The primary objective of the study is the development of a mathematical model for predicting potassium kinetics during and after the dialytic session.

The secondary objectives of the study are:

1. the definition of a correlation between the kinetics of intra and extra-cellular concentrations of potassium during and after the dialytic session and the onset of arrhythmias;
2. the use of the mathematical model to modify the blood concentration of potassium by acting on the composition of the dialysis bath in order to minimize the risk of onset of arrhythmias during and after dialysis.

Type of study: spontaneous interventional, non-pharmacological, exploratory, prospective, monocentric. Eligible patients undergo hemodialytic treatment associated with the normal clinical pathway.

The study is divided into a Period A and a Period B. Period A includes the enrolment phase (Step 0), the laboratory and instrumental measurement phase (Step 1), the development phase of the mathematical model of potassium kinetics (Step 2) and the validation phase of the mathematical model (Step 3). Period B includes the phase of the use of the mathematical model for modulating the blood concentration of potassium and minimizing the risk of onset of arrhythmias during and after dialysis (Step 4).

Study population:

The study population will consist of 6 evaluable, outpatient patients with chronic kidney failure who need to perform hemodialysis thrice weekly for their survival.

In the case of drop out of a patient will be enrolled another patient to arrive at 6 patients evaluable both at the end of Period A and at the end of Period B of the study.

Laboratory tests will be sent to two laboratories: the Bologna Metropolitan Unique Laboratory for urea dosing, and the Laboratory of U.O. Nephrology Dialysis and Transplantation for intracellular potassium dosage and for the dosage of extracellular potassium, sodium, calcemia, bicarbonatemia, blood sugar.

The measurement of intracellular potassium will be carried out by selective ion probe. The first phase (Step 1) is characterized by the execution of measurements of intra and extracellular potassium concentration, and the assessment of the concentration of urea, blood sugar and plasma electrolytes that are closely related to the kinetics of potassium. Body impedance analysis will be taken at the beginning and end of dialysis to estimate the size of intra and extracellular volumes in which the solutes are contained and the variation of these secondary volumes to dehydration obtained through dialytic treatment. During dialysis starting at 8:00 a.m., measurements will be taken every 30 minutes to estimate how widespread and convective processes of dialytic treatment affect potassium kinetics. At the same time as blood samples, 12-derived ECGs will be performed to record cardiac electrical activity in conjunction with the measurement of the concentration of electrolytes and in particular extra/intra cellular potassium. Particular attention will be given to the recognition of rhythm alterations such as premature ventricular or supraventricular contractions, alterations in corrected QT interval, and the eventual onset of actual arrhythmias. After 60 minutes of the end of dialysis, hourly measurements of urea, blood sugar, intra-and extracellular potassium, ECG will be repeated. Body impedance analysis will be repeated 60 minutes after the end of dialysis and at the end of the observation period (7:00 p.m.) after 7 hours after the end of dialysis. Measurements after the end of dialysis are necessary to evaluate the rebound of solutes at the plasma level due to the slow balance between solutes in the intravascular space and solutes in the extravascular space. Body impedance analysis after the end of dialysis are necessary to assess whether the redistribution of solutes between intra and extravascular compartment corresponds to a change in the ratio of intra-to-extracellular volumes. ECG recordings are also required at this stage at the same time as blood samples to assess the appearance after dialysis of premature ventricular or supraventricular contractions, alterations in the corrected QT interval, and the eventual onset of actual arrhythmias. Such electrocardiographic alterations may be affected by potassium rebound and can alter the relationship between intracellular and extracellular potassium. The expected time to complete the measurement phase on all 6 patients enrolled is 4 months.

All patients enrolled in the study will undergo:

1. Hemodialytic therapy using 240-minute hemodiafiltration with on line reinfusion of the endogenous ultrafiltrate (HFR) on Flexya® hemodialysis machine (Medtronic, Mirandola, Italy), the filter used will be the HFR filter (Medtronic, Mirandola, Italy) a double-chambered filter used for the HFR dialytic technique. The first part of the filter consists of a high-flux polyphenylene membrane hemofilter. Through the hemofilter an endogenous ultrafilter is obtained by separating a share of blood from plasma water thanks to a mechanical ultrafiltration process. The hourly flow of endogenous ultrafilter is automatically obtained based on the transmembrane pressure values within the hemofilter. The endogenous ultrafiltrate produced is then conducted from the hemofilter to a cartridge containing a neutral resin where a process of adsorption takes place thanks to an adsorbent surface of 700 m2/gram of resin. After the adsorption, the ultrafiltrate is returned to the blood in the whole which, in turn, reaches the second part of the HFR filter. The second chamber of the HFR filter is a low-flow polyphenylene filter where weight loss and diffusive processes occur. The blood flow from vascular access will be maintained at values > 250 ml/minute, the flow of dialysis fluid will be 500 ml/minute. Weight loss during dialytic treatment will be prescribed according to the patient's clinical needs.
2. Assess potassium, sodium, bicarbonatemia, calcemia, urea and blood sugar values, being the kinetics of potassium closely linked to that of other solutes (e.g. through global variations in osmolarity resulting in changes in intra- and extra-cellular volumes, and the participation of pumps among interacting multiple ions). The dosage of potassium, bicarbonate, calcium, sodium, glucose and urea will be carried out every 30 minutes for a total of 9 blood samples for the dialytic session (Hemodialysis 1). After 60 minutes of the end of the dialytic session each patient will undergo 7 blood samples for intra and extracellular potassium, bicarbonate, ionized calcium, sodium, urea, blood sugar every 60 minutes (Post-Hemodialysis 1). At the beginning of the next dialysis (Hemodialysis 2) blood samples of potassium, sodium, bicarbonatemia, calcemia, urea, blood sugar in particular will be performed to check the degree of potassium rebound in the interdialytic interval. During Hemodialysis 2 no further blood tests or instrumental examinations will be carried out and the patient should not remain under observation in the post-hemodialysis period.
3. Assess both extracellular potassium and intracellular potassium during dialysis sessions and in the hours following dialysis itself according to the time interval expected. The measurement of intracellular potassium will be carried out by selective ion probe.
4. ECG with 12-derived electrocardiograph for 5 minutes for a total of 16 ECG paths per patient per dialytic session. The ECG will be performed at the same time as blood samples every 30 minutes for a total of 9 tracks per dialytic session. After 60 minutes of the end of the dialysis session each patient will undergo a new ECG track every 60 minutes for a total of 7 ECGs.

(e) Body impedance analysis using Electro fluid graph machine® (Akern, Pontassieve, Italy) to assess each patient's extra intracellular compartments at time 0 (dialysis start) at 240 minutes (end of dialysis), after 60 minutes after the end of dialysis and after 7 hours after the end of dialysis.

(f) Use of the Natrium sensor (Medtronic, Mirandola, Italy) during HFR dialytic treatment to compare the conductivity values measured by Natrium with the blood levels of electrolytes measured during the dialytic treatment.

The second phase (Step 2) of the study consists of the development of a mathematical model of solutes kinetics in hemodialysis and during the post-dialytic phase. The mathematical model will be able to simulate with reasonable precision the performance of some of the main solutes and, in particular, the extra and intra-cellular potassium concentration.

The development of the mathematical model can take place when Step 1 data obtained from all 6 patients enrolled were collected.

The mathematical model will be developed by Prof. Mauro Ursino, Department of Electrical Electronic and Information Engineering, University of Bologna. The model will have the characteristics of predicting: a) the variation in the total body mass of intracellular and extracellular potassium during and after the dialytic session; b) the kinetics of intra and extracellular potassium concentration during dialysis and for the first 7 hours after the dialytic treatment. The mathematical model of potassium kinetics will include the Na/K/ATPase-dependent pump, which is the main active transport mechanism, the passive diffusion mechanism of potassium from intracellular compartment to extracellular compartment, the spread of potassium through the dialysis membrane, the variation in intradialytic volume, the rebound of potassium and solutes after dialysis, the role of plasma osmolarity. The model will include two compartments (intra and extra-cellular), the exchange of fluid volumes for osmosis and ultrafiltration, the kinetics of different solutes, the exchange by diffusion. The expected time to complete Step 2 out of 6 evaluable patients is 3 months.

Step 3. The model developed at the previous point will be used to simulate the temporal kinetics of solutes, and in particular potassium, during the intradialytic phase and in the early hours after dialysis. For this purpose, the model predictions will be compared with the in vivo results. Possibly "fitting" and minimization techniques will be used to estimate those parameters of the model with an incomplete physiological knowledge. The differences between model and data will be carefully analysed to understand whether they are due to measurement errors only, individual variability, or model defects. In the latter case, the changes to exceed the model limits will be settled. In the second case (individual variability) the investigators will look for methods of online estimation, to adapt the model to the individual patient. The mathematical model software will be implemented in the Flexya hemodialysis machine for its application during a normal online HFR session in patients enrolled in the study. During dialysis starting at 8:00 a.m., solute measurements (intra-and extracellular potassium, urea, blood sugar, bicarbonatemia, sodium, calcemia) will be taken every 30 minutes to estimate the deviation between the values predicted by the mathematical model to the various measurement gaps and the values actually measured by laboratory tests. At the same time as blood samples, 12-derived ECGs will be performed. After 60 minutes of dialysis, hourly measurements of the solutes and ECG will be repeated. Body impedance analysis will be repeated 60 minutes after the end of dialysis and at the end of the observation period (7:00 p.m.) after 7 hours after the end of dialysis. Measurements after dialysis are required for model validation and to assess the correspondence between the real concentration of solutes and the values predicted by the model. Body impedance analysis after the end of dialysis are necessary to assess whether the redistribution of solutes between intra and extravascular compartment corresponds to a change in the ratio of intra-to-extracellular volumes. ECG recordings are also required at this stage at the same time. The expected time to complete Phase 3 out of 6 evaluable patients is 6 months.

Step 4. The model, which has already been validated, is used to determine the potassium profile in the dialysis bath, able to ensure the optimal trend of intracellular potassemia in order to identify the correct form of potassium trend, able to minimize risk factors and reduce the incidence of arrhythmias. The expected time to complete Step 4 is 4 months.

Inclusion Criteria:

• end stage renal failure on chronic hemodialysis
• thrice weekly hemodialysis;
• urine output < 100 ml/day;
• low potassium diet (max 2 gr/day);
• Age > 18 years;
• Arterovenous fistula for hemodialysis with blood flow > 250 ml/min;
• Written informed consent to participate.

Exclusion Criteria:

• Intradialytic hypotension: 30% of dialysis sessions during the last month before enrollment with intradialytic systolic blood pressure reduction > 25 mmHg;
• Need of intradialytic potassium administration;
• Antiarrythmic drugs prescription;
• Recent myocardial infarction;
• Fever;
• Anemia (Hb < 8 gr%);
• Enteritis.