Third-generation model of a hydropic recipient

TTTS. Third-generation model of a hydropic recipient

In our third model,6 we simulated a sequence of events that leads to the onset and development of hydrops in the recipient twin. Three essential elements had to be added to our second model.5 The first is vasoconstrictive peptides, described as the renin–angiotensin system (RAS) mediators that reduce urine production. 

The second is the limited capacity of the fetal heart to increase its cardiac output beyond normal values following abnormally increased blood pressures,23,24 leading to a state of high-output cardiac failure. The obvious third element is an interstitial fluid compartment. Table 6.1 summarizes the 10 parameters included in this model for each twin, comprising 20 first-order differential equations. 

As before, growth of the fetal total body fluid volume (fetal blood, but here also intracellular and interstitial fluids) and growth of the fetal amniotic fluid volume are caused by the transplacental fluid flow across the placenta, eqn (7), where 

Normal fetal urine production, affecting amniotic fluid volumetric growth, is modified here by three mechanisms: 

• the pressure–diuresis curve used in our second model (see end of section on ‘secondgeneration hemodynamic and amniotic fluid dynamics model’) 

• the influence of the blood COP (i.e. filtration of fetal blood across the glomerular capillary membrane) 

• the influence of the blood concentration of RAS mediators, which reduce urine production. 

As before in eqns (5) and (9), overall growth of the two fetal blood volumes is a linear combination of natural (i.e. anticipated normal) blood volumetric growth, and the net fetofetal transfusion. However, the blood volume is no longer fixed to 10% of the total body fluid volume as in eqn (8), but follows from eqn (11) as the difference between total body fluid and intracellular plus interstitial fluid volumes. 

Natural total blood volumetric growth follows from the difference between transplacental flow and growth of amniotic, intracellular, and interstitial fluids, eqns (7) and (11). Growth of the interstitial fluid volume is governed by Starling forces, comparable to eqn (10), which determine magnitude and direction of the transvascular flow from the fetal circulation to the interstitial compartment, proportional to the difference between the vascular-interstitial hydrostatic and colloid osmotic pressure gradients: 

Growth of the fetal intracellular space was modeled proportional to the actual value and to growth of the fetal blood volume. The fetal heart has been demonstrated to operate near the maximal cardiac output plateau in the Frank–Starling curve.23,24 Therefore, fetal cardiac reserve is limited as compared to adult physiology. 

We expressed cardiac output to depend upon changes in preload and afterload. Increased preload increases the cardiac output by the Frank–Starling effect until 1.1 times the normal venous pressure, after which it increases only slightly when venous pressure is elevated. 

We calculated the (arterial) cardiac output and venous return separately, to allow an excess blood volume, ExcVenVol, to accumulate in the venous part of the circulation following forward heart failure of the recipient. The equations describing arterial and venous blood volumetric growth then follow as a linear combination of (a) the excess blood volume that is removed from the arterial circulation and added to the venous volume, 

RemExcVenVol, and (b) volumetric growth of arterial and venous blood volumes, expressed as blood volumetric growth (arterial plus venous), multiplied by the ratio of arterial or venous blood volume to total blood volume, expressed as VbArt/Vb or VbVen/Vb. Thus, eqns (5) and (9) become 

Symbol Inet denotes the net fetofetal transfusion, eqn (1). The recipient equations are indicated by the plus sign, the donor equations by the minus sign. Model input parameters and the solution of the differential equations remained as previously, albeit using a time step of 0.6 s, required to prevent the numerical solution includes an oscillatory component.