depression rating scores. METHODS: Depressed patients treated with ECT underwent brain magnetic resonance imaging before and after treatment and the EEG from each seizure was recorded (N = 29). Hippocampal volume changes and EEG parameters were recorded in addition to clinician-rated and self-reported measures of depressive symptoms. The slope of the power law in the power spectral density of the EEG was calculated. Multivariate linear models relating seizure parameters to volume change or clinical outcome were systematically and successively simplified. The best models were selected according to Akaike information criterion. RESULTS: The slope of the power law was steeper in the right than the left hemisphere (P < 0.001). Electroencephalogram measures were included in the best models of volume change for both hippocampi as well as in the models explaining clinical outcome ( P = 0.014, P = 0.004). CONCLUSIONS: In this pilot study, novel EEG measures were explored and contributed in models explaining the variation in volume change in the hippocampus and in clinical outcome after ECT.

Sleep deprivation impairs molecular clearance from the human brain.

It remains an enigma why human beings spend one-third of their life asleep. Experimental data suggest that sleep is required for clearance of waste products from brain metabolism. This has, however, never been verified in humans. The primary aim of the present study was to examine in vivo whether one night of total sleep deprivation affects molecular clearance from the human brain. Secondarily, we examined whether clearance was affected by subsequent sleep. Multiphase MRI with standardized T1 sequences was performed up to 48 h after intrathecal administration of the contrast agent gadobutrol (0.5 ml of 1 mmol/ml), which served as a tracer molecule. Using FreeSurfer software, we quantified tracer enrichment within 85 brain regions as percentage change from baseline of normalized T1 signals. The cerebral tracer enrichment was compared between two cohorts of individuals; one cohort (n = 7) underwent total sleep deprivation from Day 1 to Day 2 (sleep deprivation group) while an age and gender-matched control group (n = 17; sleep group) was allowed free sleep from Day 1 to Day 2. From Day 2 to 3 all individuals were allowed free sleep. The tracer enriched the brains of the two groups similarly. Sleep deprivation was the sole intervention. One night of sleep deprivation impaired clearance of the tracer substance from most brain regions, including the cerebral cortex, white matter and limbic structures, as demonstrated on the morning of Day 2 after intervention (sleep deprivation/sleep). Moreover, the impaired cerebral clearance in the sleep deprivation group was not compensated by subsequent sleep from Day 2 to 3. The present results provide in vivo evidence that one night of total sleep deprivation impairs molecular clearance from the human brain, and that humans do not catch up on lost sleep.

Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli : A mathematical and numerical study.

In this paper, we investigate the dynamics of a neuron-glia cell system and the underlying mechanism for the occurrence of seizures. For our mathematical and numerical investigation of the cell model we will use bifurcation analysis and some computational methods. It turns out that an increase of the potassium concentration in the reservoir is one trigger for seizures and is related to a torus bifurcation. In addition, we will study potassium dynamics of the model by considering a reduced version and we will show how both mechanisms are linked to each other. Moreover, the reduction of the potassium leak current will also induce seizures. Our study will show that an enhancement of the extracellular potassium concentration, which influences the Nernst potential of the potassium current, may lead to seizures. Furthermore, we will show that an external forcing term (e.g. electroshocks as unidirectional rectangular pulses also known as electroconvulsive therapy) will establish seizures similar to the unforced system with the increased extracellular potassium concentration. To this end, we describe the unidirectional rectangular pulses as an autonomous system of ordinary differential equations. These approaches will explain the appearance of seizures in the cellular model. Moreover, seizures, as they are measured by electroencephalography (EEG), spread on the macro-scale (cm). Therefore, we extend the cell model with a suitable homogenised monodomain model, propose a set of (numerical) experiment to complement the bifurcation analysis performed on the single-cell model. Based on these experiments, we introduce a bidomain model for a more realistic modelling of white and grey matter of the brain. Performing similar (numerical) experiment as for the monodomain model leads to a suitable comparison of both models. The individual cell model, with its seizures explained in terms of a torus bifurcation, extends directly to corresponding results in both the monodomain and bidomain models where the neural firing spreads almost synchronous through the domain as fast traveling waves, for physiologically relevant paramenters.

The myodural bridge of the American alligator (Alligator mississippiensis) alters CSF flow.

Disorders of the volume, pressure or circulation of the cerebrospinal fluid (CSF) lead to disease states in both newborns and adults; despite this significance, there is uncertainty regarding the basic mechanics of the CSF. The suboccipital muscles connect to the dura surrounding the spinal cord, forming a complex termed the 'myodural bridge'. This study tests the hypothesis that the myodural bridge functions to alter the CSF circulation. The suboccipital muscles of American alligators were surgically exposed and electrically stimulated simultaneously with direct recordings of CSF pressure and flow. Contraction of the suboccipital muscles significantly changed both CSF flow and pressure. By demonstrating another influence on CSF circulation and pulsatility, the present study increases our understanding of the mechanics underlying the movement of the CSF.

Interstitial solute transport in 3D reconstructed neuropil occurs by diffusion rather than bulk flow.

The brain lacks lymph vessels and must rely on other mechanisms for clearance of waste products, including amyloid [Formula: see text] that may form pathological aggregates if not effectively cleared. It has been proposed that flow of interstitial fluid through the brain's interstitial space provides a mechanism for waste clearance. Here we compute the permeability and simulate pressure-mediated bulk flow through 3D electron microscope (EM) reconstructions of interstitial space. The space was divided into sheets (i.e., space between two parallel membranes) and tunnels (where three or more membranes meet). Simulation results indicate that even for larger extracellular volume fractions than what is reported for sleep and for geometries with a high tunnel volume fraction, the permeability was too low to allow for any substantial bulk flow at physiological hydrostatic pressure gradients. For two different geometries with the same extracellular volume fraction the geometry with the most tunnel volume had [Formula: see text] higher permeability, but the bulk flow was still insignificant. These simulation results suggest that even large molecule solutes would be more easily cleared from the brain interstitium by diffusion than by bulk flow. Thus, diffusion within the interstitial space combined with advection along vessels is likely to substitute for the lymphatic drainage system in other organs.

Magnitude and direction of aqueductal cerebrospinal fluid flow: large variations in patients with intracranial aneurysms with or without a previous subarachnoid hemorrhage.

BACKGROUND: Net cerebrospinal fluid (CSF) flow within the cerebral aqueduct is usually considered to be antegrade, i.e., from the third to the fourth ventricle with volumes ranging between 500 and 600 ml over 24 h. Knowledge of individual CSF flow dynamics, however, is hitherto scarcely investigated. In order to explore individual CSF flow rate and direction, we assessed net aqueductal CSF flow in individuals with intracranial aneurysms with or without a previous subarachnoid hemorrhage (SAH). METHODS: A prospective observational study was performed utilizing phase-contrast magnetic resonance imaging (PC-MRI) to determine the magnitude and direction of aqueductal CSF flow with an in-depth, pixel-by-pixel approach. Estimation of net flow was used to calculate CSF flow volumes over 24 h. PC-MRI provides positive values when flow is retrograde. RESULTS: The study included eight patients with intracranial aneurysms. Four were examined within days after their SAH; three were studied in the chronic stage after SAH while one patient had an unruptured intracranial aneurysm. There was a vast variation in magnitude and direction of aqueductal CSF flow between individuals. Net aqueductal CSF flow was retrograde, i.e., directed towards the third ventricle in 5/8 individuals. For the entire patient cohort, the estimated net aqueductal CSF volumetric flow rate (independent of direction) was median 898 ml/24 h (ranges 69 ml/24 h to 12.9 l/24 h). One of the two individuals who had a very high estimated net aqueductal CSF volumetric flow rate, 8.7 l/24 h retrograde, later needed a permanent CSF shunt. CONCLUSIONS: The magnitude and direction of net aqueductal CSF flow vary extensively in patients with intracranial aneurysms. Following SAH, PC-MRI may offer the possibility to perform individualized assessments of the CSF circulation.

The association between the pulse pressure gradient at the cranio-cervical junction derived from phase-contrast magnetic resonance imaging and invasively measured pulsatile intracranial pressure in symptomatic patients with Chiari malformation type 1.

BACKGROUND: In symptomatic Chiari malformation type 1 (CMI), impaired intracranial compliance (ICC) is associated with an increased cranio-spinal pulsatile pressure gradient. Phase-contrast magnetic resonance imaging (MRI) represents a non-invasive modality for the assessment of the pulse pressure gradient at the cranio-cervical junction (CCJ). We wished to explore how the MRI-derived pulse pressure gradient (MRI-dP) compares with invasively measured pulsatile intracranial pressure (ICP) in CMI, and with healthy controls. METHODS: From phase-contrast MRI of CMI patients and healthy controls, we computed cerebrospinal fluid (CSF) flow velocities and MRI-dP at the CCJ. We assessed bidirectional flow and compared the flow between the anterior and the posterior subarachnoid space at the CCJ. We computed total intracranial volume (ICV), ventricular CSF volume (VV), and posterior cranial fossa volume (PCFV). We analyzed the static and pulsatile ICP scores from overnight monitoring in CMI patients. RESULTS: Five CMI patients and four healthy subjects were included. The CMI group had a significantly larger extent of tonsillar ectopia, smaller PCFV, and a smaller area of CSF in the FM. The pulsatile ICP (mean ICP wave amplitude, MWA) was abnormally increased in 4/5 CMI patients and correlated positively with MRI-dP. However, the MRI-dP as well as the CSF flow velocities did not differ significantly between CMI and healthy subjects. Moreover, bidirectional flow was observed in both CMI as well as healthy subjects, with no significant difference. CONCLUSIONS: In symptomatic CMI patients, we found a significant association between the pulse pressure gradient at the CCJ derived from phase-contrast MRI and the pulsatile ICP (MWA) measured invasively. However, the MRI-dP was close to identical in CMI patients and healthy subjects. Moreover, the CSF flow velocities at the CCJ and the occurrence of bidirectional flow were not different in CMI patients and healthy individuals. Further studies are required to determine the diagnostic role of phase-contrast MRI in CMI patients.

Estimates of the permeability of extra-cellular pathways through the astrocyte endfoot sheath.

BACKGROUND: Astrocyte endfoot processes are believed to cover all micro-vessels in the brain cortex and may play a significant role in fluid and substance transport into and out of the brain parenchyma. Detailed fluid mechanical models of diffusive and advective transport in the brain are promising tools to investigate theories of transport. METHODS: We derive theoretical estimates of astrocyte endfoot sheath permeability for advective and diffusive transport and its variation in microvascular networks from mouse brain cortex. The networks are based on recently published experimental data and generated endfoot patterns are based on Voronoi tessellations of the perivascular surface. We estimate corrections for projection errors in previously published data. RESULTS: We provide structural-functional relationships between vessel radius and resistance that can be directly used in flow and transport simulations. We estimate endfoot sheath filtration coefficients in the range [Formula: see text] to [Formula: see text], diffusion membrane coefficients for small solutes in the range [Formula: see text] to [Formula: see text], and gap area fractions in the range 0.2-0.6%, based on a inter-endfoot gap width of 20 nm. CONCLUSIONS: The astrocyte endfoot sheath surrounding microvessels forms a secondary barrier to extra-cellular transport, separating the extra-cellular space of the parenchyma and the perivascular space outside the endothelial layer. The filtration and membrane diffusion coefficients of the endfoot sheath are estimated to be an order of magnitude lower than those of the extra-cellular matrix while being two orders of magnitude higher than those of the vessel wall.

Human brain solute transport quantified by glymphatic MRI-informed biophysics during sleep and sleep deprivation.

Whether you are reading, running or sleeping, your brain and its fluid environment continuously interacts to distribute nutrients and clear metabolic waste. Yet, the precise mechanisms for solute transport within the human brain have remained hard to quantify using imaging techniques alone. From multi-modal human brain MRI data sets in sleeping and sleep-deprived subjects, we identify and quantify CSF tracer transport parameters using forward and inverse subject-specific computational modelling. Our findings support the notion that extracellular diffusion alone is not sufficient as a brain-wide tracer transport mechanism. Instead, we show that human MRI observations align well with transport by either by an effective diffusion coefficent 3.5[Formula: see text] that of extracellular diffusion in combination with local clearance rates corresponding to a tracer half-life of up to 5 h, or by extracellular diffusion augmented by advection with brain-wide average flow speeds on the order of 1-9 [Formula: see text]m/min. Reduced advection fully explains reduced tracer clearance after sleep-deprivation, supporting the role of sleep and sleep deprivation on human brain clearance.

Sleep cycle-dependent vascular dynamics in male mice and the predicted effects on perivascular cerebrospinal fluid flow and solute transport.

Perivascular spaces are important highways for fluid and solute transport in the brain enabling efficient waste clearance during sleep. However, the underlying mechanisms augmenting perivascular flow in sleep are unknown. Using two-photon imaging of naturally sleeping male mice we demonstrate sleep cycle-dependent vascular dynamics of pial arteries and penetrating arterioles: slow, large-amplitude oscillations in NREM sleep, a vasodilation in REM sleep, and a vasoconstriction upon awakening at the end of a sleep cycle and microarousals in NREM and intermediate sleep. These vascular dynamics are mirrored by changes in the size of the perivascular spaces of the penetrating arterioles: slow fluctuations in NREM sleep, reduction in REM sleep and an enlargement upon awakening after REM sleep and during microarousals in NREM and intermediate sleep. By biomechanical modeling we demonstrate that these sleep cycle-dependent perivascular dynamics likely enhance fluid flow and solute transport in perivascular spaces to levels comparable to cardiac pulsation-driven oscillations.

Simulating epileptic seizures using the bidomain model.

Epileptic seizures are due to excessive and synchronous neural activity. Extensive modelling of seizures has been done on the neuronal level, but it remains a challenge to scale these models up to whole brain models. Measurements of the brain's activity over several spatiotemporal scales follow a power-law distribution in terms of frequency. During normal brain activity, the power-law exponent is often found to be around 2 for frequencies between a few Hz and up to 150 Hz, but is higher during seizures and for higher frequencies. The Bidomain model has been used with success in modelling the electrical activity of the heart, but has been explored far less in the context of the brain. This study extends previous models of epileptic seizures on the neuronal level to the whole brain using the Bidomain model. Our approach is evaluated in terms of power-law distributions. The electric potentials were simulated in 7 idealized two-dimensional models and 3 three-dimensional patient-specific models derived from magnetic resonance images (MRI). Computed electric potentials were found to follow power-law distributions with slopes ranging from 2 to 5 for frequencies greater than 10-30 Hz.

Encoder-decoder neural networks for predicting future FTIR spectra - application to enzymatic protein hydrolysis.

In the process of converting food-processing by-products to value-added ingredients, fine grained control of the raw materials, enzymes and process conditions ensures the best possible yield and economic return. However, when raw material batches lack good characterization and contain high batch variation, online or at-line monitoring of the enzymatic reactions would be beneficial. We investigate the potential of deep neural networks in predicting the future state of enzymatic hydrolysis as described by Fourier-transform infrared spectra of the hydrolysates. Combined with predictions of average molecular weight, this provides a flexible and transparent tool for process monitoring and control, enabling proactive adaption of process parameters.

Investigating molecular transport in the human brain from MRI with physics-informed neural networks.

In recent years, a plethora of methods combining neural networks and partial differential equations have been developed. A widely known example are physics-informed neural networks, which solve problems involving partial differential equations by training a neural network. We apply physics-informed neural networks and the finite element method to estimate the diffusion coefficient governing the long term spread of molecules in the human brain from magnetic resonance images. Synthetic testcases are created to demonstrate that the standard formulation of the physics-informed neural network faces challenges with noisy measurements in our application. Our numerical results demonstrate that the residual of the partial differential equation after training needs to be small for accurate parameter recovery. To achieve this, we tune the weights and the norms used in the loss function and use residual based adaptive refinement of training points. We find that the diffusion coefficient estimated from magnetic resonance images with physics-informed neural networks becomes consistent with results from a finite element based approach when the residuum after training becomes small. The observations presented here are an important first step towards solving inverse problems on cohorts of patients in a semi-automated fashion with physics-informed neural networks.

CSF circulation and dispersion yield rapid clearance from intracranial compartments.

In this paper, we used a computational model to estimate the clearance of a tracer driven by the circulation of cerebrospinal fluid (CSF) produced in the choroid plexus (CP) located within the lateral ventricles. CSF was assumed to exit the subarachnoid space (SAS) via different outflow routes such as the parasagittal dura, cribriform plate, and/or meningeal lymphatics. We also modelled a reverse case where fluid was produced within the spinal canal and absorbed in the choroid plexus in line with observations on certain iNPH patients. No directional interstitial fluid flow was assumed within the brain parenchyma. Tracers were injected into the foramen magnum. The models demonstrate that convection in the subarachnoid space yields rapid clearance from both the SAS and the brain interstitial fluid and can speed up intracranial clearance from years, as would be the case for purely diffusive transport, to days.

The glymphatic system: Current understanding and modeling.

We review theoretical and numerical models of the glymphatic system, which circulates cerebrospinal fluid and interstitial fluid around the brain, facilitating solute transport. Models enable hypothesis development and predictions of transport, with clinical applications including drug delivery, stroke, cardiac arrest, and neurodegenerative disorders like Alzheimer's disease. We sort existing models into broad categories by anatomical function: Perivascular flow, transport in brain parenchyma, interfaces to perivascular spaces, efflux routes, and links to neuronal activity. Needs and opportunities for future work are highlighted wherever possible; new models, expanded models, and novel experiments to inform models could all have tremendous value for advancing the field.

Flow characteristics in a canine aneurysm model: a comparison of 4D accelerated phase-contrast MR measurements and computational fluid dynamics simulations.

PURPOSE: Our purpose was to compare quantitatively velocity fields in and around experimental canine aneurysms as measured using an accelerated 4D PC-MR angiography (MRA) method and calculated based on animal-specific CFD simulations. METHODS: Two animals with a surgically created bifurcation aneurysm were imaged using an accelerated 4D PC-MRA method. Meshes were created based on the geometries obtained from the PC-MRA and simulations using "subject-specific" pulsatile velocity waveforms and geometries were then solved using a commercial CFD solver. Qualitative visual assessments and quantitative comparisons of the time-resolved velocity fields obtained from the PC-MRA measurements and the CFD simulations were performed using a defined similarity metric combining both angular and magnitude differences of vector fields. RESULTS: PC-MRA and image-based CFD not only yielded visually consistent representations of 3D streamlines in and around both aneurysms, but also showed good agreement with regard to the spatial velocity distributions. The estimated similarity between time-resolved velocity fields from both techniques was reasonably high (mean value >0.60; one being the highest and zero being the lowest). Relative differences in inflow and outflow zones among selected planes were also reasonable (on the order of 10%-20%). The correlation between CFD-calculated and PC-MRA-measured time-averaged wall shear stresses was low (0.22 and 0.31, p < 0.001). CONCLUSIONS: In two experimental canine aneurysms, PC-MRA and image-based CFD showed favorable agreement in intra-aneurismal velocity fields. Combining these two complementary techniques likely will further improve the ability to characterize and interpret the complex flow that occurs in human intracranial aneurysms.

Direction and magnitude of cerebrospinal fluid flow vary substantially across central nervous system diseases.

BACKGROUND: Several central nervous system diseases are associated with disturbed cerebrospinal fluid (CSF) flow patterns and have typically been characterized in vivo by phase-contrast magnetic resonance imaging (MRI). This technique is, however, limited by its applicability in space and time. Phase-contrast MRI has yet to be compared directly with CSF tracer enhanced imaging, which can be considered gold standard for assessing long-term CSF flow dynamics within the intracranial compartment. METHODS: Here, we studied patients with various CSF disorders and compared MRI biomarkers of CSF space anatomy and phase-contrast MRI at level of the aqueduct and cranio-cervical junction with dynamic intrathecal contrast-enhanced MRI using the contrast agent gadobutrol as CSF tracer. Tracer enrichment of cerebral ventricles was graded 0-4 by visual assessment. An intracranial pressure (ICP) score was used as surrogate marker of intracranial compliance. RESULTS: The study included 94 patients and disclosed marked variation of CSF flow measures across disease categories. The grade of supra-aqueductal reflux of tracer varied, with strong reflux (grades 3-4) in half of patients. Ventricular tracer reflux correlated with stroke volume and aqueductal CSF pressure gradient. CSF flow in the cerebral aqueduct was retrograde (from 4th to 3rd ventricle) in one third of patients, with estimated CSF net flow volume about 1.0 L/24 h. In the cranio-cervical junction, net flow was cranially directed in 78% patients, with estimated CSF net flow volume about 4.7 L/24 h. CONCLUSIONS: The present observations provide in vivo quantitative evidence for substantial variation in direction and magnitude of CSF flow, with re-direction of aqueductal flow in communicating hydrocephalus, and significant extra-cranial CSF production. The grading of ventricular reflux of tracer shows promise as a clinical useful method to assess CSF flow pattern disturbances in patients.

Variations in the cerebrospinal fluid dynamics of the American alligator (Alligator mississippiensis).

BACKGROUND: Studies of mammalian CSF dynamics have been focused on three things: paravascular flow, pressure and pulsatility, and "bulk" flow; and three (respective) potential motive forces have been identified: vasomotor, cardiac, and ventilatory. There are unresolved questions in each area, and few links between the different areas. The American alligator (Alligator mississippiensis) has pronounced plasticity in its ventilatory and cardiovascular systems. This study was designed to test the hypothesis that the greater cardiovascular and ventilatory plasticity of A. mississippiensis would result in more variation within the CSF dynamics of this species. METHODS: Pressure transducers were surgically implanted into the cranial subarachnoid space of 12 sub-adult alligators; CSF pressure and pulsatility were monitored along with EKG and the exhalatory gases. In four of the alligators a second pressure transducer was implanted into the spinal subarachnoid space. In five of the alligators the CSF was labeled with artificial microspheres and Doppler ultrasonography used to quantify aspects of the spinal CSF flow. RESULTS: Both temporal and frequency analyses of the CSF pulsations showed highly variable contributions of both the cardiac and ventilatory cycles. Unlike the mammalian condition, the CSF pressure pulsations in the alligator are often of long (~ 3 s) duration, and similar duration CSF unidirectional flow pulses were recorded along the spinal cord. Reduction of the duration of the CSF pulsations, as during tachycardia, can lead to a "summation" of the pulsations. There appears to be a minimum duration (~ 1 s) of isolated CSF pulsations. Simultaneous recordings of cranial and spinal CSF pressures reveal a 200 ms delay in the propagation of the pressure pulse from the cranium to the vertebral canal. CONCLUSIONS: Most of the CSF flow dynamics recorded from the alligators, are similar to what has been reported from studies of the human CSF. It is hypothesized that the link between ventilatory mechanics and CSF pulsations in the alligator is mediated by displacement of the spinal dura. The results of the study suggest that understanding the CSF dynamics of Alligator may provide unique insights into the evolutionary origins and functional regulation of the human CSF dynamics.

Intracranial pressure elevation alters CSF clearance pathways.

BACKGROUND: Infusion testing is a common procedure to determine whether shunting will be beneficial in patients with normal pressure hydrocephalus. The method has a well-developed theoretical foundation and corresponding mathematical models that describe the CSF circulation from the choroid plexus to the arachnoid granulations. Here, we investigate to what extent the proposed glymphatic or paravascular pathway (or similar pathways) modifies the results of the traditional mathematical models. METHODS: We used a compartment model to estimate pressure in the subarachnoid space and the paravascular spaces. For the arachnoid granulations, the cribriform plate and the glymphatic circulation, resistances were calculated and used to estimate pressure and flow before and during an infusion test. Finally, different variations to the model were tested to evaluate the sensitivity of selected parameters. RESULTS: At baseline intracranial pressure (ICP), we found a very small paravascular flow directed into the subarachnoid space, while 60% of the fluid left through the arachnoid granulations and 40% left through the cribriform plate. However, during the infusion, 80% of the fluid left through the arachnoid granulations, 20% through the cribriform plate and flow in the PVS was stagnant. Resistance through the glymphatic system was computed to be 2.73 mmHg/(mL/min), considerably lower than other fluid pathways, giving non-realistic ICP during infusion if combined with a lymphatic drainage route. CONCLUSIONS: The relative distribution of CSF flow to different clearance pathways depends on ICP, with the arachnoid granulations as the main contributor to outflow. As such, ICP increase is an important factor that should be addressed when determining the pathways of injected substances in the subarachnoid space. Our results suggest that the glymphatic resistance is too high to allow for pressure driven flow by arterial pulsations and at the same time too small to allow for a direct drainage route from PVS to cervical lymphatics.