Heterogeneities in regional volumes of distribution and flows in rabbit heart

Quantitative Perfusion Analysis of First-Pass Contrast Enhancement Kinetics: Application to MRI of Myocardial Perfusion in Coronary Artery Disease

Purpose

Perfusion analysis from first-pass contrast enhancement kinetics requires modeling tissue contrast exchange. This study presents a new approach for numerical implementation of the tissue homogeneity model, incorporating flexible distance steps along the capillary (NTH_f).

Methods

The proposed NTH_f model considers contrast exchange in fluid packets flowing along the capillary, incorporating flexible distance steps, thus allowing more efficient and stable calculations of the transit of tracer through the tissue. We prospectively studied 8 patients (62 ± 13 years old) with suspected CAD, who underwent first-pass perfusion CMR imaging at rest and stress prior to angiography. Myocardial blood flow (MBF) and myocardial perfusion reserve index (MPRI) were estimated using both the NTH_f and the conventional adiabatic approximation of the TH models. Coronary artery lesions detected at angiography were clinically assigned to one of three categories of stenosis severity (‘insignificant’, ‘mild to moderate’ and ‘severe’) and related to corresponding myocardial territories.

Results

The mean MBF (ml/g/min) at rest/stress and MPRI were 0.80 ± 0.33/1.25 ± 0.45 and 1.68 ± 0.54 in the insignificant regions, 0.74 ± 0.21/1.09 ± 0.28 and 1.54 ± 0.46 in the mild to moderate regions, and 0.79 ± 0.28/0.63 ± 0.34 and 0.85 ± 0.48 in the severe regions, respectively. The correlation coefficients of MBFs at rest/stress and MPRI between the NTH_f and AATH models were r = 0.97/0.93 and r = 0.91, respectively.

Conclusions

The proposed NTH_f model allows efficient quantitative analysis of the transit of tracer through tissue, particularly at higher flow. Results of initial application to MRI of myocardial perfusion in CAD are encouraging.

Comparison of blood flow models and acquisitions for quantitative myocardial perfusion estimation from dynamic CT

Myocardial blood flow (MBF) can be estimated from dynamic contrast enhanced (DCE) cardiac CT acquisitions, leading to quantitative assessment of regional perfusion. The need for low radiation dose and the lack of consensus on MBF estimation methods motivates this study to refine the selection of acquisition protocols and models for CT-derived MBF. DCE cardiac CT acquisitions were simulated for a range of flow states (MBF = 0.5, 1, 2, 3 ml (min g)(-1), cardiac output = 3, 5, 8 L min(-1)). Patient kinetics were generated by a mathematical model of iodine exchange incorporating numerous physiological features including heterogenenous microvascular flow, permeability and capillary contrast gradients. CT acquisitions were simulated for multiple realizations of realistic x-ray flux levels. CT acquisitions that reduce radiation exposure were implemented by varying both temporal sampling (1, 2, and 3 s sampling intervals) and tube currents (140, 70, and 25 mAs). For all acquisitions, we compared three quantitative MBF estimation methods (two-compartment model, an axially-distributed model, and the adiabatic approximation to the tissue homogeneous model) and a qualitative slope-based method. In total, over 11 000 time attenuation curves were used to evaluate MBF estimation in multiple patient and imaging scenarios. After iodine-based beam hardening correction, the slope method consistently underestimated flow by on average 47.5% and the quantitative models provided estimates with less than 6.5% average bias and increasing variance with increasing dose reductions. The three quantitative models performed equally well, offering estimates with essentially identical root mean squared error (RMSE) for matched acquisitions. MBF estimates using the qualitative slope method were inferior in terms of bias and RMSE compared to the quantitative methods. MBF estimate error was equal at matched dose reductions for all quantitative methods and range of techniques evaluated. This suggests that there is no particular advantage between quantitative estimation methods nor to performing dose reduction via tube current reduction compared to temporal sampling reduction. These data are important for optimizing implementation of cardiac dynamic CT in clinical practice and in prospective CT MBF trials.

Modeling serotonin uptake in the lung shows endothelial transporters dominate over cleft permeation

A four-region (capillary plasma, endothelium, interstitial fluid, cell) multipath model was configured to describe the kinetics of blood-tissue exchange for small solutes in the lung, accounting for regional flow heterogeneity, permeation of cell membranes and through interendothelial clefts, and intracellular reactions. Serotonin uptake data from the Multiple indicator dilution "bolus sweep" experiments of Rickaby and coworkers (Rickaby DA, Linehan JH, Bronikowski TA, Dawson CA. J Appl Physiol 51: 405-414, 1981; Rickaby DA, Dawson CA, and Linehan JH. J Appl Physiol 56: 1170-1177, 1984) and Malcorps et al. (Malcorps CM, Dawson CA, Linehan JH, Bronikowski TA, Rickaby DA, Herman AG, Will JA. J Appl Physiol 57: 720-730, 1984) were analyzed to distinguish facilitated transport into the endothelial cells (EC) and the inhibition of tracer transport by nontracer serotonin in the bolus of injectate from the free uninhibited permeation through the clefts into the interstitial fluid space. The permeability-surface area products (PS) for serotonin via the inter-EC clefts were ~0.3 ml·g⁻¹·min⁻¹, low compared with the transporter-mediated maximum PS of 13 ml·g⁻¹·min⁻¹ (with Km = ~0.3 μM and Vmax = ~4 nmol·g⁻¹·min⁻¹). The estimates of serotonin PS values for EC transporters from their multiple data sets were similar and were influenced only modestly by accounting for the cleft permeability in parallel. The cleft PS estimates in these Ringer-perfused lungs are less than half of those for anesthetized dogs (Yipintsoi T. Circ Res 39: 523-531, 1976) with normal hematocrits, but are compatible with passive noncarrier-mediated transport observed later in the same laboratory (Dawson CA, Linehan JH, Rickaby DA, Bronikowski TA. Ann Biomed Eng 15: 217-227, 1987; Peeters FAM, Bronikowski TA, Dawson CA, Linehan JH, Bult H, Herman AG. J Appl Physiol 66: 2328-2337, 1989) The identification and quantitation of the cleft pathway conductance from these studies affirms the importance of the cleft permeation.

T1 mapping of the myocardium: intra-individual assessment of the effect of field strength, cardiac cycle and variation by myocardial region

BACKGROUND

Myocardial T1 relaxation time (T1 time) and extracellular volume fraction (ECV) are altered in the presence of myocardial fibrosis. The purpose of this study was to evaluate acquisition factors that may result in variation of measured T1 time and ECV including magnetic field strength, cardiac phase and myocardial region.

METHODS

31 study subjects were enrolled and underwent one cardiovascular MR exam at 1.5 T and two exams at 3 T, each on separate days. A Modified Look-Locker Inversion Recovery (MOLLI) sequence was acquired before and 5, 10, 12, 20, 25 and 30 min after administration of 0.15 mmol/kg gadopentetate dimeglumine (Gd-DTPA; Magnevist) at 1.5 T (exam 1). For exam 2, MOLLI sequences were acquired at 3 T both during diastole and systole, before and after administration of Gd-DTPA (0.15 mmol/kg Magnevist).Exam 3 was identical to exam 2 except gadobenate dimeglumine was administered (Gd-BOPTA; 0.1 mmol/kg Multihance). T1 times were measured in myocardium and blood. ECV was calculated by (ΔR1myocardium/ΔR1blood)*(1-hematocrit).

RESULTS

Before gadolinium, T1 times of myocardium and blood were significantly greater at 3 T versus 1.5 T (28% and 31% greater, respectively, p < 0.001); after gadolinium, 3 T values remained greater than those at 1.5 T (14% and 12% greater for myocardium and blood at 3 T with Gd-DTPA, respectively, p < 0.0001 and 18% and 15% greater at 3 T with Gd-BOPTA, respectively, p < 0.0001). However, ECV did not vary significantly with field strength when using the same contrast agent at equimolar dose (p = 0.2). Myocardial T1 time was 1% shorter at systole compared to diastole pre-contrast and 2% shorter at diastole compared to systole post-contrast (p < 0.01). ECV values were greater during diastole compared to systole on average by 0.01 (p < 0.01 to p < 0.0001). ECV was significantly higher for the septum compared to the non-septal myocardium for all three exams (p < 0.0001-0.01) with mean absolute differences of 0.01, 0.004, and 0.07, respectively, for exams 1, 2 and 3.

CONCLUSION

ECV is similar at field strengths of 1.5 T and 3 T. Due to minor variations in T1 time and ECV during the cardiac cycle and in different myocardial regions, T1 measurements should be obtained at the same cardiac phase and myocardial region in order to obtain consistent results.

Estimation of hepatic distributional volumes using non-labeled reference markers

Hepatic distributional volumes were investigated in the in situ perfused rat liver. Perfusion experiments were conducted using Krebs bicarbonate buffer delivered via the portal vein in single-pass mode at a total flow rate of 15 mL/min. A bolus dose of normal erythrocytes (RBC, vascular marker) and Evans blue (EB, extracellular marker) respectively was administered in the presence and absence of protein. At the end of the experiment, liver total water content was determined by desiccation and freeze-drying methods. Similar moment analysis results and superimposable effluent curves were obtained in the presence (RBC, mean transit time [MTT]: 7.31 +/- 0.45 s and volume of distribution [V]: 0.17 +/- 0.01 mL/g; EB, MTT: 10.9 +/- 0.62 s and V: 0.25 +/- 0.02 mL/g) and in the absence (RBC, MTT: 7.55 +/- 0.84 s and V: 0.18 +/- 0.02 mL/g; EB, MTT: 9.24 +/- 0.77 s and V: 0.20 +/- 0.02 mL/g) of protein, which indicates that the hepatic distribution of RBC and EB within the liver is not influenced by protein. Furthermore, the almost identical results obtained with the desiccation and freeze-drying methods clearly suggest that the freeze-drying method can be used as an alternative to desiccation for the estimation of liver water content.

Modeling of oxygen transport and cellular energetics explains observations on in vivo cardiac energy metabolism

Observations on the relationship between cardiac work rate and the levels of energy metabolites adenosine triphosphate (ATP), adenosine diphosphate (ADP), and phosphocreatine (CrP) have not been satisfactorily explained by theoretical models of cardiac energy metabolism. Specifically, the in vivo stability of ATP, ADP, and CrP levels in response to changes in work and respiratory rate has eluded explanation. Here a previously developed model of mitochondrial oxidative phosphorylation, which was developed based on data obtained from isolated cardiac mitochondria, is integrated with a spatially distributed model of oxygen transport in the myocardium to analyze data obtained from several laboratories over the past two decades. The model includes the components of the respiratory chain, the F₀F₁-ATPase, adenine nucleotide translocase, and the mitochondrial phosphate transporter at the mitochondrial level; adenylate kinase, creatine kinase, and ATP consumption in the cytoplasm; and oxygen transport between capillaries, interstitial fluid, and cardiomyocytes. The integrated model is able to reproduce experimental observations on ATP, ADP, CrP, and inorganic phosphate levels in canine hearts over a range of workload and during coronary hypoperfusion and predicts that cytoplasmic inorganic phosphate level is a key regulator of the rate of mitochondrial respiration at workloads for which the rate of cardiac oxygen consumption is less than or equal to approximately 12 μmol per minute per gram of tissue. At work rates corresponding to oxygen consumption higher than 12 μmol min⁻¹ g⁻¹, model predictions deviate from the experimental data, indicating that at high work rates, additional regulatory mechanisms that are not currently incorporated into the model may be important. Nevertheless, the integrated model explains metabolite levels observed at low to moderate workloads and the changes in metabolite levels and tissue oxygenation observed during graded hypoperfusion. These findings suggest that the observed stability of energy metabolites emerges as a property of a properly constructed model of cardiac substrate transport and mitochondrial metabolism. In addition, the validated model provides quantitative predictions of changes in phosphate metabolites during cardiac ischemia.

To function properly over a range of work rates, the heart must maintain its metabolic energy level within a range that is narrow relative to changes in the rate of energy utilization. Decades of observations have revealed that in cardiac muscle cells, the supply of adenosine triphosphate (ATP)—the primary currency of intracellular energy transfer—is controlled to maintain intracellular concentrations of ATP and related compounds within narrow ranges. Yet the development of a mechanistic understanding of this tight control has lagged behind experimental observation. This paper introduces a computational model that links ATP synthesis in a subcellular body called the mitochondrion with ATP utilization in the cytoplasm, and reveals that the primary control mechanism operating in the system is feedback of substrate concentrations for ATP synthesis. In other words, changes in the concentrations of the products generated by the utilization of ATP in the cell (adenosine diphosphate and inorganic phosphate) effect changes in the rate at which mitochondria utilize those products to resynthesize ATP.

GENTEX, a general multiscale model for in vivo tissue exchanges and intraorgan metabolism

Endothelial cells lining myocardial capillaries not only impede transport of blood solutes to the contractile cells, but also take up and release substrates, competing with myocytes. Solutes permeating this barrier exhibit concentration gradients along the capillary. This paper introduces a generic model, GENTEX, to characterize blood-tissue exchanges. GENTEX is a whole organ model of the vascular network providing intraorgan flow heterogeneity and accounts for substrate transmembrane transport, binding and metabolism in erythrocytes, plasma, endothelial cells, interstitial space and cardiomyocytes. The model is tested here for the analysis of multiple tracer indicator dilution data on purine nucleoside metabolism in the isolated Krebs-Henseleit-perfused non-working hearts. It has been also used for analysing NMR contrast data for regional myocardial flows and for positron emission tomographic studies of cardiac receptor kinetics. The facilitating transporters, binding sites and enzymatic reactions are nonlinear elements and allow competition between substrates and a reaction sequence of up to five substrate-product reactions in a metabolic network. Strategies for application start with experiment designs incorporating inert reference tracers. For the estimation of endothelial and sarcolemmal permeability-surface area products and metabolism of the substrates and products, model solutions were optimized to fit the data from pairs of tracer injections (of either inosine or adenosine, plus the reference tracers) injected under the same circumstances a few minutes later. The results provide a self-consistent description of nucleoside metabolism in a beating well-perfused rabbit heart, and illustrate the power of the model to fit multiple datasets simultaneously.

Simultaneous blood-tissue exchange of oxygen, carbon dioxide, bicarbonate, and hydrogen ion

A detailed nonlinear four-region (red blood cell, plasma, interstitial fluid, and parenchymal cell) axially distributed convection-diffusion-permeation-reaction-binding computational model is developed to study the simultaneous transport and exchange of oxygen (O2) and carbon dioxide (CO2) in the blood-tissue exchange system of the heart. Since the pH variation in blood and tissue influences the transport and exchange of O2 and CO2 (Bohr and Haldane effects), and since most CO2 is transported as HCO3(-) (bicarbonate) via the CO2 hydration (buffering) reaction, the transport and exchange of HCO3(-) and H+ are also simulated along with that of O2 and CO2. Furthermore, the model accounts for the competitive nonlinear binding of O2 and CO2 with the hemoglobin inside the red blood cells (nonlinear O2-CO2 interactions, Bohr and Haldane effects), and myoglobin-facilitated transport of O2 inside the parenchymal cells. The consumption of O2 through cytochrome-c oxidase reaction inside the parenchymal cells is based on Michaelis-Menten kinetics. The corresponding production of CO2 is determined by respiratory quotient (RQ), depending on the relative consumption of carbohydrate, protein, and fat. The model gives a physiologically realistic description of O2 transport and metabolism in the microcirculation of the heart. Furthermore, because model solutions for tracer transients and steady states can be computed highly efficiently, this model may be the preferred vehicle for routine data analysis where repetitive solutions and parameter optimization are required, as is the case in PET imaging for estimating myocardial O2 consumption.

Intracoronary administration of FGF-2: a computational model of myocardial deposition and retention

This study uses a computational model to characterize the myocardial deposition and retention of basic fibroblast growth factor (FGF-2) at the cellular level after intracoronary (IC) administration of exogenous FGF-2. The model is applied to the in situ conditions present within the myocardium of a dog for which the plasma pharmacokinetics resulting from IC injection of FGF-2 were recorded. Our estimates show that the processes involved in FGF-2 signaling are not diffusion limited; rather, the response time is determined by the reaction time of FGF-2 binding to cell surface receptors. Additionally, the processes of receptor secretion and internalization are found to play crucial roles in the FGF-2 dynamics; future experiments are required to quantify these processes. The model predictions obtained in this study suggest that IC administration of FGF-2 via either a single bolus or repetitive injections causes a transient increase (time scale of hours) in myocardial FGF-2 concentration if the endogenous level of free interstitial FGF-2 is low enough to allow permeation of FGF-2 molecules from the microvascular to the interstitial spaces. The model shows that the majority (64%) of the extracellular FGF-2 ligands are located within the interstitium, and similar fractions are found in the basement membrane and extracellular matrix. Among the FGF-2 molecules found within the interstitium, 2% are free and 98% are bound to interstitial heparan sulfate proteoglycans. These results support the theory of extracellular control of the bioavailability of FGF-2 via dynamic storage of FGF-2 within the basement membrane and extracellular matrix.

Myocardial oxygenation in isolated hearts predicted by an anatomically realistic microvascular transport model

An anatomically realistic model for oxygen transport in cardiac tissue is introduced for analyzing data measured from isolated perfused guinea pig hearts. The model is constructed to match the microvascular anatomy of cardiac tissue based on available morphometric data. Transport in the three-dimensional system (divided into distinct microvascular, interstitial, and parenchymal spaces) is simulated. The model is used to interpret experimental data on mean cardiac tissue myoglobin saturation and to reveal differences in tissue oxygenation between buffer-perfused and red blood cell-perfused isolated hearts. Interpretation of measured mean myoglobin saturation is strongly dependent on the oxygen content of the perfusate (e.g., red blood cell-containing vs. cell-free perfusate). Model calculations match experimental values of mean tissue myoglobin saturation, measured mean myoglobin, and venous oxygen tension and can be used to predict distributions of intracellular oxygen tension. Calculations reveal that approximately 20% of the tissue is hypoxic with an oxygen tension of <0.5 mmHg when the buffer is equilibrated with 95% oxygen to give an arterial oxygen tension of over 600 mmHg. The addition of red blood cells to give a hematocrit of only 5% prevents tissue hypoxia. It is incorrect to assume that the usual buffer-perfused Langendorff heart preparation is adequately oxygenated for flows in the range of < or =10 ml. min-1. ml tissue-1.

An integrative model of coupled water and solute exchange in the heart

Physiologists have devised many models for interpreting water and solute exchange data in whole organs, but the models have typically neglected key aspects of the underlying physiology to present the simplest possible model for a given experimental situation. We have developed a physiologically realistic model of microcirculatory water and solute exchange and applied it to diverse observations of water and solute exchange in the heart. Model simulations are consistent with the results of osmotic weight transient, tracer indicator dilution, and steady-state lymph sampling experiments. The key model features that permit this unification are the use of an axially distributed blood-tissue exchange region, inclusion of a lymphatic drain in the interstitium, and the independent computation of transcapillary solute and solvent fluxes through three different pathways.

Transient transcapillary exchange of water driven by osmotic forces in the heart

Osmotic transient responses in organ weight after changes in perfusate osmolarity have implied steric hindrance to small-molecule transcapillary exchange, but tracer methods do not. We obtained osmotic weight transient data in isolated, Ringer-perfused rabbit hearts with NaCl, urea, glucose, sucrose, raffinose, inulin, and albumin and analyzed the data with a new anatomically and physicochemically based model accounting for 1) transendothelial water flux, 2) two sizes of porous passages across the capillary wall, 3) axial intracapillary concentration gradients, and 4) water fluxes between myocytes and interstitium. During steady-state conditions approximately 28% of the transcapillary water flux going to form lymph was through the endothelial cell membranes [capillary hydraulic conductivity (Lp) = 1.8 +/- 0.6 x 10-8 cm. s-1. mmHg-1], presumably mainly through aquaporin channels. The interendothelial clefts (with Lp = 4.4 +/- 1.3 x 10-8 cm. s-1. mmHg-1) account for 67% of the water flux; clefts are so wide (equivalent pore radius was 7 +/- 0.2 nm, covering approximately 0.02% of the capillary surface area) that there is no apparent hindrance for molecules as large as raffinose. Infrequent large pores account for the remaining 5% of the flux. During osmotic transients due to 30 mM increases in concentrations of small solutes, the transendothelial water flux was in the opposite direction and almost 800 times as large and was entirely transendothelial because no solute gradient forms across the pores. During albumin transients, gradients persisted for long times because albumin does not permeate small pores; the water fluxes per milliosmolar osmolarity change were 200 times larger than steady-state water flux. The analysis completely reconciles data from osmotic transient, tracer dilution, and lymph sampling techniques.

A computational model of oxygen transport from red blood cells to mitochondria

A computational model of oxygen transport from red blood cells to mitochondria with subsequent reaction to water is presented. This computational model consists of a five region convection-diffusion-reaction mathematical model which is solved using a standard numerical time-split method. The unique feature of this mathematical model is the treatment of the red blood cells and the plasma as two separate flows. The numerical method is second order accurate overall. This computational model is useful for analyzing residue data from positron emission tomography or data from multiple indicator dilution curves.

The mechanical and metabolic basis of myocardial blood flow heterogeneity

Precise measurements of regional myocardial blood flow heterogeneity had to be developed before one could seek causation for the heterogeneity. Deposition techniques (particles or molecular microspheres) are the most precise, but imaging techniques have begun to provide high enough resolution to allow in vivo studies. Assigning causation has been difficult. There is no apparent association with the regional concentrations of energy-related enzymes or substrates, but these are measures of status, not of metabolism. There is statistical correlation between flow and regional substrate uptake and utilization. Attribution of regional flow variation to vascular anatomy or to vasomotor control appears not to be causative on a long-term basis. The closest relationships appear to be with mechanical function, but one cannot say for sure whether this is related to ATP hydrolysis at the crossbridge or associated metabolic reactions such as calcium uptake by the sarcoplasmic reticulum.

Estimation of aqueous distributional spaces in the dual perfused rat liver

1. The aim of this study was to estimate the aqueous distributional spaces of the liver as a function of the route of input: portal vein (PV) versus hepatic artery (HA). 2. Studies were performed in the situ single (PV) and dual (PV-HA) perfused rat liver (n = 6-10) using Krebs bicarbonate buffer at constant PV (12 ml min-1) and HA (3 ml min-1) flow rates. An impulse input-output response technique was employed, varying the route of input, using non-labelled erythrocytes (intravascular marker), 125I-albumin and [14C]sucrose (extracellular markers), and [14C]urea and 3H2O (total water markers) as the reference indicators. 3. Distributional spaces were estimated using two different methods, namely standard and specific. The standard method was applied to hepatic outflow data obtained from the single PV perfused liver. The specific method was used when operating in the dual perfused mode to provide an estimate of the excess space perfused solely by the HA input. Specific spaces, interstitial and intracellular volumes, were estimated by difference. 4. The results were evaluated by means of visual inspection of the outflow profiles and comparison of the distributional spaces. Different hepatic effluent profiles obtained as a function of the route of input indicated that these two inputs did not completely mix within the liver. Estimates of the distributional spaces supported this observation, and further suggested that the arterial input perfuses 9-12 % more hepatic tissue than the venous input. 5. The knowledge obtained from the existence of a specific arterial space can be extended to help make predictions about the fate of an eliminated compound following arterial administration. Any difference between the HA and PV in terms of hepatic recovery could be attributed to this excess space and its enzyme density.

Endothelial adenosine transporter characterization in perfused guinea pig hearts

Adenosine (Ado), a smooth muscle vasodilator and modulator of cardiac function, is taken up by many cell types via a saturable transporter, blockable by dipyridamole. To quantitate the influences of endothelial cells in governing the blood-tissue exchange of Ado and its concentration in the interstitial fluid, one must define the permeability-surface area products (PS) for Ado via passive transport through interendothelial gaps [PS(g)(Ado)] and across the endothelial cell luminal membrane (PS(ecl)) in their normal in vivo setting. With the use of the multiple-indicator dilution (MID) technique in Krebs-Ringer perfused, isolated guinea pig hearts (preserving endothelial myocyte geometry) and by separating Ado metabolites by HPLC, we found permeability-surface area products for an extracellular solute, sucrose, via passive transport through interendothelial gaps [PS(g)(Suc)] to be 1.9 +/- 0.6 ml. g(-1). min(-1) (n = 16 MID curves in 4 hearts) and took PS(g)(Ado) to be 1. 2 times PS(g)(Suc). MID curves were obtained with background nontracer Ado concentrations up to 800 micrometer, partially saturating the transporter and reducing its effective PS(ecl) for Ado. The estimated maximum value for PS(ecl) in the absence of background adenosine was 1.1 +/- 0.1 ml. g(-1). min(-1) [maximum rate of transporter conformational change to move the substrate from one side of the membrane to the other (maximal velocity; V(max)) times surface area of 125 +/- 11 nmol. g(-1). min(-1)], and the Michaelis-Menten constant (K(m)) was 114 +/- 12 microM, where +/- indicates 95% confidence limits. Physiologically, only high Ado release with hypoxia or ischemia will partially saturate the transporter.

Heterogeneity of local myocardial flow and oxidative metabolism

In mammalian hearts, local myocardial flow (LMF) varies between 20 and 200% of the mean. It is not clear whether oxidative metabolism has a similar degree of heterogeneity. Therefore, we investigated the relation between LMF and local oxidative metabolism in isolated rabbit hearts. Buffer oxygenation with (18)O(2) resulted in labeled myocardial oxidation water (H(2)(18)O). In four hearts, myocardial oxygen consumption (MVO(2)) was calculated from the H(2)(18)O production and compared with that calculated according to Fick. In eight additional hearts, LMF was measured using microspheres. Coronary venous H(2)(18)O kinetics and local H(2)(18)O residues were determined and analyzed by mathematical modeling. MVO(2) recovery from H(2)(18)O was >93% compared with that according to Fick. LMF ranged from 1.91 to 11.24 ml. min(-1). g(-1), and local H(2)(18)O residue ranged from 0.41 to 1.04 micromol/g. Both variables correlated (r = 0.62, n = 64, P < 0.001). Measurements in nine hearts were fitted by modeling using capillary permeability-surface area products (PS(c)) from 2 to 10 ml. min(-1). g(-1). With flow-proportional PS(c), a 3.33-fold difference in LMF was associated with a 6.45-fold difference in local MVO(2). Both LMF and local oxidative metabolism are spatially heterogeneous, and they correlate to one another.

Cardiac endothelial transport and metabolism of adenosine and inosine

The influence of transmembrane flux limitations on cellular metabolism of purine nucleosides was assessed in whole organ studies. Transcapillary transport of the purine nucleosides adenosine (Ado) and inosine (Ino) via paracellular diffusion through interendothelial clefts in parallel with carrier-mediated transendothelial fluxes was studied in isolated, Krebs-Henseleit-perfused rabbit and guinea pig hearts. After injection into coronary inflow, multiple-indicator dilution curves were obtained from coronary outflow for 90 s for 131I-labeled albumin (intravascular reference tracer), [3H]arabinofuranosyl hypoxanthine (AraH; extracellular reference tracer and nonreactive adenosine analog), and either [14C]Ado or [14C]Ino. Ado or Ino was separated from their degradative products, hypoxanthine, xanthine, and uric acid, in each outflow sample by HPLC and radioisotope counting. Ado and Ino, but not AraH, permeate the luminal membrane of endothelial cells via a saturable transporter with permeability-surface area product PS(ecl) and also diffuse passively through interendothelial clefts with the same conductance (PSg) as AraH. These parallel conductances were estimated via fitting with an axially distributed, multi-pathway, four-region blood-tissue exchange model. PSg for AraH were approximately 4 and 2.5 ml. g(-1). min(-1) in rabbits and guinea pigs, respectively. In contrast, transplasmalemmal conductances (endothelial PS(ecl)) were approximately 0.2 ml. g(-1). min(-1) for both Ado and Ino in rabbit hearts but approximately 2 ml. g(-1). min(-1) in guinea pig hearts, an order of magnitude different. Purine nucleoside metabolism also differs between guinea pig and rabbit cardiac endothelium. In guinea pig heart, 50% of the tracer Ado bolus was retained, 35% was washed out as Ado, and 15% was lost as effluent metabolites; 25% of Ino was retained, 50% washed out, and 25% was lost as metabolites. In rabbit heart, 45% of Ado was retained and 5% lost as metabolites, and 7% of Ino was retained and 3% lost as metabolites. We conclude that endothelial transport of Ado and Ino is a prime determinant of their metabolic fates: where transport rates are high, metabolic transformation is high.

Measurement of the distribution volume of gadopentetate dimeglumine at echo-planar MR imaging to quantify myocardial infarction: comparison with 99mTc-DTPA autoradiography in rats

PURPOSE

To measure the fractional distribution volume of gadopentetate dimeglumine in normal and reperfused infarcted myocardium at magnetic resonance (MR) imaging by using the fractional distribution volume of technetium 99m-diethylenetriaminepentaacetic acid (DTPA) as an independent reference.

MATERIALS AND METHODS

Rats were subjected to 1 hour of coronary artery occlusion and 1 hour of reperfusion before inversion-recovery echo-planar imaging or autoradiography. Regional change in relaxation rate (delta R1) ratios for myocardium over blood were compared with radioactivity ratios for myocardium over blood after the injection of 99mTc-DTPA.

RESULTS

Both delta R1 and radioactivity ratios demonstrated equilibrium distribution and hence represent partition coefficients (lambda). The fractional distribution volumes were greater in infarcted myocardium (0.90 +/- 0.05 for gadopentetate dimeglumine and 0.89 +/- 0.04 for 99mTc-DTPA) than in normal myocardium (0.23 +/- 0.02 for gadopentetate dimeglumine and 0.16 +/- 0.01 for 99mTc-DTPA). Area at risk at autoradiography was not significantly different from that at histomorphometry. The infarction size defined by using triphenyltetrazolium chloride was 13% +/- 4 smaller than that defined by using autoradiography.

CONCLUSION

The fractional distribution volumes of gadopentetate dimeglumine and 99mTc-DTPA are similar and indicate extracellular distribution in normal myocardium and intracellular as well as extracellular distribution in reperfused infarction. Because the failure of cells to exclude these agents is indicative of necrosis, contrast medium-enhanced MR imaging may be useful to quantify myocardial infarction.

Potassium and thallium uptake in dog myocardium

We sought to ascertain the rates and mechanisms of uptake of markers for regional myocardial blood flows.

METHODS

The rates of exchange of potassium and thallium across capillary walls and cell membranes in isolated blood-perfused dog hearts were estimated from multiple indicator dilution curves recorded for 131I-albumin, 42K and 201Tl from the coronary sinus outflow following injection into arterial inflow. Analysis involved fitting the observed dilution curves with a model composed of a capillary-interstitial fluid-cell exchange region and nonexchanging larger vessels.

RESULTS

Capillary permeability surface products (PSc) for potassium and thallium were similar, 0.82 +/- 0.33 (mean +/- s.d., n = 19) and 0.87 +/- 0.32 ml min-1 g-1 (n = 24) with a ratio for simultaneous pairs of 1.02 +/- 0.27 (n = 19). For the myocardial cells, PSpc averaged 3.7 +/- 3.1 ml min-1 g-1 (n = 19) for K+ and 9.5 +/- 3.9 (n = 24) for Tl+; the ratio of potassium to thallium averaged 0.40 +/- 0.19 (n = 18), thereby omitting a single high value for potassium. This high cellular influx for thallium is interpreted as due to its passage through ionic channels for both Na+ and K+.

CONCLUSION

The high permeabilities and large volumes of distribution make thallium and potassium among the best ionic deposition markers for regional flow. Their utility for this purpose is compromised by significant capillary barrier limitation retarding uptake; so regional flow is underestimated modestly in high-flow regions particularly.

Coronary microcirculation in health and disease. Summary of an NHLBI workshop

This article summarizes a 2-day workshop on the coronary microcirculation held in Bethesda, Md, in September 1994 and sponsored by the National Heart, Lung, and Blood Institute of the National Institutes of Health. The workshop explored a variety of topics pertaining to coronary microvascular physiology and pathophysiology. The latest methodologies that are being used to investigate the coronary microvasculature, including endoscopic microscopy of the intramural coronary microvasculature and micro-x-ray computerized tomography, were discussed. The most recent advances in the regulation of the coronary microcirculation-for example, myogenic and flow-dependent responses, KATP channels, and regional heterogeneity-were reported. The workshop touched on the relation of the microcirculation to clinically important conditions and offered recommendations for future research in this important area. Comparisons are made to recent advances in the peripheral circulation and current gaps in our knowledge concerning the coronary microcirculation. In recent years, research on the coronary microcirculation has made substantial advances, in part as a result of investigations in the peripheral microcirculation but also because of the application of unique methodologies. This research is providing new ways to investigate abnormalities of myocardial perfusion, an area of inquiry that until recently has been limited to examination of coronary pressure-flow relationships.

Modeling regional myocardial flows from residue functions of an intravascular indicator

The purpose of the present study was to determine the accuracy and the sources of error in estimating regional myocardial blood flow and vascular volume from experimental residue functions obtained by external imaging of an intravascular indicator. For the analysis, a spatially distributed mathematical model was used that describes transport through a multiple-pathway vascular system. Reliability of the parameter estimates was tested by using sensitivity function analysis and by analyzing "pseudodata": realistic model solutions to which random noise was added. Increased uncertainty in the estimates of flow in the pseudodata was observed when flow was near maximal physiological values, when dispersion of the vascular input was more than twice the dispersion of the microvascular system for an impulse input, and when the sampling frequency was < 2 samples/s. Estimates of regional blood volume were more reliable than estimates of flow. Failure to account for normal flow heterogeneity caused systematic underestimates of flow. To illustrate the method used for estimating regional flow, magnetic resonance imaging was used to obtain myocardial residue functions after left atrial injections of polylysine-Gd-diethylenetriaminepentaacetic acid, an intravascular contrast agent, in anesthetized chronically instrumental dogs. To test the increase in dispersion of the vascular input after central venous injections, magnetic resonance imaging data obtained in human subjects were compared with left ventricular blood pool curves obtained in dogs. It is concluded that if coronary flow is in the normal range, when the vascular input is a short bolus, and the heart is imaged at least once per cardiac cycle, then regional myocardial blood flow and vascular volume may be reliably estimated by analyzing residue functions of an intravascular indicator, providing a noninvasive approach with potential clinical application.

Modeling [15O]oxygen tracer data for estimating oxygen consumption

The most direct measure of oxidative tissue metabolism is the conversion rate of oxygen to water via mitochondrial respiration. To calculate oxygen consumption from the analysis of tissue residue curves or outflow dilution curves after injection of labeled oxygen one needs realistic mathematical models that account for convection, diffusion, and transformation in the tissue. A linear, three-region, axially distributed model accounts for intravascular convection, penetration of capillary and parenchymal cell barriers (with the use of appropriate binding spaces to account for oxygen binding to hemoglobin and myoglobin), the metabolism to [15O]water in parenchymal cells, and [15O]water transport into the venous effluent. Model solutions fit residue and outflow dilution data obtained in an isolated, red blood cell-perfused rabbit heart preparation and give estimates of the rate of oxygen consumption similar to those obtained experimentally from the flow times the arteriovenous differences in oxygen contents. The proposed application is for the assessment of regional oxidative metabolism in vivo from tissue 15O-residue curves obtained by positron emission tomography.

Modeling blood flow heterogeneity

It has been known for some time that regional blood flows within an organ are not uniform. Useful measures of heterogeneity of regional blood flows are the standard deviation and coefficient of variation or relative dispersion of the probability density function (PDF) of regional flows obtained from the regional concentrations of tracers that are deposited in proportion to blood flow. When a mathematical model is used to analyze dilution curves after tracer solute administration, for many solutes it is important to account for flow heterogeneity and the wide range of transit times through multiple pathways in parallel. Failure to do so leads to bias in the estimates of volumes of distribution and membrane conductances. Since in practice the number of paths used should be relatively small, the analysis is sensitive to the choice of the individual elements used to approximate the distribution of flows or transit times. Presented here is a method for modeling heterogeneous flow through an organ using a scheme that covers both the high flow and long transit time extremes of the flow distribution. With this method, numerical experiments are performed to determine the errors made in estimating parameters when flow heterogeneity is ignored, in both the absence and presence of noise. The magnitude of the errors in the estimates depends upon the system parameters, the amount of flow heterogeneity present, and whether the shape of the input function is known. In some cases, some parameters may be estimated to within 10% when heterogeneity is ignored (homogeneous model), but errors of 15-20% may result, even when the level of heterogeneity is modest. In repeated trials in the presence of 5% noise, the mean of the estimates was always closer to the true value with the heterogeneous model than when heterogeneity was ignored, but the distributions of the estimates from the homogeneous and heterogeneous models overlapped for some parameters when outflow dilution curves were analyzed. The separation between the distributions was further reduced when tissue content curves were analyzed. It is concluded that multipath models accounting for flow heterogeneity are a vehicle for assessing the effects of flow heterogeneity under the conditions applicable to specific laboratory protocols, that efforts should be made to assess the actual level of flow heterogeneity in the organ being studied, and that the errors in parameter estimates are generally smaller when the input function is known rather than estimated by deconvolution.

Fractal 15O-labeled water washout from the heart

To characterize the washout of water from the heart, we used a flow-limited (not diffusion- or permeability-limited) marker for blood-tissue exchange, namely, tracer-labeled water. Experiments were performed by injecting 15O-labeled water into the inflow to isolated blood-perfused rabbit hearts and by recording the tracer content in the heart and in the outflow simultaneously for up to 5 minutes. The data exhibit a particular combination of power law forms: (1) The downslopes of the residue and outflow curves were both power law functions, with the residue diminishing as t-alpha and the outflow as t-alpha-1, where alpha is interpreted to be the dimensionless exponent of a fractal power law relation characterizing the self-similarity inherent in each curve. (2) The fractional escape rate, given by the outflow curve divided by the residue curve, diminished almost exactly as t-1. In 18 sets of curves, alpha averaged 2.21 +/- 0.27. These results lead to an improved method for extrapolating the downslopes of indicator dilution curves to estimate their areas and therefore the blood flows. The evidence also points strongly to the conclusions that myocardial water washout is a fractal process and that stirred tank models are inappropriate for the heart.

Regional myocardial blood volume and flow: first-pass MR imaging with polylysine-Gd-DTPA

The authors investigated the utility of an intravascular magnetic resonance (MR) contrast agent, poly-L-lysine-gadolinium diethylenetriaminepentaacetic acid (DTPA), for differentiating acutely ischemic from normally perfused myocardium with first-pass MR imaging. Hypoperfused regions, identified with microspheres, on the first-pass images displayed significantly decreased signal intensities compared with normally perfused myocardium (P < .0007). Estimates of regional myocardial blood content, obtained by measuring the ratio of areas under the signal intensity-versus-time curves in tissue regions and the left ventricular chamber, averaged 0.12 mL/g +/- 0.04 (n = 35), compared with a value of 0.11 mL/g +/- 0.05 measured with radiolabeled albumin in the same tissue regions. To obtain MR estimates of regional myocardial blood flow, in situ calibration curves were used to transform first-pass intensity-time curves into content-time curves for analysis with a multiple-pathway, axially distributed model. Flow estimates, obtained by automated parameter optimization, averaged 1.2 mL/min/g +/- 0.5 (n = 29), compared with 1.3 mL/min/g +/- 0.3 obtained with tracer microspheres in the same tissue specimens at the same time. The results represent a combination of T1-weighted first-pass imaging, intravascular relaxation agents, and a spatially distributed perfusion model to obtain absolute regional myocardial blood flow and volume.

Correlation of heterogeneous blood flow and fatty acid uptake in the normal dog heart

Blood flow heterogeneity in normal myocardium may be caused by heterogeneous metabolic demand. We studied, from 80 tissue samples of the left ventricle (LV) of eight anesthetised, open-chest dogs (with prior beta-blockade (metoprolol) in four dogs), the radioactivity of 201Thallium-chloride (201Tl), an indicator of blood flow, and of the fatty acid 131-Iodine-heptadecanoic acid (131I-HDA), an indicator of metabolic demand, 3 min after intravenous injection. Global LV uptake (in percent of injected dose x 10(-2), per g tissue; mean +/- SD) was 4.94 +/- 0.71 for 201Tl and 4.48 +/- 0.58 for 131I-HDA in the dogs without beta-blockade, and 2.08 +/- 0.26 and 1.69 +/- 0.20, respectively, in dogs with beta-blockade (p < 0.05). Beta-blockade thus decreased the fraction of cardiac output delivered to the LV, concurrently with a decreased heart rate and arterial blood pressure (p < 0.05) and, thus, global metabolic demand and fatty acid uptake. Regional radioactivities per gram were normalized for mean LV radioactivities and heterogeneity was expressed as the coefficient of variation (CV). For pooled data (n = 320) in dogs without beta-blockade, regional 201Tl and 131I-HDA radioactivities varied from a factor of 0.1 to 1.6 and 0.3 to 1.8 of mean radioactivities, with a CV of 22.9 and 19.4%, respectively, and correlated (r = 0.77, p < 0.005). For pooled data (n = 320) in dogs with beta-blockade, regional 201Tl and 131I-HDA radioactivities varied from a factor of 0.2 to 1.5 and 0.2 to 1.6 of mean radioactivity and CV was 23.6% and 24.8%, respectively; r = 0.92 (p < 0.005). The endo/epi ratio for both radioactivities exceeded unity in each dog. In normal myocardium, blood flow and fatty acid uptake are thus heterogeneous, both transmurally and circumferentially, and matched, concomitantly with coupling of global blood flow to global metabolic demand and fatty acid uptake. This supports the idea that heterogeneous myocardial O2 supply reflects heterogeneous metabolic demand.

Mathematical modelling in nuclear medicine

Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space. Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging. One formulates a model first by defining what it should represent: this is the hypothesis. When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. This is what one would like to test against data. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations. The former are known as distributed models and the latter as lumped compartmental or mixing chamber models. Since both are derived from the same ideas, the parameters are usually the same; their differences are in their ability to represent the hypothesis correctly, quantitatively, and sometimes in their computability. In this essay we review the philosophical and practical aspects of such modelling analysis for translating image sequences into physiological terms.

A comparison of ascorbate and glucose transport in the heart

Multiple indicator-dilution experiments were done to compare the transcapillary exchange of tracer amounts of L-[14C]ascorbate and D-[3H]glucose (against an intravascular reference 131I-albumin) in Ringer-perfused (5 mM glucose) isolated rabbit hearts. The indicator-dilution curves for the two were virtually superimposed over the first 40-80 s. Estimates of the capillary permeability-surface area products, PSc, were the same, 2.3 +/- 0.7 (SD) ml X g-1 X min-1 (n = 18), in accord with the coincidence of their instantaneous extractions. The similarity of glucose and ascorbate permeabilities is explained by the similarity in molecular weights and passive diffusivity, their lipophobic nature, and the paucity of carrier-mediated endothelial transport for either molecule. The data were analyzed via a model composed of aggregates of spatially distributed capillary-tissue units (capillary blood, interstitium, myocytes) accounting for the heterogeneity of regional flows. The interstitial volumes in this preparation are enlarged, 0.30 +/- 0.04 ml/g. There is substantial entry into myocardial cells, the cell permeability-surface area products being approximately 2-3 ml X g-1 X min-1 for ascorbate and glucose. The estimated volumes of interstitial and intracellular space, 0.30 and 0.47 ml X g-1 X min-1, reflect interstitial edema and are very close to measured values, giving reassurance concerning the methods of modeling analysis.