Molecular Communications in Blood Vessels: Models, Analysis, and Enabling Technologies

MC basics.  Before continuing, we should outline the general structure of an MC system, including the main elements that allow the creation of a molecular transmission chain: information encoding, the communication medium, information transmission in the medium, propagation through this medium, reception, and information decoding for subsequent actions.²¹ In most MC proposals, information is conveyed by a stream of chemical compounds, also referred to as carriers, generated by the transmitter (TX) and transported by the aqueous medium of the channel. The exchange of information is based on the mechanism of interaction between carriers and target proteins, present on the surface of the receiver cell (RX). According to this model, information may be encoded in the concentration of the released compounds, in their release time within the symbol interval, in the type of compounds, or in any combination of these.¹⁵ These carriers are released by the TX into the environment through which the transfer takes place, depicted by a propagation model. This can be purely diffusive, as occurs within the cell cytoplasm, or include privileged directions, as occurs in the bloodstream. The receiving process is typically quite complex, as it involves the physical and chemical processes that determine the reception of carriers.

Why blood vessels?  As they are a natural means of transporting information, blood vessels are attractive to MC researchers. In fact, in addition to transporting vital elements such as oxygen and sugars, they allow the exchange of chemical compounds between organs, which is the basis of the coordination of biological processes; blood vessels therefore transport information at a systemic level. They form a circular closed path that branches out throughout the body through vessels with variable sections, as depicted in Figure 1. In addition, capillaries allow the exchange of chemical compounds (and therefore, of information) with organs.

Despite researchers’ interest in using MC in the bloodstream, analyzing and modeling these systems is challenging. The transport mechanism in blood vessels is determined by the movement of the main blood particles, namely red blood cells (RBCs), white blood cells (WBCs), and platelets. The combination of their kinematic behavior, induced by the cardiac pump, determines the overall behavior of the channel. Therefore, the resulting propagation environment is complex to model, even for simple systems.

The objective of this article is to illustrate the research challenges and proposed solutions for the application of MC systems in blood vessels. Its first contribution is a description of the models of MC in blood vessels, considering some elements are not easy to find in the reference literature. An example is how red blood cells (RBCs) influence the velocity profile in small vessels and induce a significant interaction of molecules dispersed in the blood with the endothelium, activating a series of physiological processes. A further contribution is a summary of the most popular analysis methodologies of MC in blood vessels, including the suitability of different solutions with respect to the complexity of the bloodstream environment. The final contribution is a discussion of the enabling technologies that allow interactions between the considered MC systems and the external world. This is aimed at identifying the most suitable technologies for the creation of an MC device intended for monitoring patient health parameters, to be applied to the skin (dermal device). We use the architectural design of this device as a running example throughout the article, aiding our discussion of models and analysis techniques for MC in blood vessels, as well as the main challenges for their adoption in real systems.

Models of transmitted signals.  Although there are several options for encoding digital information in MC, as discussed earlier, some of them cannot be easily used in the bloodstream. In fact, the presence of the drag force acting on the blood flow, together with the RBC tumbling, could significantly alter the transmitted signal and erase the features associated with the transported information. Thus, simple and robust transmitted signals are necessary. Some alternatives for implementing reliable transmissions in the blood environment are reported below and summarized in Table 1.

The ON-OFF pattern is used to transfer digital information, encoded in the sequence of bursts¹⁵ (modeling 1s) and silence (modeling 0s). It can be considered a good solution in LBVs, since a high flow velocity may limit the burst spreading and the impact of RBCs is not excessive. Differently, in SBVs the slow flow intensity favors a dispersion regime (diffusion dominates advection; see the discussion in “Models for signal propagation”) making bursts difficult to distinguish. In LBVs, branching can significantly alter the burst size in unpredictable ways, a problem less evident in SBVs.

The second option consists of transmitting known activation signals. In this case, the information is encoded in the type of burst sequence and/or molecules used. Since the targets in this case are essentially the endothelium or organs, SBVs seem to be the ideal environment in which to use this solution. In fact, the slow flow velocity and presence of RBCs favor interaction with the endothelium, enabling activation and monitoring functions. In addition, the size and shape of carriers influence molecules’ margination and interaction with the endothelium. Indeed, while spherical particles seem to produce slightly better margination than flattened carriers (for example, ellipsoids), ellipsoidal particles show slower rotational dynamics near vessel walls, favoring their adhesion.²⁷ Furthermore, larger, micron-size particles are more favorable for absorption than sub-micron-size ones.²⁷ Rod-shaped carriers also have interesting absorption properties. Long filamentous rod nanoparticles are preferable in low-pressure environments, whereas short rods or spherical nanoparticles have better delivery efficiency to the endothelium³⁴ under high-pressure conditions. Thus, usage of known activation signals in SBVs actually represents the most suitable environment for the monitoring device shown in Figure 2.

Continuous delivery is mainly aimed at drug delivery.⁹ Although LBVs can be used for transport, the main targets are SBVs, where drug molecules can be absorbed by the endothelium or organs. To size the emission rate, it is necessary to consider branching in large vessels, making this rate large enough to reach the target rate at the destination.

Bio-compatibility issues.  Blood carries many signaling molecules, such as hormones, whose job is not to provide nourishment to cells, but rather to regulate a wide range of physiological activities. To ensure biocompatibility with such an environment, the best choice for information particles is to use types of molecules that may already be present in the blood, or similar ones. The drawback of this approach, however, is that such molecules could interfere with the artificially transmitted ones. To distinguish artificial MCs from natural ones, it is necessary to use significant signal energy (that is, large bursts of molecules) or reduce the communication range to very short distances. In the first case, the use of large quantities of molecules could in turn interfere with underlying natural communications, potentially causing unwanted side effects. To avoid them, it is necessary to reduce the burst size and, consequently, the communication range to a few millimeters, which may be of limited use. However, in the bloodstream MC can be used mainly to implement a biocompatible communication system to trigger specific behaviors at the receiver site, such as drug release, or to implement non-invasive monitoring through short-range communication. Thus, information is not necessarily encoded in the sequence of emitted bursts, but rather in the presence of the signal itself and its macroscopic features at the receiver site. This information can be conveyed by a single burst of molecules or by a continuous release at a given rate. Different information can be transferred by using different molecules or patterns. TX and RX could even be implemented in the same device, with the TX releasing molecules and the RX estimating the value of some blood parameters on the basis of the received signal, for example, viscosity.¹⁶

Models of signal propagation.  The cardiovascular system is modeled as a network of branching ducts composed of sections of different sizes and lengths, where the heart functions as a central pumping system (see Figure 1). The blood that flows through this network is made up of cells suspended in plasma. The fluidity of the blood is influenced by some physical properties, such as concentration, deformability, and the aggregability of circulating blood cells and other elements dispersed in the plasma, as well as flow conditions in the macro and microcirculation (for example, shear stress, shear rates, and viscosity.¹⁴)

Shear stress is the tangential force of blood on the surface of the endothelium in blood vessels. A high shear stress is typical of laminar flows, while low values are typical of turbulent flows. The shear rate represents the velocity gradient between adjacent layers of blood.¹⁴ A high shear rate is present when the flow is fast, as in arteries, or when the diameter is large. Low values occur when flow is slow, as in veins, or when the diameter decreases. Finally, the blood viscosity increases as the shear rate decreases. Since the RBCs are able to deform (high shear rate) and aggregate (low shear rate), blood is a non-Newtonian fluid. Thus, under normal circumstances, capillaries, or more generally the SBVs, can be modeled using a parabolic velocity profile, neglecting turbulence (Poiseuille flow, as shown in Figure 1^8,19), taking into account the effects of the blood cells suspended in a Newtonian fluid (that is, the plasma component^6,11,19,31). This comes from the Navier-Stokes equations, which also describe the drag force exerted on suspended particles.^8,9 However, RBCs tend to aggregate, forming a plug flow region in the center of the vessel, causing a flattened parabolic velocity profile known as a Casson profile^11,35 (see Figure 1), due to the increased blood viscosity at low shear rates. This is a more realistic model for the blood-velocity profile in small vessels without turbulence.

Assuming that the volume of blood is constant, from the Bernoulli’s theorem,⁸ stating that the volume flow rate Q through a tube is constant, if a single rigid tube has a cross-sectional area A that varies along its length, the speed of the flow varies accordingly. Hence, given two points x and y along the pipe, if A_x > A_y then v_x < v_y. It follows that the average velocity $\overline{v}$ of the blood flow through each section of the circulatory system is given by the ratio between the flow rate Q and the total cross-sectional area A of that level, that is, $\overline{v}=Q/A$. By extending the Bernoulli principle to the whole circulatory system sketched in Figure 1, it follows that the cumulative cross-sectional area of LBVs, for example A₁ for arteries, is smaller than the cumulative area of the thinner ones (A₂ for SBVs) due to the much larger number of the latter. Thus, for the circulatory system, the result is that A₁ is lower than A₂ and, as a consequence, the blood velocity in each vessel follows an opposite relationship; that is, v₁ is higher than v₂.

MC in blood vessels are strongly influenced by the functioning of the cardio-circulatory system. For short range communications, the laminar flow assumes a parabolic/Casson profile, especially in SBVs. Hence, the flow velocity is maximum at the center of the vessel and vanishes near the walls. A burst of molecules released in this environment tends to follow a similar shape to the velocity profile, as shown in Tan et al.³¹ This is an ideal behavior that occurs in small-section vessels only, for short distances, when the presence of tumbling RBCs is neglected.

For large distance L from the emission point and a slow average velocity, the system converges to the so-called dispersion regime, in which diffusion dominates advection.^8,12 It occurs when the Peclet number, defined as $P_e=\left(\overline{v}R\right)/D$, results in P_e ≪ 4L/R, where R is the radius of the vessel and D is the particle diffusion coefficient.^8,12 This phenomenon typically happens for low-speed SBVs. This means that, at a sufficiently large distance L from the emission point, the movement is due mainly to diffusion pushed by the mean flow velocity $\overline{v}$, and the particle distribution on the cross section of the vessel is independent of the release point.

In small vessels, the presence of RBCs influences particle distribution, forcing the system into a different steady state. The small molecules are no longer uniformly distributed in the cross-section of the vessels, but rather are pushed toward the vessel walls by tumbling RBCs.³¹ Consequently, most of molecules will be traveling in a region known as the cell free layer (CFL), free from RBCs and close to the vessel walls, with an approximate average speed $\overline{v}$ due to the active transport of the flow.

Since most phenomena of interest in MC occur at a low flow rate, we neglect turbulence that occurs in large vessels and focus on small ones. This is why the enabling technologies illustrated in a later section are related to transmitters and receivers fixed on the endothelium to implement the monitoring device shown in Figure 2. A taxonomy of the presented propagation models is shown in Figure 3.

To summarize, the use of spherical particles of greater mass (for example, comparable to that of WBCs/RBCs) allows their transport to be confined toward the axis of the vessels, where the speeds are higher. In contrast, when it is necessary to exchange information near the endothelium, which is the cellular lining of the vessels, it is preferable to use light particles. However, the shape of the particles also needs to be taken into account, as larger, flattened micrometer particles have better margination and absorption capabilities than sub-micron spherical particles,²⁷ since they have a larger contact surface area.

Models of the reception process.  In the literature, several models have been proposed for the process of carrier (ligand) reception in MC.

The so-called transparent receiver²¹ is just an abstraction: It models a device, either natural or artificial, capable of sensing molecules without interfering with them. Clearly this is an oversimplification of a monitoring process, capable of estimating the concentration of a given type of circulating molecules, for example, proteins.

All other models take into account the surface receptors of the cell. An example of a ligand-receptor pair is Interleukin-6 (IL-6, ligand) binding to the membrane receptor IR-6R during the cytokine storm in the early phase of COVID-19.¹⁷ The absorbing receiver²¹ models a device able to absorb all molecules hitting its surface. It is an abstraction of a device whose surface receptors can cover most of its surface, which may be reasonable for some cases. The receiver with a finite number of absorbing receptors is a more refined model. Surface receptors cover only a fraction of the receiver, which is a more realistic assumption. However, each time a molecule hits one of these receptors, it is absorbed and immediately removed from the communication environment.¹⁵ Finally, the most realistic models take into account both a finite number of receptors and the possibility for each of them to establish a reversible bond with a molecule, which can be broken, as in Awan et al.,⁵ Lauffenburger and Linderman,²² and Pierobon et al.²⁸ Usually, these models are based on birth-and-death processes describing the temporal occupancy of receptors. We underline that the latter is only a basic model, on the basis of which it is possible to define other, more sophisticated ones, taking into account, for example, potential chemical reactions triggered by the surface bonds.

The reception taxonomy is shown in Figure 4. It also includes a possible mapping to fixed and mobile RX, considering both natural cells and artificial devices, and both LBV and SBV environments.

Analytical tools.  The main difficulty in adopting fully analytical models is to reliably represent highly complex environments, such as blood vessels. We can consider two classes of models: those that represent an abstract view of a portion of or the entire circulatory system, and those that focus on small sections. In the first case, a good model is represented by a network of elements, where each blood vessel is abstracted by an equivalent electrical circuit.⁹ Resistance is related to blood viscosity and vessel diameter; inductance models the inertia of the blood due to blood pressure; and capacitance measures the elasticity of the blood vessel. Additional equations model advection, diffusion, particle adhesion, and absorption/reaction processes. However, closed-form solutions are typically difficult to obtain and local phenomena due to interaction with blood cells are neglected. Other models are inspired by microfluidic environments. Although it is possible to obtain closed-form solutions for the motion of nanoparticles,¹² they cannot fully capture the dynamics of the bloodstream, since they neglect the presence of blood cells or endothelium permeability²⁹ and produce oversimplified models.

Finally, other models focus on the interaction between molecules and the endothelium through the Markov process.^17,28 Although closed-form solutions can be obtained, their validity is limited to small sections of a vessel, so they can model only very local phenomena.

Simulators.  When analytical tools fail in providing a solution, a good alternative is to use a simulation. We can distinguish two main approaches: finite elements methods (FEM) and particle-based simulations.

The first approach is a method for numerically solving a complex system of equations. These equations typically model multiphysics phenomena, including flow, mechanical interactions with tissues, and chemical transport of drugs across the vascular wall. This allows simulating objects or structures of arbitrary and complex 3D shape, almost impossible to model with analytical methods. This approach is pursued by commercial solvers, such as the COMSOL simulation tool, which can be used to simulate the entire circulatory system⁹ or implemented in custom solvers dedicated to detailed analysis of specific phenomena. In the first case, complex interactions occurring in the bloodstream are modeled at a high level of abstraction. In the latter case, complex models, such as that presented in Tan et al.,³¹ may be used for accurate representation of RBCs shape, their tumbling movement, or their interaction with molecules in microvasculature. However, only very short sections of a vessels, on the order of a few tens of micrometers, can be modeled.

The other class of simulation tools are particle-based simulators, such as BiNS2 (see Fellicetti et al.¹⁶ and references therein). In this case, moving particles and blood cells are modeled as spheres of a different size. The simulation consists of updating the motion equation for each particle, further modeling their interaction in case of collision or when their surfaces are at very close distances, on the order of a few nanometers. Furthermore, the boundaries can model the endothelium and its interactions with moving objects, such as partially inelastic collisions and absorption, by simulating receptors on its surface. This allows for more accurate results than FEM approaches applied to large-scale systems, and less accurate results than these approaches applied to micro-scale systems.

However, the time required to run a simulation of this type, even if accelerated with GPUs, may be several days, even to simulate just a few seconds of the real system. Since chemical reactions occurring in the receiver take much longer times (for example, minutes^22,25), it is advisable to decouple the simulation of the signal transmission and propagation through the channel from the operation that takes place at the receiver. For modeling the latter, analytical tools can perform quite well in terms of both accuracy and computation time. An example is given in Felicetti et al.,¹⁷ where carriers’ propagation and their mechanical interaction with the endothelium is simulated, whereas their absorption and subsequent endothelium behavior is represented by Markovian models.

Testbeds.  Most testbeds used to mimic the bloodstream environment use microfluidic settings. Although microfluidic models cannot capture the full, complex behavior of the blood circulation, they could be used for implementing some components of more complex, small-scale testbeds. The platform described in Fischera et al.¹⁸ is a typical example of a prototype of flow-driven MC. Although this prototype does not make use of blood cells, it is possible to include them inside the pipe, so as to obtain a platform emulating a non-turbulent bloodstream environment. In this direction, the testbed described in Thomas et al.³³ was used to validate the simulation results reported in Tan et al.,³¹ focusing on the characterization of particle delivery in microcirculation. The microfluidic channels were fabricated using a standard soft lithography process. The polydimethylsiloxane (PDMS) device was bonded on clean glass slides after proper treatment, and the PDMS surface was covered with a specific protein (NeutrAvidin) to bind with fluorescent nanoparticles. A mixture of RBCs and nanoparticles was injected into the microfluidic device using a syringe pump, collecting results through imaging using a fluorescent microscope. Despite the channel not having all the characteristics of microvasculature, its size is suitable for obtaining realistic results.

Although the great advantage of simulations compared with experiments is that they allow full control over the evolution of all system parameters at any time, the reliability of simulation results depends on the correctness of the implemented models. Thus, the value of extracting measurements from real systems mimicking the target ones is invaluable, especially for validating theoretical or simulation results. From a broader perspective, recent advances in microfluidics and molecular biology allow the lab-on-a-chip technology to manipulate biochemical reactions at very small volumes, handling fluids in quantities of just a few picoliters. This allows thousands of biochemical operations to be integrated on a single chip by fractionating a single drop of blood sample, obtaining precise diagnoses of potential diseases.^1,32 A further step in this direction is human-organ-on-a-chip technology.³⁸ It allows investigating interactions between organs and tissues, connected by microfluidic channels, which emulate microcirculation via pure diffusion, without pumping the blood between different tissues, as described in Wu et al.³⁸ They can also use blood, as in the skin-on-a-chip application proposed by Mori et al.²⁶ It focuses on perfusable vascular channels coated with endothelial cells, which are cultured in a skin-equivalent device connected to an external pump and tubes. The analysis of the vascular absorption and molecular permeability from the epidermal layer into the vascular channels allows studies and tests of skin biology.

Thin thermal sensors.  The receiver part of the device can be inspired by the epidermal thin sensors presented in Webb et al.,³⁷ which allow monitoring variations of the blood flow. It is non-invasive, ultra-thin (< 150μm), and flexible, with stretchable mechanics and the ability to resist continuous and rapid bodily motions. The device incorporates an array of thin, metallic thermal actuators and sensors designed for monitoring blood flow under a targeted skin surface of about 1 cm². A large, central thermal actuator provides power to the vessel at temperatures below the threshold of sensation. A set of surrounding sensors enables the measurement of the resulting thermal distribution. Finally, an array of bonding pads allows the attachment of a thin, flexible cable to interface with external acquisition electronics.

Its main limitation is its sensitivity, which increases with the decrease in vessel depth (~2 mm). Furthermore, to implement the RX, it may suffer from a limited ability to detect MC signals, unless a chemical reaction that releases heat is triggered.

Fluorophores and fluorescent proteins.  For the detection mechanism at the RX on the right side of Figure 2, it is possible to exploit the in-vivo fluorescent imaging technique based on fluorophores and fluorescent proteins, which can emit light signals of specific wavelengths.^4,20 To realize the full chain, it is possible to resort to the innate, targeted recognition ability exposed by the aptamers molecules.^30,40 In fact, aptamers enable the dynamic tracking of molecules, with one arm able to bind to a fluorescent protein and the other to the targeted molecules to be detected. Furthermore, they can be rapidly produced by chemical synthesis according to specific needs. The aptamer-fluorescent protein compound, stored in the reservoir of molecules shown in Figure 2, perfuses into the blood vessel to bind to the target receptor molecules exposed by the endothelium, whose exposure can also be triggered by the release of activation molecules stored in the second reservoir of molecules.

Microneedles.  Microneedle arrays^7,13,36 are a low-cost alternative for the transdermal perfusion of molecules into blood vessels (TX function). They can improve the delivery of molecules through the skin by bypassing the stratum corneum layer of the skin, which acts as a barrier, thus overcoming the various problems associated with conventional administration. The main principle is to penetrate the skin without drawing blood, thus creating micrometer-size pathways that lead molecules directly to the epidermis or upper dermis region, where they can directly enter the systemic circulation.

This technology can be used in two situations, for transdermal delivery of drugs and for sensing, as it can be used to extract analytes from the skin for both ex-vivo analysis and in-situ sensing. For delivery, it is highly effective and easy to use when large molecules cannot be easily administered orally or transdermally. For sensing, microneedles need to be modified on the surface to bind to specific biomarkers and selectively extract compounds for analysis.

There are different fabrication options, including solid, dissolvable, hydrogel, coated, and hollow microneedles.

On the other hand, their small size allows the administration of only limited quantities of molecules (that is, from microgram to low milligram doses). In addition, they can cause transient skin irritation, mild and punctate erythema, as well as skin infection caused by microbial penetration through residual holes in the skin. For the considered monitoring device, they can be used in both the TX and RX sections, although the limited number of molecules available for delivery may result in potentially weak MC signals.

Reverse iontophoresis.  This technology is based on the analysis of interstitial fluid, a body fluid with a lot of physiological information. It is a promising method for obtaining health-status information because interstitial fluid can be easily assessed by implanted or percutaneous measurements. Reverse iontophoresis extracts this fluid by applying an electric field to the skin, allowing noninvasive, epidermal physiological parameter monitoring.³⁹ An example of the application of this technology is the two-electrode system presented in Chen et al.,¹⁰ a skin-like biosensor system for non-invasive and highly accurate intravascular blood glucose monitoring. It makes use of electro-osmosis for the glucose transport in the reverse iontophoresis process. The glucose molar flux is determined by the potential gradient across the skin and the molar concentration of the initial solute. With accurate calibration of the system, it is suitable for medical-grade glucose monitoring and insulin therapy with micro pumps. However, its preparation requires a paper battery, which must be removed from the skin to allow attaching the biosensor to the cathode area for glucose measurement. The need for using ionic or charged molecules when implanting the device could interfere with other physiological mechanisms, such as glucose control; thus, microneedles are preferable.