Quantitative transport mapping (QTM) of the kidney with an approximate microvascular network

Purpose

Proof‐of‐concept study of mapping renal blood flow vector field according to the inverse solution to a mass transport model of time resolved tracer‐labeled MRI data.

Theory and Methods

To determine tissue perfusion according to the underlying physics of spatiotemporal tracer concentration variation, the mass transport equation is integrated over a voxel with an approximate microvascular network for fitting time‐resolved tracer imaging data. The inverse solution to the voxelized transport equation provides the blood flow vector field, which is referred to as quantitative transport mapping (QTM). A numerical microvascular network modeling the kidney with computational fluid dynamics reference was used to verify the accuracy of QTM and the current Kety’s method that uses a global arterial input function. Multiple post‐label delay arterial spin labeling (ASL) of the kidney on seven subjects was used to assess QTM in vivo feasibility.

Results

Against the ground truth in the numerical model, the error in flow estimated by QTM (18.6%) was smaller than that in Kety’s method (45.7%, 2.5‐fold reduction). The in vivo kidney perfusion quantification by QTM (cortex: 443 ± 58 mL/100 g/min and medulla: 190 ± 90 mL/100 g/min) was in the range of that by Kety’s method (482 ± 51 mL/100 g/min in the cortex and 242 ± 73 mL/100 g/min in the medulla), and QTM provided better flow homogeneity in the cortex region.

Conclusions

QTM flow velocity mapping is feasible from multi‐delay ASL MRI data based on inverting the transport equation. In a numerical simulation, QTM with deconvolution in space and time provided more accurate perfusion quantification than Kety’s method with deconvolution in time only.

A Glucose-Dependent Pharmacokinetic/ Pharmacodynamic Model of ACE Inhibition in Kidney Cells

Diabetic kidney disease (DKD) is a major cause of renal failure. Podocytes are terminally differentiated renal epithelial cells that are key targets of damage due to DKD. Podocytes express a glucose-stimulated local renin-angiotensin system (RAS) that produces angiotensin II (ANG II). Local RAS differs from systemic RAS, which has been studied widely. Hyperglycemia increases the production of ANG II by podocyte cells, leading to podocyte injury. Angiotensin-converting enzyme (ACE) is involved in the production of ANG II, and ACE inhibitors are drugs used to suppress elevated ANG II concentration. As systemic RAS differs from the local RAS in podocytes, ACE inhibitor drugs should act differently in local versus systemic contexts. Experimental and computational studies have considered the pharmacokinetics (PK) and pharmacodynamics (PD) of ACE inhibition of the systemic RAS. Here, a PK/PD model for ACE inhibition is developed for the local RAS in podocytes. The model takes constant or dynamic subject-specific glucose concentration input to predict the ANG II concentration and the corresponding effects of drug doses locally and systemically. The model is developed for normal and impaired renal function in combination with different glucose conditions, thus enabling the study of various pathophysiological conditions. Parameter uncertainty is also analyzed. Such a model can improve the study of the effects of drugs at the cellular level and can aid in development of therapeutic approaches to slow the progression of DKD.

Investigation of aquaporins and apparent diffusion coefficient from ultra-high b-values in a rat model of diabetic nephropathy

Background

To assess kidney damage in a rat model of type-2 diabetic nephropathy based on apparent diffusion coefficient (ADC) data obtained from ultra-high b-values and discuss its relationship to the expression of aquaporins (AQPs).

Methods

This study was approved by the institutional Animal Care and Use Committee. Thirty male Sprague-Dawley rats were randomised into two groups: (1) untreated controls and (2) diabetes mellitus (DM). All rats underwent diffusion-weighted imaging (DWI) with 18 b-values (0–4500 s/mm²). Maps of low ADC (ADC_low), standard ADC (ADC_st) and ultra-high ADC (ADC_uh) were calculated from low b-values (0–200 s/mm²), standard b-values (300–1500 s/mm²) and ultra-high b-values (1700–4500 s/mm²), respectively. The expression of AQPs in the kidneys was studied using immunohistochemistry. Laboratory parameters of diabetic and kidney functions, ADC_low, ADC_st, ADC_uh, and the optical density (OD) of AQP expression in the two groups were compared using an independent t test. Correlations between ADCs and the OD of AQP expression were evaluated by Pearson’s correlation analysis.

Results

ADC_uh were significantly higher in the cortex (CO), outer stripe of the outer medulla (OS) and inner stripe of the outer medulla (IS), and the OD values of AQ-2 were significantly higher in the OS, IS and inner medulla (IM) in DM animals compared with control animals. ADC_uh and OD values of AQP-2 expression were positively correlated in the OS, IS and IM of the kidney.

Conclusions

ADC_uh may work as useful metrics for early detection of kidney damage in diabetic nephropathy and may be associated with AQP-2 expression.

In vivo imaging of systemic transport and elimination of xenobiotics and endogenous molecules in mice

We describe a two-photon microscopy-based method to evaluate the in vivo systemic transport of compounds. This method comprises imaging of the intact liver, kidney and intestine, the main organs responsible for uptake and elimination of xenobiotics and endogenous molecules. The image quality of the acquired movies was sufficient to distinguish subcellular structures like organelles and vesicles. Quantification of the movement of fluorescent dextran and fluorescent cholic acid derivatives in different organs and their sub-compartments over time revealed significant dynamic differences. Calculated half-lives were similar in the capillaries of all investigated organs but differed in the specific sub-compartments, such as parenchymal cells and bile canaliculi of the liver, glomeruli, proximal and distal tubules of the kidney and lymph vessels (lacteals) of the small intestine. Moreover, tools to image immune cells, which can influence transport processes in inflamed tissues, are described. This powerful approach provides new possibilities for the analysis of compound transport in multiple organs and can support physiologically based pharmacokinetic modeling, in order to obtain more precise predictions at the whole body scale.

The Esophagiome: concept, status, and future perspectives

The term "Esophagiome" is meant to imply a holistic, multiscale treatment of esophageal function from cellular and muscle physiology to the mechanical responses that transport and mix fluid contents. The development and application of multiscale mathematical models of esophageal function are central to the Esophagiome concept. These model elements underlie the development of a "virtual esophagus" modeling framework to characterize and analyze function and disease by quantitatively contrasting normal and pathophysiological function. Functional models incorporate anatomical details with sensory-motor properties and functional responses, especially related to biomechanical functions, such as bolus transport and gastrointestinal fluid mixing. This brief review provides insight into Esophagiome research. Future advanced models can provide predictive evaluations of the therapeutic consequences of surgical and endoscopic treatments and will aim to facilitate clinical diagnostics and treatment.

Applied Concepts in PBPK Modeling: How to Build a PBPK/PD Model

The aim of this tutorial is to introduce the fundamental concepts of physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) modeling with a special focus on their practical implementation in a typical PBPK model building workflow. To illustrate basic steps in PBPK model building, a PBPK model for ciprofloxacin will be constructed and coupled to a pharmacodynamic model to simulate the antibacterial activity of ciprofloxacin treatment.

Key to Opening Kidney for In Vitro-In Vivo Extrapolation Entrance in Health and Disease: Part I: In Vitro Systems and Physiological Data

The programme for the 2015 AAPS Annual Meeting and Exhibition (Orlando, FL; 25-29 October 2015) included a sunrise session presenting an overview of the state-of-the-art tools for in vitro-in vivo extrapolation (IVIVE) and mechanistic prediction of renal drug disposition. These concepts are based on approaches developed for prediction of hepatic clearance, with consideration of scaling factors physiologically relevant to kidney and the unique and complex structural organisation of this organ. Physiologically relevant kidney models require a number of parameters for mechanistic description of processes, supported by quantitative information on renal physiology (system parameters) and in vitro/in silico drug-related data. This review expands upon the themes raised during the session and highlights the importance of high quality in vitro drug data generated in appropriate experimental setup and robust system-related information for successful IVIVE of renal drug disposition. The different in vitro systems available for studying renal drug metabolism and transport are summarised and recent developments involving state-of-the-art technologies highlighted. Current gaps and uncertainties associated with system parameters related to human kidney for the development of physiologically based pharmacokinetic (PBPK) model and quantitative prediction of renal drug disposition, excretion, and/or metabolism are identified.

Systems Medicine in Pharmaceutical Research and Development

The development of new drug therapies requires substantial and ever increasing investments from the pharmaceutical company. Ten years ago, the average time from early target identification and optimization until initial market authorization of a new drug compound took more than 10 years and involved costs in the order of one billion US dollars. Recent studies indicate even a significant growth of costs in the meanwhile, mainly driven by the increasing complexity of diseases addressed by pharmaceutical research.Modeling and simulation are proven approaches to handle highly complex systems; hence, systems medicine is expected to control the spiral of complexity of diseases and increasing costs. Today, the main focus of systems medicine applications in industry is on mechanistic modeling. Biological mechanisms are represented by explicit equations enabling insight into the cooperation of all relevant mechanisms. Mechanistic modeling is widely accepted in pharmacokinetics, but prediction from cell behavior to patients is rarely possible due to lacks in our understanding of the controlling mechanisms. Data-driven modeling aims to compensate these lacks by the use of advanced statistical and machine learning methods. Future progress in pharmaceutical research and development will require integrated hybrid modeling technologies allowing realization of the benefits of both mechanistic and data-driven modeling. In this chapter, we sketch typical industrial application areas for both modeling techniques and derive the requirements for future technology development.

Implementation of a model of bodily fluids regulation

The classic model of blood pressure regulation by Guyton et al. (Annu Rev Physiol 34:13–46, 1972a; Ann Biomed Eng 1:254–281, 1972b) set a new standard for quantitative exploration of physiological function and led to important new insights, some of which still remain the focus of debate, such as whether the kidney plays the primary role in the genesis of hypertension (Montani et al. in Exp Physiol 24:41–54, 2009a; Exp Physiol 94:382–388, 2009b; Osborn et al. in Exp Physiol 94:389–396, 2009a; Exp Physiol 94:388–389, 2009b). Key to the success of this model was the fact that the authors made the computer code (in FORTRAN) freely available and eventually provided a convivial user interface for exploration of model behavior on early microcomputers (Montani et al. in Int J Bio-med Comput 24:41–54, 1989). Ikeda et al. (Ann Biomed Eng 7:135–166, 1979) developed an offshoot of the Guyton model targeting especially the regulation of body fluids and acid–base balance; their model provides extended renal and respiratory functions and would be a good basis for further extensions. In the interest of providing a simple, useable version of Ikeda et al.’s model and to facilitate further such extensions, we present a practical implementation of the model of Ikeda et al. (Ann Biomed Eng 7:135–166, 1979), using the ODE solver Berkeley Madonna.

Virtual Systems Pharmacology (ViSP) software for simulation from mechanistic systems-level models

Multiple software programs are available for designing and running large scale system-level pharmacology models used in the drug development process. Depending on the problem, scientists may be forced to use several modeling tools that could increase model development time, IT costs and so on. Therefore, it is desirable to have a single platform that allows setting up and running large-scale simulations for the models that have been developed with different modeling tools. We developed a workflow and a software platform in which a model file is compiled into a self-contained executable that is no longer dependent on the software that was used to create the model. At the same time the full model specifics is preserved by presenting all model parameters as input parameters for the executable. This platform was implemented as a model agnostic, therapeutic area agnostic and web-based application with a database back-end that can be used to configure, manage and execute large-scale simulations for multiple models by multiple users. The user interface is designed to be easily configurable to reflect the specifics of the model and the user's particular needs and the back-end database has been implemented to store and manage all aspects of the systems, such as Models, Virtual Patients, User Interface Settings, and Results. The platform can be adapted and deployed on an existing cluster or cloud computing environment. Its use was demonstrated with a metabolic disease systems pharmacology model that simulates the effects of two antidiabetic drugs, metformin and fasiglifam, in type 2 diabetes mellitus patients.

Assessment of impaired vascular reactivity in a rat model of diabetic nephropathy: effect of nitric oxide synthesis inhibition on intrarenal diffusion and oxygenation measured by magnetic resonance imaging

Diabetes is associated with impaired vascular reactivity and the development of diabetic nephropathy. In a rat model of streptozotocin-induced diabetic nephropathy, the effects of systemic nitric oxide (NO) synthesis inhibition on intrarenal diffusion and oxygenation were determined by noninvasive magnetic resonance diffusion tensor imaging and blood O2 level-dependent (BOLD) imaging, respectively. Eight weeks after the induction of diabetes, 21 rats [ n = 7 rats each in the untreated control group, diabetes mellitus (DM) group, and DM with uninephrectomy (DM UNX) group] were examined by MRI. Diffusion tensor imaging and BOLD sequences were acquired before and after NO synthesis inhibition with N-nitro-l-arginine methyl ester (l-NAME). In the same rats, mean arterial pressure and vascular conductance were determined with and without the influence of l-NAME. In control animals, NO synthesis inhibition was associated with a significant increase of mean arterial pressure of 33.8 ± 4.3 mmHg ( P < 0.001) and a decrease of vascular conductance of −17.8 ± 2.0 μl·min−1·100 mmHg−1 ( P < 0.001). These changes were attenuated in both DM and DM UNX groups with no significant difference between before and after l-NAME measurements in DM UNX animals. Similarly, l-NAME challenge induced a significant reduction of renal transverse relaxation time (T2*) at MRI in control animals, indicating reduced renal oxygenation after l-NAME injection compared with baseline. DM UNX animals did not show a significant T2* reduction after NO synthesis inhibition in the renal cortex and attenuated T2* reduction in the outer medulla. MRI parameters of tissue diffusion were not affected by l-NAME in all groups. In conclusion, BOLD imaging proved valuable to noninvasively measure renal vascular reactivity upon NO synthesis inhibition in control animals and to detect impaired vascular reactivity in animals with diabetic nephropathy.

Computational medicine: translating models to clinical care

Because of the inherent complexity of coupled nonlinear biological systems, the development of computational models is necessary for achieving a quantitative understanding of their structure and function in health and disease. Statistical learning is applied to high-dimensional biomolecular data to create models that describe relationships between molecules and networks. Multiscale modeling links networks to cells, organs, and organ systems. Computational approaches are used to characterize anatomic shape and its variations in health and disease. In each case, the purposes of modeling are to capture all that we know about disease and to develop improved therapies tailored to the needs of individuals. We discuss advances in computational medicine, with specific examples in the fields of cancer, diabetes, cardiology, and neurology. Advances in translating these computational methods to the clinic are described, as well as challenges in applying models for improving patient health.

Multiscale mechanistic modeling in pharmaceutical research and development

Discontinuation of drug development projects due to lack of efficacy or adverse events is one of the main cost drivers in pharmaceutical research and development (R&D). Investments have to be written-off and contribute to the total costs of a successful drug candidate receiving marketing authorization and allowing return on invest. A vital risk for pharmaceutical innovator companies is late stage clinical failure since costs for individual clinical trials may exceed the one billion Euro threshold. To guide investment decisions and to safeguard maximum medical benefit and safety for patients recruited in clinical trials, it is therefore essential to understand the clinical consequences of all information and data generated. The complexity of the physiological and pathophysiological processes and the sheer amount of information available overcharge the mental capacity of any human being and prevent a prediction of the success in clinical development. A rigorous integration of knowledge, assumption, and experimental data into computational models promises a significant improvement of the rationalization of decision making in pharmaceutical industry. We here give an overview of the current status of modeling and simulation in pharmaceutical R&D and outline the perspectives of more recent developments in mechanistic modeling. Specific modeling approaches for different biological scales ranging from intracellular processes to whole organism physiology are introduced and an example for integrative multiscale modeling of therapeutic efficiency in clinical oncology trials is showcased.

Magnetic resonance diffusion tensor imaging for evaluation of histopathological changes in a rat model of diabetic nephropathy

OBJECTIVES

The aim of this study was to investigate whether magnetic resonance (MR) diffusion tensor imaging (DTI) allows assessment of renal pathologies in a rat model of diabetic nephropathy.

MATERIALS AND METHODS

Twenty-one male Sprague-Dawley rats were divided into 3 groups: (1) untreated controls, (2) diabetes (DM), (3) diabetes with uninephrectomy (DM UNX) to accelerate renal impairment. Eight weeks after diabetes induction with streptozotocin, MR imaging was performed in a 1.5-T scanner using an 8-channel wrist coil. Morphological proton density images and echoplanar DTI were obtained (b = 0 and 300 s/mm, 6 diffusion directions). Renal apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values were calculated for each of the different anatomical layers of the kidney. Imaging results, laboratory parameters of diabetic state and kidney function, and renal histopathological changes (glomerulosclerosis, tubular dilatation, and renal fibrosis) were compared between groups. Correlations between FA and histopathological changes were evaluated.

RESULTS

All diabetic animals developed hyperglycemia and hypoinsulinemia. Uremia, albuminuria, and histopathological changes were most pronounced in DM UNX animals. Fractional anisotropy was significantly reduced in DM UNX animals in the cortex (CO) (0.167; confidence interval [CI], 0.151-0.184; P < 0.001), outer stripe of the outer medulla (OS) (0.254; CI, 0.225-0.283; P = 0.038), and inner medulla (IM) (0.459; CI, 0.395-0.523; P = 0.008) compared with control animals (CO, 0.251; CI, 0.224-0.277; OS, 0.309; CI, 0.267-0.350; IM, 0.559; CI, 0.515-0.603). In DM-without-UNX animals, only cortical FA was significantly lower than in controls (P < 0.001). Between groups, ADC values were not different, except for cortical ADC, which was higher in DM UNX animals than in controls. Significant negative correlations were observed between the FA of different anatomical layers and the extent of glomerulosclerosis (CO, P = 0.003, r = -0.65; and OS, P = 0.022, r = -0.52), tubulointerstitial fibrosis (IM, P = 0.028, r = -0.50), and tubular dilatation (CO, P = 0.015, r = -0.55; and IM, P = 0.006, r = -0.61), respectively.

CONCLUSIONS

Magnetic resonance DTI by reduction of FA identified renal pathologies of diabetic nephropathy such as glomerulosclerosis, interstitial fibrosis, and tubular damage. Representing different stages of disease, DM and DM UNX animals could be differentiated. Thus, MR DTI may be valuable for noninvasive detection and monitoring of renal pathology in patients with diabetes.

Mechanisms of pressure-diuresis and pressure-natriuresis in Dahl salt-resistant and Dahl salt-sensitive rats

Background

Data on blood flow regulation, renal filtration, and urine output in salt-sensitive Dahl S rats fed on high-salt (hypertensive) and low-salt (prehypertensive) diets and salt-resistant Dahl R rats fed on high-salt diets were analyzed using a mathematical model of renal blood flow regulation, glomerular filtration, and solute transport in a nephron.

Results

The mechanism of pressure-diuresis and pressure-natriuresis that emerges from simulation of the integrated systems is that relatively small increases in glomerular filtration that follow from increases in renal arterial pressure cause relatively large increases in urine and sodium output. Furthermore, analysis reveals the minimal differences between the experimental cases necessary to explain the observed data. It is determined that differences in renal afferent and efferent arterial resistances are able to explain all of the qualitative differences in observed flows, filtration rates, and glomerular pressure as well as the differences in the pressure-natriuresis and pressure-diuresis relationships in the three groups. The model is able to satisfactorily explain data from all three groups without varying parameters associated with glomerular filtration or solute transport in the nephron component of the model.

Conclusions

Thus the differences between the experimental groups are explained solely in terms of difference in blood flow regulation. This finding is consistent with the hypothesis that, if a shift in the pressure-natriuresis relationship is the primary cause of elevated arterial pressure in the Dahl S rat, then alternation in how renal afferent and efferent arterial resistances are regulated represents the primary cause of chronic hypertension in the Dahl S rat.

Modeling transport in the kidney: investigating function and dysfunction

Mathematical models of water and solute transport in the kidney have significantly expanded our understanding of renal function in both health and disease. This review describes recent theoretical developments and emphasizes the relevance of model findings to major unresolved questions and controversies. These include the fundamental processes by which urine is concentrated in the inner medulla, the ultrastructural basis of proteinuria, irregular flow oscillation patterns in spontaneously hypertensive rats, and the mechanisms underlying the hypotensive effects of thiazides. Macroscopic models of water, NaCl, and urea transport in populations of nephrons have served to test, confirm, or refute a number of hypotheses related to the urine concentrating mechanism. Other macroscopic models focus on the mechanisms, role, and irregularities of renal hemodynamic control and on the regulation of renal oxygenation. At the mesoscale, models of glomerular filtration have yielded significant insight into the ultrastructural basis underlying a number of disorders. At the cellular scale, models of epithelial solute transport and pericyte Ca2+ signaling are being used to elucidate transport pathways and the effects of hormones and drugs. Areas where further theoretical progress is conditional on experimental advances are also identified.