## 2 Background  
### Pathophysiology of AMI  
Cardiac troponins are a protein complex involved in the contraction of the cardiac muscle. They are composed of three different subunits, (i) cardiac troponin C (cTnC), (ii) cardiac troponin I (cTnI), and (iii) cardiac troponin T (cTnT), Figure 1(i). In the presence of an electrical stimulus, the cell is activated, causing a rapid increase in the intracellular concentration of Ca\({}^{2+}\), which can bind cardiac troponin C (cTnC), favoring conformational changes in tropomyosin. As a result, the myosin and actin filaments are free to slide over each other, allowing the muscle fibers to contract. In a healthy cardiomyocyte, Figure 1(ii), the integrity and functionality of all fibers and of the protein complex are maintained: therefore, the concentration of cTnT is undetectable in peripheral blood. Figure 1: (i) Cardiac troponin complex is composed of three different protein subunits, each of which has a specific role in cardiac contraction: (1) subunit C, designed to bind the \(Ca^{2+}\), (2) subunit I, binds to actin in thin myofilaments, and (3) subunit T, connected to tropomyosin. (ii) In a typical healthy cardiomyocyte, all the fibers appear intact, and none of the three cardiac troponin subunits is appreciably detectable in the systemic circulation. (iii) During an AMI, the myocardial tissue downstream of the vascular obstruction goes into necrosis: the myofib disintegrate and the cellular membrane breaks down, allowing components of the troponin complex to reach the circulatory system. Several abnormalities can be observed on ECG tracings. Among them, an elevation in the ST segment, especially during the initial phase of an AMI, is associated with a larger clinical risk, suggesting complete coronary obstruction. This type of AMI is called STEMI (ST-elevation myocardial infarction) and requires prioritized management, being associated with a higher risk for mortality and clinical complications, especially in the absence of timely restoration of blood flow to the infarcted area. After the onset of AMI, the blood flow downstream of the obstruction impedes the normal blood supply to the underlying tissue, causing its death; see Figure 1(iii). At the cellular level, the necrosis of this tissue implicates the progressive desegregation of the fibers, and the diffusion of cTns subunits from the disrupted sarcomere, first into the cytosol, and then into the plasma, where it is possible to measure the concentration levels of the cTns through specific assays; see Figure 1(iii). In the plasma of AMI patients, cTnT concentrations describe a typical biphasic curve, see Figure 1(iii), in which the first peak is due to the early and rapid leakage of the cTnT molecules contained in the cytoplasm, following the rupture of the outer cell membrane, while the second one is due to the slow release of the sarcomeric cTnT, following the degradation of the cardiac fibers. It is possible to characterize two main clinical classes of AMI patients, which require different approaches in both diagnosis and treatment. These classes are represented by:  
1. STEMI (ST-segment elevation AMI): in this class of patients, the obstruction usually completely blocks the blood supply to the tissues downstream of it. In this case, the extension of the cardiac damage is such that it causes alterations in the electrical activity of the heart, resulting in a visible elevation of the ST-segment on the ECG, [21]; see Figure 1(iii). 2. NSTEMI (non-ST-segment elevation AMI): the occlusion is only partial; therefore, a reduced blood flow is guaranteed downstream of the obstruction; these patients exhibit an ECG without visible alteration [22]. In the present study, we focus our attention on STEMI patients, since the release profile and its dynamic are well-known from a clinical point of view, [23; 24], with the possibility to associate a specific mathematical behavior.