Sex-specific long-term blood pressure regulation: Modeling and analysis

Predicting sex differences in the effects of diuretics in renal epithelial transport during angiotensin II-induced hypertension

Chronic angiotensin II (ANG II) infusion is an experimental model that induces hypertension in rodents. The natriuresis, diuresis, and blood pressure responses differ between males and females. This is perhaps not unexpected, given the rodent kidney, which plays a key role in blood pressure regulation, exhibits marked sex differences. Under normotensive conditions, compared with males, the female rat nephron exhibits lower Na+/H+ exchanger 3 (NHE3) activity along the proximal tubule but higher Na+ transporter activities along the distal segments. ANG II infusion-induced hypertension induces a pressure natriuretic response that reduces NHE3 activity and shifts Na+ transport capacity downstream. The goals of this study were to apply a computational model of epithelial transport along a rat nephron 1) to understand how a 14-day ANG II infusion impacts segmental electrolyte transport in male and female rat nephrons and 2) to identify and explain any sex differences in the effects of loop diuretics, thiazide diuretics, and K+-sparing diuretics. Model simulations suggest that the NHE3 downregulation in the proximal tubule is a major contributor to natriuresis and diuresis in hypertension, with the effects stronger in males. All three diuretics are predicted to induce stronger natriuretic and diuretic effects under hypertension compared with normotension, with relative increases in sodium excretion higher in hypertensive females than in males. The stronger natriuretic responses can be explained by the downstream shift of Na+ transport load in hypertension and by the larger distal transport load in females, both of which limit the ability of the distal segments to further elevate their Na+ transport.NEW & NOTEWORTHY Sex differences in the prevalence of hypertension are found in human and animal models. The kidney, which regulates blood pressure, exhibits sex differences in morphology, hemodynamics, and membrane transporter distributions. This computational modeling study provides insights into how the sexually dimorphic responses to a 14-day angiotensin II infusion differentially impact segmental electrolyte transport in rats. Simulations of diuretic administration explain how the natriuretic and diuretic effects differ between normotension and hypertension and between the sexes.

A modeling analysis of whole body potassium regulation on a high-potassium diet: proximal tubule and tubuloglomerular feedback effects

Potassium (K+) is an essential electrolyte that plays a key role in many physiological processes, including mineralcorticoid action, systemic blood-pressure regulation, and hormone secretion and action. Indeed, maintaining K+ balance is critical for normal cell function, as too high or too low K+ levels can have serious and potentially deadly health consequences. K+ homeostasis is achieved by an intricate balance between the intracellular and extracellular fluid as well as balance between K+ intake and excretion. This is achieved via the coordinated actions of regulatory mechanisms such as the gastrointestinal feedforward effect, insulin and aldosterone upregulation of Na+-K+-ATPase uptake, and hormone and electrolyte impacts on renal K+ handling. We recently developed a mathematical model of whole body K+ regulation to unravel the individual impacts of these regulatory mechanisms. In this study, we extend our mathematical model to incorporate recent experimental findings that showed decreased fractional proximal tubule reabsorption under a high-K+ diet. We conducted model simulations and sensitivity analyses to investigate how these renal alterations impact whole body K+ regulation. Model predictions quantify the sensitivity of K+ regulation to various levels of proximal tubule K+ reabsorption adaptation and tubuloglomerular feedback. Our results suggest that the reduced proximal tubule K+ reabsorption under a high-K+ diet could achieve K+ balance in isolation, but the resulting tubuloglomerular feedback reduces filtration rate and thus K+ excretion.NEW & NOTEWORTHY Potassium homeostasis is maintained in the body by a complex system of regulatory mechanisms. This system, when healthy, maintains a small extracellular potassium concentration, despite large fluctuations of dietary potassium. The complexities of the system make this problem well suited for investigation with mathematical modeling. In this study, we extend our mathematical model to consider recent experimental results on renal potassium handling on a high potassium diet and investigate the impacts from a whole body perspective.

"Hi, how can i help you?": embracing artificial intelligence in kidney research

In recent years, biology and precision medicine have benefited from major advancements in generating large-scale molecular and biomedical datasets and in analyzing those data using advanced machine learning algorithms. Machine learning applications in kidney physiology and pathophysiology include segmenting kidney structures from imaging data and predicting conditions like acute kidney injury or chronic kidney disease using electronic health records. Despite the potential of machine learning to revolutionize nephrology by providing innovative diagnostic and therapeutic tools, its adoption in kidney research has been slower than in other organ systems. Several factors contribute to this underutilization. The complexity of the kidney as an organ, with intricate physiology and specialized cell populations, makes it challenging to extrapolate bulk omics data to specific processes. In addition, kidney diseases often present with overlapping manifestations and morphological changes, making diagnosis and treatment complex. Moreover, kidney diseases receive less funding compared with other pathologies, leading to lower awareness and limited public-private partnerships. To promote the use of machine learning in kidney research, this review provides an introduction to machine learning and reviews its notable applications in renal research, such as morphological analysis, omics data examination, and disease diagnosis and prognosis. Challenges and limitations associated with data-driven predictive techniques are also discussed. The goal of this review is to raise awareness and encourage the kidney research community to embrace machine learning as a powerful tool that can drive advancements in understanding kidney diseases and improving patient care.

Sex matters: the frequently overlooked importance of considering sex in computational models

Personalised medicine and the development of a virtual human or a digital twin comprises visions of the future of medicine. To realise these innovations, an understanding of the biology and physiology of all people are required if we wish to apply these technologies at a population level. Sex differences in health and biology is one aspect that has frequently been overlooked, with young white males being seen as the "average" human being. This has not been helped by the lack of inclusion of female cells and animals in biomedical research and preclinical studies or the historic exclusion, and still low in proportion, of women in clinical trials. However, there are many known differences in health between the sexes across all scales of biology which can manifest in differences in susceptibility to diseases, symptoms in a given disease, and outcomes to a given treatment. Neglecting these important differences in the development of any health technologies could lead to adverse outcomes for both males and females. Here we highlight just some of the sex differences in the cardio-respiratory systems with the goal of raising awareness that these differences exist. We discuss modelling studies that have considered sex differences and touch on how and when to create sex-specific models. Scientific studies should ensure sex differences are included right from the study planning phase and results reported using sex as a biological variable. Computational models must have sex-specific versions to ensure a movement towards personalised medicine is realised.

Gene-based association study reveals a distinct female genetic signal in primary hypertension

Hypertension is a polygenic disease that affects over 1.2 billion adults aged 30-79 worldwide. It is a major risk factor for renal, cerebrovascular, and cardiovascular diseases. The heritability of hypertension is estimated to be high; nevertheless, our understanding of its underlying mechanisms remains scarce and incomplete. This study covered the entries from European ancestry from the UK-Biobank (UKB), with 74,090 cases diagnosed with essential (primary) hypertension and 200,734 controls. We compared the findings from large-scale genome-wide association studies (GWAS) to the gene-based method of proteome-wide association studies (PWAS). We focused on 70 statistically significant associated genes, most of which failed to reach significance in variant-based GWAS. A total of 30% of the PWAS-associated genes were validated against independent cohorts, including the Finnish Biobank. Furthermore, gene-based analyses that were performed on both sexes revealed sex-dependent genetics with a stronger genetic component associated with females. Analysis of systolic and diastolic blood pressure measurements confirms a strong genetic effect associated with females. We demonstrated that gene-based approaches provide insight into the underlying biology of hypertension. Specifically, the expression profiles of the identified genes exposed the enrichment of endothelial cells from multiple organs. Furthermore, females' top-ranked significant genes are involved in cellular immunity. We conclude that studying hypertension and blood pressure via gene-based association methods improves interpretability and exposes sex-dependent genetic effects, which enhances clinical utility.

The intrarenal renin-angiotensin system in hypertension: insights from mathematical modelling

The renin-angiotensin system (RAS) plays a pivotal role in the maintenance of volume homeostasis and blood pressure. In addition to the well-studied systemic RAS, local RAS have been documented in various tissues, including the kidney. Given the role of the intrarenal RAS in the pathogenesis of hypertension, a role established via various pharmacologic and genetic studies, substantial efforts have been made to unravel the processes that govern intrarenal RAS activity. In particular, several mechanisms have been proposed to explain the rise in intrarenal angiotensin II (Ang II) that accompanies Ang II infusion, including increased angiotensin type 1 receptor (AT1R)-mediated uptake of Ang II and enhanced intrarenal Ang II production. However, experimentally isolating their contribution to the intrarenal accumulation of Ang II in Ang II-induced hypertension is challenging, given that they are fundamentally connected. Computational modelling is advantageous because the feedback underlying each mechanism can be removed and the effect on intrarenal Ang II can be studied. In this work, the mechanisms governing the intrarenal accumulation of Ang II during Ang II infusion experiments are delineated and the role of the intrarenal RAS in Ang II-induced hypertension is studied. To accomplish this, a compartmental ODE model of the systemic and intrarenal RAS is developed and Ang II infusion experiments are simulated. Simulations indicate that AT1R-mediated uptake of Ang II is the primary mechanism by which Ang II accumulates in the kidney during Ang II infusion. Enhanced local Ang II production is unnecessary. The results demonstrate the role of the intrarenal RAS in the pathogenesis of Ang II-induced hypertension and consequently, clinical hypertension associated with an overactive RAS.

Understanding the Mechanisms and Treatment of Heart Failure: Quantitative Systems Pharmacology Models with a Focus on SGLT2 Inhibitors and Sex-Specific Differences

Heart failure (HF), which is a major clinical and public health challenge, commonly develops when the myocardial muscle is unable to pump an adequate amount of blood at typical cardiac pressures to fulfill the body's metabolic needs, and compensatory mechanisms are compromised or fail to adjust. Treatments consist of targeting the maladaptive response of the neurohormonal system, thereby decreasing symptoms by relieving congestion. Sodium-glucose co-transporter 2 (SGLT2) inhibitors, which are a recent antihyperglycemic drug, have been found to significantly improve HF complications and mortality. They act through many pleiotropic effects, and show better improvements compared to others existing pharmacological therapies. Mathematical modeling is a tool used to describe the pathophysiological processes of the disease, quantify clinically relevant outcomes in response to therapies, and provide a predictive framework to improve therapeutic scheduling and strategies. In this review, we describe the pathophysiology of HF, its treatment, and how an integrated mathematical model of the cardiorenal system was built to capture body fluid and solute homeostasis. We also provide insights into sex-specific differences between males and females, thereby encouraging the development of more effective sex-based therapies in the case of heart failure.

Influence of administration time and sex on natriuretic, diuretic, and kaliuretic effects of diuretics

Sex differences in renal function and blood pressure have been widely described across many species. Blood pressure dips during sleep and peaks in the early morning. Similarly, glomerular filtration rate, filtered electrolyte loads, urine volume, and urinary excretion all exhibit notable diurnal rhythms, which reflect, in part, the regulation of renal transporter proteins by circadian clock genes. That regulation is sexually dimorphic; as such, sex and time of day are not two independent regulators of kidney function and blood pressure. The objective of the present study was to assess the effect of sex and administration time on the natriuretic and diuretic effects of loop, thiazide, and K⁺-sparing diuretics, which are common treatments for hypertension. Loop diuretics inhibit Na⁺-K⁺-2Cl^- cotransporters on the apical membrane of the thick ascending limb, thiazide diuretics inhibit Na⁺-Cl^- cotransporters on the distal convoluted tubule, and K⁺-sparing diuretics inhibit epithelial Na⁺ channels on the connecting tubule and collecting duct. We simulated Na⁺ transporter inhibition using sex- and time-of-day-specific computational models of mouse kidney function. The simulation results highlighted significant sex and time-of-day differences in the drug response. Loop diuretics induced larger natriuretic and diuretic effects during the active phase. The natriuretic and diuretic effects of thiazide diuretics exhibited sex and time-of-day differences, whereas these effects of K⁺-sparing diuretics exhibited a significant time-of-day difference in females only. The kaliuretic effect depended on the type of diuretics and time of administration. The present computational models can be a useful tool in chronotherapy, to tailor drug administration time to match the body's diurnal rhythms to optimize the drug effect.NEW & NOTEWORTHY Sex influences cardiovascular disease, and the timing of onset of acute cardiovascular events exhibits circadian rhythms. Kidney function also exhibits sex differences and circadian rhythms. How do the natriuretic and diuretic effects of diuretics, a common treatment for hypertension that targets the kidneys, differ between the sexes? And how do these effects vary during the day? To answer these questions, we conducted computer simulations to assess the effects of loop, thiazide, and K⁺-sparing diuretics.

A mathematical model of potassium homeostasis: Effect of feedforward and feedback controls

Maintaining normal potassium (K+) concentrations in the extra- and intracellular fluid is critical for cell function. K+ homeostasis is achieved by ensuring proper distribution between extra- and intracellular fluid compartments and by matching K+ excretion with intake. The Na+-K+-ATPase pump facilitates K+ uptake into the skeletal muscle, where most K+ is stored. Na+-K+-ATPase activity is stimulated by insulin and aldosterone. The kidneys regulate long term K+ homeostasis by controlling the amount of K+ excreted through urine. Renal handling of K+ is mediated by a number of regulatory mechanisms, including an aldosterone-mediated feedback control, in which high extracellular K+ concentration stimulates aldosterone secretion, which enhances urine K+ excretion, and a gastrointestinal feedforward control mechanism, in which dietary K+ intake increases K+ excretion. Recently, a muscle-kidney cross talk signal has been hypothesized, where the K+ concentration in skeletal muscle cells directly affects urine K+ excretion without changes in extracellular K+ concentration. To understand how these mechanisms coordinate under different K+ challenges, we have developed a compartmental model of whole-body K+ regulation. The model represents the intra- and extracellular fluid compartments in a human (male) as well as a detailed kidney compartment. We included (i) the gastrointestinal feedforward control mechanism, (ii) the effect of insulin and (iii) aldosterone on Na+-K+-ATPase K+ uptake, and (iv) aldosterone stimulation of renal K+ secretion. We used this model to investigate the impact of regulatory mechanisms on K+ homeostasis. Model predictions showed how the regulatory mechanisms synthesize to ensure that the extra- and intracelluller fluid K+ concentrations remain in normal range in times of K+ loading and fasting. Additionally, we predict that without the hypothesized muscle-kidney cross talk signal, the model was unable to predict a return to normal extracellular K+ concentration after a period of high K+ loading or depletion.

Subject-wise model generalization through pooling and patching for regression: Application on non-invasive systolic blood pressure estimation

BACKGROUND

Subject-wise modeling using machine learning is useful in many applications requiring low error and complexity, such as wearable medical devices. However, regression accuracy depends highly on the data available to train the model and the model's generalization ability. Adversely, the prediction error may increase severely if unknown data patterns test the model; such a model is known to be overfitted. In medicine-related applications, such as Non-Invasive Blood Pressure (NIBP) estimation, the high error renders the estimation model useless and dangerous.

METHODS

This paper presents a novel algorithm to handle overfitting by editing the training data to achieve generalization for subject-wise models. The pooling and patching (PaP) algorithms use a relatively short record segment of a subject as a Key-Segment (KS) to search through a larger dataset for similar subjects. Then samples taken from the matched subjects' pool records are used to patch the original subject's KS. Due to the significance of systolic blood pressure (SBP) and the complexity of its variability, non-invasive estimation of SBP from electrocardiography (ECG) and photoplethysmography (PPG) is introduced as an application to assess the algorithm. The study was performed on 2051 subjects with a wide range of age, height, weight, length, and health status. The subjects' records were taken from a large public dataset, VitalDB, which is acquired from subjects undergoing different surgeries. Finally, all the results are obtained without using other model generalization techniques.

RESULTS

The generalization effect of the proposed algorithm, PaP, significantly outperformed cross-validation, which is widely used in regression model generalization. Moreover, the testing results show that a KS of 200 to 2000 samples is sufficient for providing high accuracy for much longer testing data of about 12000 to 24000 samples long, which is less than %10 of the record length on average. Furthermore, compared to other works based on the same dataset, PaP provides a significantly lower mean error of -0.75 ± 5.51 mmHg, with a small training data portion of 15% over 2051 subjects.

Sex and species differences in epithelial transport in rat and mouse kidneys: Modeling and analysis

The goal of this study was to investigate the functional implications of sex and species differences in the pattern of transporters along nephrons in the rat and mouse kidney, as reported by Veiras et al. (J Am Soc Nephrol 28: 3504–3517, 2017). To do so, we developed the first sex-specific computational models of epithelial water and solute transport along the nephrons from male and female mouse kidneys, and conducted simulations along with our published rat models. These models account for the sex differences in the abundance of apical and basolateral transporters, glomerular filtration rate, and tubular dimensions. Model simulations predict that 73% and 57% of filtered Na+ is reabsorbed by the proximal tubules of male and female rat kidneys, respectively. Due to their smaller transport area and lower NHE3 activity, the proximal tubules in the mouse kidney reabsorb a significantly smaller fraction of the filtered Na+, at 53% in male and only 34% in female. The lower proximal fractional Na+ reabsorption in female kidneys of both rat and mouse is due primarily to their smaller transport area, lower Na+/H+ exchanger activity, and lower claudin-2 abundance, culminating in significantly larger fractional delivery of water and Na+ to the downstream nephron segments in female kidneys. Conversely, the female distal nephron exhibits a higher abundance of key Na+ transporters, including Na+-Cl− cotransporters in both species, epithelial Na+ channels for the female rat, and Na+-K+-Cl−cotransporters for the female mouse. The higher abundance of transporters accounts for the enhanced water and Na+ transport along the female rat and mouse distal nephrons, relative to the respective male, resulting in similar urine excretion between the sexes. Model simulations indicate that the sex and species differences in renal transporter patterns may partially explain the experimental observation that, in response to a saline load, the diuretic and natriuretic responses were more rapid in female rats than males, but no significant sex difference was found in mice. These computational models can serve as a valuable tool for analyzing findings from experimental studies conducted in rats and mice, especially those involving genetic modifications.

Does wearing a mask while exercising amid COVID-19 pandemic affect hemodynamic and hematologic function among healthy individuals? Implications of mask modality, sex, and exercise intensity

OBJECTIVES

We investigated how wearing a mask - and its modality (surgical vs. N95) - affect hemodynamic and hematologic function in males and females across two exercise intensities (submaximal (SUB) and maximal (MAX)).

METHODS

144 individuals participated in the present study and were randomly allocated to three mask groups of 48 (N95, SURGICAL, and NO MASK) with two exercise subgroups for each mask group (MAX, n = 24; SUB, n = 24) for both sexes. Participants in each experimental group (N95SUB, N95MAX; SURSUB, SURMAX; SUB, MAX) were assessed for their hemodynamic and hematologic function at baseline and during recovery after exercise.

RESULTS

No significant differences were noted for either hemodynamic or hematologic function at post-exercise as compared to baseline with regard to mask modality (P > 0.05). Heart rate (HR) for maximal intensity were significantly greater at 1 min post-exercise in N95 as compared to SURGICAL (P < 0.05). No differences were noted for hemodynamic and hematologic function with N95 and SURGICAL compared to NOMASK for either intensity (P > 0.05). Females showed significantly greater HR values at 1 min post-exercise in N95 as compared to NO MASK, but no significant differences were noted for hematological function between sexes (P > 0.05).

CONCLUSION

Our findings show that wearing a face mask (N95/surgical) while exercising has no detrimental effects on hemodynamic/hematologic function in both males and females, and suggest that wearing a mask, particularly a surgical mask, while exercising during the ongoing pandemic is safe and poses no risk to individual's health. Future studies examining physiological responses to chronic exercise with masks are warranted.

Determining risk factors for triple whammy acute kidney injury

Concurrent use of a diuretic, a renin-angiotensin system (RAS) inhibitor, and a non-steroidal anti-inflammatory drug (NSAID) significantly increases the risk of acute kidney injury (AKI). This phenomenon is known as "triple whammy". Diuretics and RAS inhibitors, such as an angiotensin converting enzyme (ACE) inhibitor or angiotensin receptor blocker, are often prescribed in tandem for the treatment of hypertension, whereas some NSAIDs, such as ibuprofen, are available over the counter. As such, concurrent treatment with all three drugs is common. The goals of this study are to better understand the mechanisms underlying the development of triple whammy AKI and to identify physiological factors that may increase an individual's susceptibility. To accomplish these goals, we utilize sex-specific computational models of long-term blood pressure regulation. These models include variables describing the heart and circulation, kidney function, sodium and water reabsorption in the nephron and the RAS and are parameterized separately for men and women. Hypertension is modeled as overactive renal sympathetic nervous activity. Model simulations suggest that low water intake, the myogenic response, and drug sensitivity may predispose patients with hypertension to develop triple whammy-induced AKI. Triple treatment involving an ACE inhibitor, furosemide, and NSAID results in blood pressure levels similar to double treatment with ACEI and furosemide. Additionally, the male and female hypertensive models act similarly in most situations, except for the ACE inhibitor and NSAID double treatment.

Adaptive Changes in single-nephron GFR, Tubular Morphology, and Transport in a Pregnant Rat Nephron: Modeling and Analysis

Normal pregnancy is characterized by massive increases in plasma volume and electrolyte retention. Given that the kidneys regulate homeostasis of electrolytes and volume, the organ undergoes major adaptations in morphology, hemodynamics, and transport to achieve the volume and electrolyte retention required in pregnancy. These adaptations are complex, sometimes counterintuitive, and not fully understood. In addition, the demands of the developing fetus and placenta change throughout the pregnancy. For example, during late pregnancy, K⁺ retention and thus enhanced renal K⁺ reabsorption is required despite many kaliuretic factors. The goal of this study is to unravel how known adaptive changes along the nephrons contribute to the ability of the kidney to meet volume and electrolyte requirements in mid- and late pregnancy. We developed computational models of solute and water transport in the superficial nephron of the kidney of a rat in mid- and late pregnancy. The mid-pregnant and late-pregnant rat superficial nephron models predict that morphological adaptations and increased activity of the sodium hydrogen exchanger 3 (NHE3) and epithelial sodium channel (ENaC) are essential for enhanced Na⁺ reabsorption observed during pregnancy. Model simulations showed that for sufficient K⁺ reabsorption, increased H ⁺-K ⁺-ATPase activity and decreased K⁺ secretion along the distal segments is required in both mid- and late-pregnancy. Furthermore, certain known sex differences in renal transporter pattern (e.g., the higher NHE3 protein abundance but lower activity in the proximal tubules of virgin female rats compared to male) may serve to better prepare the female for the increased transport demand in pregnancy.

Sex differences in solute and water handling in the human kidney: Modeling and functional implications

The kidneys maintain homeostasis by controlling the amount of water and electrolytes in the blood. That function is accomplished by the nephrons, which transform glomerular filtrate into urine by a transport process mediated by membrane transporters. We postulate that the distribution of renal transporters along the nephron is markedly different between men and women, as recently shown in rodents. We hypothesize that the larger abundance of a renal Na+ transport in the proximal tubules in females may also better prepare them for the fluid retention adaptations required during pregnancy and lactation. Also, kidneys play a key role in blood pressure regulation, and a popular class of anti-hypertensive medications and angiotensin converting enzymes (ACE) inhibitors have been reported to be less effective in women. Model simulations suggest that the blunted natriuretic and diuretic effects of ACE inhibition in women can be attributed, in part, to their higher distal baseline transport capacity.

Modeling within-Host SARS-CoV-2 Infection Dynamics and Potential Treatments

The goal of this study was to develop a mathematical model to simulate the actions of drugs that target SARS-CoV-2 virus infection. To accomplish that goal, we have developed a mathematical model that describes the control of a SARS-CoV-2 infection by the innate and adaptive immune components. Invasion of the virus triggers the innate immunity, whereby interferon renders some of the target cells resistant to infection, and infected cells are removed by effector cells. The adaptive immune response is represented by plasma cells and virus-specific antibodies. The model is parameterized and then validated against viral load measurements collected in COVID-19 patients. We apply the model to simulate three potential anti-SARS-CoV-2 therapies: (1) Remdesivir, a repurposed drug that has been shown to inhibit the transcription of SARS-CoV-2, (2) an alternative (hypothetical) therapy that inhibits the virus' entry into host cells, and (3) convalescent plasma transfusion therapy. Simulation results point to the importance of early intervention, i.e., for any of the three therapies to be effective, it must be administered sufficiently early, not more than a day or two after the onset of symptoms. The model can serve as a key component in integrative platforms for rapid in silico testing of potential COVID-19 therapies and vaccines.

His and her mathematical models of physiological systems

Beyond the reproductive system and reproductive behaviors, men and women exhibit major differences in many organ systems, including the anatomy of the brain, the activities of the stress and immune systems, and the metabolic and cardiovascular functions. A comprehensive understanding of the impact of these sex differences on health and disease is crucial to the development of effective sex-based therapies. Mathematical modeling has the potential of facilitating and contributing to advancing the understanding of sex differences in health and disease. Indeed, explosion of mathematical models have been developed in recent decades for different aspects of human physiology and pathophysiology. This review contains a survey of sex-specific mathematical models of physiological systems, describe insights that have been revealed in those modeling studies, and discuss future opportunities.

A Computational Model of Kidney Function in a Patient with Diabetes

At the onset of diabetes, the kidney grows large and the glomerular filtration rate becomes abnormally high. These structural and hemodynamics changes affect kidney function and may contribute to the development of chronic kidney disease. The goal of this study is to analyze how kidney function is altered in patients with diabetes and the renal effects of an anti-hyperglyceamic therapy that inhibits the sodium-glucose cotransporter 2 (SGLT2) in the proximal convoluted tubules. To accomplish that goal, we have developed a computational model of kidney function in a patient with diabetes and conducted simulations to study the effects of diabetes and SGLT2 inhibition on solute and water transport along the nephrons. Simulation results indicate that diabetes-induced hyperfiltration and tubular hypertrophy enhances Na+ transport, especially along the proximal tubules and thick ascending limbs. These simulations suggest that SGLT2 inhibition may attenuate glomerular hyperfiltration by limiting Na+-glucose transport, raising luminal [Cl-] at the macula densa, restoring the tubuloglomerular feedback signal, thereby reducing single-nephron glomerular filtration rate.

Sex differences in soluble prorenin receptor in patients with type 2 diabetes

BACKGROUND

The soluble prorenin receptor (sPRR), a member of the renin-angiotensin system (RAS), is elevated in plasma of patients with preeclampsia, hypertension, chronic kidney disease (CKD), and type 2 diabetes. Our goal was to examine the relationship between sPRR and RAS activation to define whether sexual dimorphisms in sPRR might explain sex disparities in renal outcomes in patients with type 2 diabetes.

METHODS

Two hundred sixty-nine participants were included in the study (mean age, 48 ± 16 years; 42% men, 58% women), including 173 controls and 96 subjects with type 2 diabetes. In plasma and urine, we measured sPRR, plasma renin activity (PRA), and prorenin. In the urine, we also measured angiotensinogen along with other biomarkers of renal dysfunction.

RESULTS

Plasma sPRR and PRA were significantly higher in women with type 2 diabetes compared to men. In these women, plasma sPRR was positively correlated with PRA, age, and body mass index (BMI). In contrast, in men the sPRR in urine but not in plasma positively correlated with eGFR in urine, but negatively correlated with urine renin activity, plasma glucose, age, and BMI.

CONCLUSIONS

In patients with type 2 diabetes, sPRR contributes to RAS stimulation in a sex-dependent fashion. In diabetic women, increased plasma sPRR parallels the activation of systemic RAS; while in diabetic men, decreased sPRR in urine matches intrarenal RAS stimulation. sPRR might be a potential indicator of intrarenal RAS activation and renal dysfunction in men and women with type 2 diabetes.

Impact of sex and pathophysiology on optimal drug choice in hypertensive rats: quantitative insights for precision medicine

Less than half of all hypertensive patients receiving treatment are successful in normalizing their blood pressure. Despite the complexity and heterogeneity of hypertension, the current antihypertensive guidelines are not tailored to the individual patient. As a step toward individualized treatment, we develop a quantitative systems pharmacology model of blood pressure regulation in the spontaneously hypertensive rat (SHR) and generate sex-specific virtual populations of SHRs to account for the heterogeneity between the sexes and within the pathophysiology of hypertension. We then used the mechanistic model integrated with machine learning tools to study how variability in these mechanisms leads to differential responses in rodents to the four primary classes of antihypertensive drugs. We found that both the sex and the pathophysiological profile of the individual play a major role in the response to hypertensive treatments. These results provide insight into potential areas to apply precision medicine in human primary hypertension.

Modeling the Molecular Impact of SARS-CoV-2 Infection on the Renin-Angiotensin System

SARS-CoV-2 infection is mediated by the binding of its spike protein to the angiotensin-converting enzyme 2 (ACE2), which plays a pivotal role in the renin-angiotensin system (RAS). The study of RAS dysregulation due to SARS-CoV-2 infection is fundamentally important for a better understanding of the pathogenic mechanisms and risk factors associated with COVID-19 coronavirus disease and to design effective therapeutic strategies. In this context, we developed a mathematical model of RAS based on data regarding protein and peptide concentrations; the model was tested on clinical data from healthy normotensive and hypertensive individuals. We used our model to analyze the impact of SARS-CoV-2 infection on RAS, which we modeled through a downregulation of ACE2 as a function of viral load. We also used it to predict the effect of RAS-targeting drugs, such as RAS-blockers, human recombinant ACE2, and angiotensin 1-7 peptide, on COVID-19 patients; the model predicted an improvement of the clinical outcome for some drugs and a worsening for others. Our model and its predictions constitute a valuable framework for in silico testing of hypotheses about the COVID-19 pathogenic mechanisms and the effect of drugs aiming to restore RAS functionality.

Use of Angiotensin-Converting Enzyme Inhibitors and Angiotensin II Receptor Blockers During the COVID-19 Pandemic: A Modeling Analysis

Angiotensin-converting enzyme inhibitors (ACEi) and angiotensin II receptor blockers (ARB) are frequently prescribed for a range of diseases including hypertension, proteinuric chronic kidney disease, and heart failure. There is evidence indicating that these drugs upregulate ACE2, a key component of the renin-angiotensin system (RAS) and is found on the cells of a number of tissues, including the epithelial cells in the lungs. While ACE2 has a beneficial role in many diseases such as hypertension, diabetes, and cardiovascular disease, it also serves as a receptor for both SARS-CoV and SARS-CoV-2 via binding with the spike protein of the virus, thereby allowing it entry into host cells. Thus, it has been suggested that these therapies can theoretically increase the risk of SARS- CoV-2 infection and cause more severe COVID-19. Given the success of ACEi and ARBs in cardiovascular diseases, we seek to gain insights into the implications of these medications in the pathogenesis of COVID-19. To that end, we have developed a mathematical model that represents the RAS, binding of ACE2 with SARS-CoV-2 and the subsequent cell entry, and the host's acute inflammatory response. The model can simulate different levels of SARS-CoV-2 exposure, and represent the effect of commonly prescribed anti-hypertensive medications, ACEi and ARB, and predict tissue damage. Model simulations indicate that whether the extent of tissue damage may be exacerbated by ACEi or ARB treatment depends on a number of factors, including the level of existing inflammation, dosage, and the effect of the drugs on ACE2 protein abundance. The findings of this study can serve as the first step in the development of appropriate and more comprehensive guidelines for the prescription of ACEi and ARB in the current and future coronavirus pandemics.

Sex differences in solute transport along the nephrons: effects of Na+ transport inhibition

Each day, ~1.7 kg of NaCl and 180 liters of water are reabsorbed by nephron segments in humans, with urinary excretion fine tuned to meet homeostatic requirements. These tasks are coordinated by a spectrum of renal Na⁺ transporters and channels. The goal of the present study was to investigate the extent to which inhibitors of transepithelial Na⁺ transport (T_Na) along the nephron alter urinary solute excretion and how those effects may vary between male and female subjects. To accomplish that goal, we developed sex-specific multinephron models that represent detailed transcellular and paracellular transport processes along the nephrons of male and female rat kidneys. We simulated inhibition of Na⁺/H⁺ exchanger 3 (NHE3), bumetanide-sensitive Na⁺-K⁺-2Cl^- cotransporter (NKCC2), Na⁺-Cl^- cotransporter (NCC), and amiloride-sensitive epithelial Na⁺ channel (ENaC). NHE3 inhibition simulations predicted a substantially reduced proximal tubule T_Na, and NKCC2 inhibition substantially reduced thick ascending limb T_Na. Both gave rise to diuresis, natriuresis, and kaliuresis, with those effects stronger in female rats. While NCC inhibition was predicted to have only minor impact on renal T_Na, it nonetheless had a notable effect of enhancing excretion of Na⁺, K⁺, and Cl^-, particularly in female rats. Inhibition of ENaC was predicted to have opposite effects on the excretion of Na⁺ (increased) and K⁺ (decreased) and to have only a minor impact on whole kidney T_Na. Unlike inhibition of other transporters, ENaC inhibition induced stronger natriuresis and diuresis in male rats than female rats. Overall, model predictions agreed well with measured changes in Na⁺ and K⁺ excretion in response to diuretics and Na⁺ transporter mutations.

Cardiac and renal function interactions in heart failure with reduced ejection fraction: A mathematical modeling analysis

Congestive heart failure is characterized by suppressed cardiac output and arterial filling pressure, leading to renal retention of salt and water, contributing to further volume overload. Mathematical modeling provides a means to investigate the integrated function and dysfunction of heart and kidney in heart failure. This study updates our previously reported integrated model of cardiac and renal functions to account for the fluid exchange between the blood and interstitium across the capillary membrane, allowing the simulation of edema. A state of heart failure with reduced ejection fraction (HF-rEF) was then produced by altering cardiac parameters reflecting cardiac injury and cardiovascular disease, including heart contractility, myocyte hypertrophy, arterial stiffness, and systemic resistance. After matching baseline characteristics of the SOLVD clinical study, parameters governing rates of cardiac remodeling were calibrated to describe the progression of cardiac hemodynamic variables observed over one year in the placebo arm of the SOLVD clinical study. The model was then validated by reproducing improvements in cardiac function in the enalapril arm of SOLVD. The model was then applied to prospectively predict the response to the sodium-glucose co-transporter 2 (SGLT2) inhibitor dapagliflozin, which has been shown to reduce heart failure events in HF-rEF patients in the recent DAPAHF clinical trial by incompletely understood mechanisms. The simulations predict that dapagliflozin slows cardiac remodeling by reducing preload on the heart, and relieves congestion by clearing interstitial fluid without excessively reducing blood volume. This provides a quantitative mechanistic explanation for the observed benefits of SGLT2i in HF-rEF. The model also provides a tool for further investigation of heart failure drug therapies.

Sex-Specific Determinants of Coronary Artery Disease and Atherosclerotic Risk Factors: Estrogen and Beyond

The way we view coronary artery disease in women has changed dramatically over the past decades. From an initial perspective that coronary artery disease was a male disorder and that women were protected by estrogens, there has been the gradual appreciation that this is an equal opportunity disease. Postmenopausal women are more likely than men to be hypertensive, dyslipidemic, and have multiple risk factors. Beyond the appreciation of estrogen's global effects on cardiovascular and metabolic function, our further advances in the understanding of sex-specific risks and management will be based on a greater understanding of the diversity of estrogen-mediated receptor pathways, including appreciation of the sometimes divergent effects of estrogen when acting either via the classic estrogen receptor or the more recently appreciated G protein-coupled estrogen receptor. In addition, the importance of sex-specific regulation of cardiometabolic processes beyond the sex hormones, specifically via SRY regulation, is only beginning to be understood. Finally, the author summarizes his recent studies demonstrating sex-specific G protein-coupled estrogen receptor regulation of blood pressure and cholesterol metabolism that may serve as a paradigm for the elucidation of sex-specific determinants of cardiovascular risk and the basis for sex-specific management of those risks.

Sex-specific computational models for blood pressure regulation in the rat

In the past decades, substantial effort has been devoted to the development of computational models of the cardiovascular system. Some of these models simulate blood pressure regulation in humans and include components of the circulatory, renal, and neurohormonal systems. Although such human models are intended to have clinical value in that they can be used to assess the effects and reveal mechanisms of hypertensive therapeutic treatments, rodent models would be more useful in assisting the interpretation of animal experiments. Also, despite well-known sexual dimorphism in blood pressure regulation, almost all published models are gender neutral. Given these observations, the goal of this project is to develop the first computational models of blood pressure regulation for male and female rats. The resulting sex-specific models represent the interplay among cardiovascular function, renal hemodynamics, and kidney function in the rat; they also include the actions of the renal sympathetic nerve activity and the renin-angiotensin-aldosterone system as well as physiological sex differences. We explore mechanisms responsible for blood pressure and renal autoregulation and notable sexual dimorphism. Model simulations suggest that fluid and sodium handling in the kidney of female rats, which differs significantly from males, may contribute to their observed lower salt sensitivity as compared with males. Additionally, model simulations highlight sodium handling in the kidney and renal sympathetic nerve activity sensitivity as key players in the increased resistance of females to angiotensin II-induced hypertension as compared with males.

Joint effects of risk factors on adverse events associated with adult blood donations

The process for blood donation is considered safe, but some adverse events have been reported. Risk factors for adverse events were assessed in this study.A retrospective case-control study was conducted to investigate the risk factors for adverse events after blood donation between 2010 and 2013. Variables such as gender, age, body mass index (BMI), donation status, donation volume, donation site, pre-donation systolic blood pressure (SBP), and pre-donation diastolic blood pressure were compared between donors with and without adverse events. Multiple logistic regression analysis was performed to assess the joint effects of age, gender, and donation status on adverse events.The incidence of adverse events among adult blood donations was 1287/1,253,678 (0.1%). On multivariate logistic regression analysis, blood donors aged <35 years (odds ratio [OR], 2.99, 95% confidence interval [CI], 2.57-3.48), of female gender (OR, 3.30, 95% CI, 2.62-4.15), and with first-time donor status (OR, 6.40, 95% CI, 5.17-7.93), donation of 500 mL (OR, 2.22, 95% CI, 1.83-2.69), predonation SBP <124 mm Hg (OR, 1.25, 95% CI,1.05-1.48) and BMI <24 kg/m (OR, 1.67, 95% CI, 1.42-1.96) were associated with increased likelihood of adverse event. Further analysis with joint effects method revealed that first-time female donors aged <35 years are associated with the highest odds of adverse events when compared with repeat male donors aged ≧35 years (OR, 100.57, 95% CI, 48.45-208.75).The findings of our study should prove useful in identifying donors at risk and planning appropriate strategies for the prevention of adverse effects.

Sex Differences in Blood Pressure Hemodynamics in Middle-Aged Adults With Overweight and Obesity

High blood pressure (BP) is the strongest modifiable risk factor for cardiovascular disease. Overweight/obesity is a major risk factor of high BP. Multiple sex differences exist in mechanistic pathways that increase BP in overweight/obesity. They may result in a sex-specific pattern of BP hemodynamics—males and females may vary in the relative contributions of stroke volume, total peripheral resistance (TPR), and heart rate to higher BP. We investigated this possibility in a population-based sample of middle-aged adults (36–65 years). The total sample (n=618) included 289 males and 329 females; 79% of males and 66% of females were overweight. In all, we measured BP, stroke volume, TPR, and heart rate beat-by-beat during a 52-minute protocol that included changes in posture and mental stress. We assessed the relative contributions of stroke volume, TPR, and heart rate to BP at each minute of the protocol. We observed marked sex differences in BP hemodynamics in overweight/obese individuals: the main determinant of higher BP was TPR in males (49% versus only 35% in females, P =0.008), whereas it was stroke volume in females (51% versus only 35% in males, P =0.006). These sex differences were most apparent when standing or sitting at rest. No such differences were seen in normal-weight individuals in whom the main determinant of higher BP was TPR in both sexes. Our study suggests that, in middle-aged adults, marked sex differences exist in BP hemodynamics, contributing to high BP in overweight/obese but not normal-weight individuals. As such, this study may contribute to precision medicine in hypertension.

Understanding sex differences in long-term blood pressure regulation: insights from experimental studies and computational modeling

Sex differences in blood pressure and the prevalence of hypertension are found in humans and animal models. Moreover, there has been a recent explosion of data concerning sex differences in nitric oxide, the renin-angiotensin-aldosterone system, inflammation, and kidney function. These data have the potential to reveal the mechanisms underlying male-female differences in blood pressure control. To elucidate the interactions among the multitude of physiological processes involved, one may apply computational models. In this review, we describe published computational models that represent key players in blood pressure regulation, and highlight sex-specific models and their findings.

Afferent arteriole responsiveness to endothelin receptor activation: does sex matter?

BACKGROUND

The pathogenesis of hypertension is distinct between men and women. Endothelin-1 (ET-1) is a potential contributor to sex differences in the pathophysiology of hypertension. ET-1 participates in blood pressure regulation through activation of endothelin A (ET_A) and endothelin B (ET_B) receptors including those in the vasculature. Previous studies demonstrated that sex and sex hormones evoke discrepancies in ET-1-mediated control of vascular tone in different vascular beds. However, little is known about sex- and sex hormone-related differences in ET-1-dependent renal microvascular reactivity. Accordingly, we hypothesized that loss of sex hormones impairs afferent arteriole reactivity to ET-1.

METHODS

Male and female Sprague Dawley rats were subjected to gonadectomy or sham surgery (n = 6/group). After 3 weeks, kidneys from those rats were prepared for assessment of renal microvascular responses to ET-1 (ET_A and ET_B agonist, 10^-12 to 10^-8 M) and sarafotoxin 6c (S6c, ET_B agonist, 10^-12 to 10^-8 M) using the blood-perfused juxtamedullary nephron preparation.

RESULTS

Control afferent arteriole diameters at 100 mmHg were similar between sham male and female rats averaging 14.6 ± 0.3 and 15.3 ± 0.3 μm, respectively. Gonadectomy had no significant effect on control arteriole diameter. In sham males, ET-1 produced significant concentration-dependent decreases in afferent arteriole diameter, with 10^-8 M ET-1 decreasing diameter by 84 ± 1%. ET-1 induced similar concentration-dependent vasoconstrictor responses in sham female rats, with 10^-8 M ET-1 decreasing the diameter by 82 ± 1%. The afferent arteriolar vasoconstrictor responses to ET-1 were unchanged by ovariectomy or orchiectomy. Selective ET_B receptor activation by S6c induced a concentration-dependent decline in afferent arteriole diameter, with 10^-8 M S6c decreasing diameter by 77 ± 3 and 76 ± 3% in sham male and female rats, respectively. Notably, ovariectomy augmented the vasoconstrictor response to S6c (10^-12 to 10^-9 M), whereas orchiectomy had no significant impact on the responsiveness to ET_B receptor activation.

CONCLUSION

These data demonstrate that sex does not significantly influence afferent arteriole reactivity to ET receptor activation. Gonadectomy potentiated the responsiveness of the afferent arteriole to ET_B-induced vasoconstriction in females, but not males, suggesting that female sex hormones influence ET_B-mediated vasoconstriction in the renal microcirculation.