Alles Wat U Moet Weten Over Erythema Migrans en Huidziekten

Materials and Methods

The mathematical model

Our model for pathogen-host dynamics captures the spread of the Lyme disease rash using parameters that have direct physical interpretations. The model contains spirochetes that grow with a replication rate, r. As the spirochetes disseminate through the collagen-rich extracellular matrix, transient adhesions to the matrix result in the formation of two spirochete populations, a translocating population, which we denote as T, and a stationary population (4), S. The switch between these two states is defined by first-order reactions with transition rate constants k_on for binding to the matrix (T→S) and k_off for unbinding from the matrix (S→T). When stationary spirochetes release from the matrix and become translocating spirochetes, they often change direction. Therefore, on long timescales, the spirochetes exhibit diffusive behavior. The diffusion coefficient is then related to the average velocity of the translocators divided by the off rate, D = ν 2 /k_off, where ν is the velocity of the spirochetes.

Macrophages migrate toward invading spirochetes. Movement of the macrophages is modeled using the Keller-Segel model for chemotaxis (14), which sets the speed that the macrophages migrate toward a population of bacteria as being proportional to the gradient of the bacterial concentration. A chemotactic rate constant, χ, defines the speed. Using that macrophages can move at a rate of microns per minute allows us to estimate χ. Active macrophages phagocytose the spirochetes. Experiments suggest that the rate of phagocytosis is dependent on the ratio of macrophages to spirochetes (15). We, therefore, model phagocytosis as a second-order reaction that depends on both the macrophage and spirochete concentrations with a clearing rate constant c. Finally, macrophages are cleared from the dermis with a clearing rate constant, d.

Erythema migrans

Erythema migrans is een huidafwijking die gezien wordt bij ziekte van Lyme. Het is vaak het eerste symptoom van de ziekte (stadium1). De ziekte van Lyme is een infectieziekte die wordt overgebracht door teken. In Nederland is ongeveer 20% van de teken besmet met de bacterie. Na een tekenbeet van een besmette teek, is de kans op de ziekte van Lyme minder dan 5% als de teek binnen 24 uur verwijderd is

Results and Discussion

To construct our model for the evolution of the EM rash, we first consider the spirochete-specific dynamic processes that occur in the host ( Fig. 1 A). The bacteria translocate through the dermis with velocity ν, which is estimated to be ∼1–4 μm/s based on intravital imaging and in vitro measurements in gelatin matrices (4). Spirochetes also bind to the ECM using adhesion molecules expressed on the outer membrane with rate constant k_on. These stuck or stationary bacteria unbind with rate constant k_off and translocate away from this location, often in a new direction. The rate constants are likely of ∼0.01 s −1 (4). Because the bacteria swim in roughly straight paths and can randomly change direction, dissemination through the dermis is modeled as a diffusive process, with diffusion coefficient D ∼ ν 2 /k_off. The bacteria also replicate at a rate r (∼1–2 days −1 ) (18).

Next, we consider the pathogen-host interactions ( Fig. 1 B). Identification of the invading spirochetes triggers cytokine release that causes monocytes from the blood to become activated macrophages. We lump this entire activation pathway into a single, first-order process with a rate constant a (∼1 days −1 ) (8). The macrophages track the bacteria using chemotaxis, their speed is proportional to the gradient of the bacterial concentration. A rate constant c (∼5 days −1 ) defines the rate that bacteria are cleared from the dermis by the macrophages. The macrophages are cleared or die at a rate d (∼0.2 days −1 ) (19), which is likely comparable to the timescale associated with the antiinflammatory response. Parameters values are given in Table S1 in the Supporting Material.

Clinical observations of erythema migrans in patients with Lyme disease are classified into three separate morphologies: homogenous erythemas, which are solid, fairly uniform colored rashes ( Fig. 2 a), central clearing rashes, which are rashes whose cleared center is surrounded by a single ring ( Fig. 2 b), and central erythemas, which are the characteristic bull’s-eye rashes that can have single or multiple rings ( Fig. 2 c). We used our model to simulate the spatiotemporal dynamics of spirochetes and activated macrophages in the dermis. Because inflammation causes the rash, we use the density of macrophages as an indicator of the rash appearance. Simulations of this model then reproduce all three rash morphologies ( Fig. 2 , d–f) and predict that the principle contributor to the formation of the different Lyme disease rashes is the rate at which active macrophages are cleared from the dermis. A fourfold increase in this parameter is sufficient to transform a homogenous erythema to a central clearing rash, and less than twofold further increase, leads to a central erythema. Combinations of the macrophage clearing rate with the bacterial replication rate and the incubation period for the infection were also found to affect the morphology of the Lyme disease rash ( Fig. 2 , j and k).

Systemic signs and symptoms of disseminated Lyme disease

The symptoms of second stage, early disseminated, Lyme disease can be difficult to attribute. Symptoms include severe fatigue, fever, pain, intermittent weakness and achiness of the muscles and joints, numbness in arms and legs, vision changes, and cognitive dysfunction such as short-term memory difficulties and problems multitasking. These symptoms are not specific for Lyme disease and can make the diagnosis of second stage Lyme disease very challenging.

More pronounced and recognizable Lyme disease nervous system manifestations include facial paralysis (Bell palsy), or meningitis with severe headache and stiff neck. Notable cardiac manifestations include passing out or feeling faint from an abnormally slow heart rate, irregular heart palpitations, or unexplained difficulty tolerating exercise.

Meningitis and carditis are both potentially serious Lyme disease conditions and warrant immediate medical attention.

Histologie

Unterschieden wird ein superfizieller Typ von einem profunden Typ, wobei zunehmend die Ansicht vertreten wird, dass es sich hierbei um 2 unterschiedliche Entitäten handelt.

• Der superfizielle Typ zeigt ein superfizielles perivaskuläres und interstitielles Lymphozyteninfiltrat dem bei 1/3 der Fälle eosinophile Leukozyten beigemengt sind, vereinzelt auch neutrophile Granulozyten. Eine Histoeosinophilie kann das feingewebliche Bild auch dominieren.Vereinzelt finden sich auch Erythrozytenextravasate. Exozytose mit fokaler Spongiose und Parakeratose ist regelmäßig nachweisbar. Selten ist intraepidermale Blasenbildung.
• Der profunde Typ zeigt dichte, meist strikt perivaskulär angeordnete Infiltrathülsen aus Lymphozyten in der mittleren und/oder tiefen Dermis, bei 1/3 der Fälle eosinophile Leukozyten in unterschiedlicher Beimischung. Das Epithel zeigt vereinzelt vakuoläre Degeneration und Dyskeratosen. Nicht selten werden in der oberen Dermis Melanophagen angetroffen. Spongiose und Parakeratose fehlen bei diesem Typ komplett. Es gibt einige Autoren die den profunden Typ als eigenständiges (deep figurate erythema) Krankheitsbild einordnen.