Unraveling the Mechanistic Links Between Blood Pressure Regulation and Calcium-Magnesium Homeostasis: Insights into Hypertension, Hyperparathyroidism, and Mineral Disorders

Unraveling the Mechanistic Links Between Blood Pressure Regulation and Calcium-Magnesium Homeostasis: Insights into Hypertension, Hyperparathyroidism, and Mineral Disorders | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Unraveling the Mechanistic Links Between Blood Pressure Regulation and Calcium-Magnesium Homeostasis: Insights into Hypertension, Hyperparathyroidism, and Mineral Disorders Pritha Dutta , Anita T. Layton doi: https://doi.org/10.1101/2025.10.26.684662 Pritha Dutta 1 Department of Applied Mathematics, University of Waterloo , Waterloo, Ontario, N2L 3G1, Canada Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: p7dutta{at}uwaterloo.ca Anita T. Layton 1 Department of Applied Mathematics, University of Waterloo , Waterloo, Ontario, N2L 3G1, Canada 2 Department of Biology, Cheriton School of Computer Science, and School of Pharmacology, University of Waterloo , Waterloo, Ontario, N2L 3G1, Canada 3 Cheriton School of Computer Science, University of Waterloo , Waterloo, Ontario, N2L 3G1, Canada 4 School of Pharmacology, University of Waterloo , Waterloo, Ontario, N2L 3G1, Canada Find this author on Google Scholar Find this author on PubMed Search for this author on this site Abstract Full Text Info/History Metrics Preview PDF Abstract The systems regulating blood pressure and calcium-magnesium (Ca 2+ -Mg 2+ ) homeostasis are increasingly recognized to have significant, clinically relevant interactions, where alterations in one can lead to significant changes in the other. In this study, we developed a computational model integrating blood pressure regulation and Ca 2 □-Mg 2 □ homeostasis in a male rat. We simulated various conditions, including hypertension, Ca 2 □, Mg 2 □, and vitamin D 3 deficiencies, and primary hyperparathyroidism. Simulations of hypertension, induced by various stimuli like increased renin or aldosterone secretion, demonstrated significant effects on parathyroid hormone (PTH), calcitriol, renal Ca 2 □/Mg 2 □ handling, and bone resorption. Dietary Ca 2 □, Mg 2 □, and vitamin D 3 deficiencies elevated mean arterial pressure, with Mg 2 □ deficiency having a stronger effect. Furthermore, the model predicted that primary hyperparathyroidism elevates PTH, Ca 2 □, and calcitriol, leading to increased mean arterial pressure and bone loss. Overall, this model provides valuable insights into the mechanistic links between blood pressure regulation and Ca 2 □-Mg 2 □ homeostasis, offering insights into clinical conditions like hypertension and hyperparathyroidism. 1. Introduction Hypertension is the leading cause of cardiovascular disease worldwide ( 1 ), and its prevalence has been rising in recent years due to factors such as an aging population and lifestyle changes, including decreased physical activity and the widespread consumption of Western diets ( 2 ). Furthermore, a significant portion of the global population fails to meet the recommended dietary intake of magnesium (Mg 2 □) and calcium (Ca 2 □) ( 3 , 4 ). For example, the standard diet in the United States provides only about 50% of the recommended daily intake of Mg 2 □ ( 5 ), and the 2017-2018 National Health and Nutrition Examination Survey (NHANES) found that nearly half of the US population did not meet their estimated average requirements for Ca 2+ ( 6 ). Additionally, approximately 100,000 people in the US are diagnosed with primary hyperparathyroidism each year ( 7 ). Given these factors, it is essential to understand how blood pressure regulation and Ca 2+ -Mg 2+ homeostasis are affected by these conditions. The systems regulating blood pressure and Ca 2+ -Mg 2+ homeostasis are increasingly recognized to have significant, clinically relevant interactions ( 8 – 10 ). A key component of blood pressure regulation is the renin-angiotensin-aldosterone system (RAAS). Ca 2+ , Mg 2+ , and their regulatory hormones, parathyroid hormone (PTH) and calcitriol (1,25(OH) 2 D 3 ; active form of vitamin D 3 ), play a crucial role in regulating various elements of the RAAS ( 8 – 10 ). For instance, Ca 2+ and calcitriol influence renin secretion from the juxtaglomerular (JG) cells in the kidneys ( 11 – 14 ). Additionally, Ca 2+ , Mg 2+ , and PTH regulate aldosterone secretion from the adrenal gland ( 15 – 19 ) as well as vascular resistance ( 20 – 22 ). Both aldosterone and angiotensin II also influence PTH secretion from the parathyroid gland ( 23 ). Furthermore, PTH and Ca 2+ control sodium (Na + ) reabsorption in the proximal tubule and thick ascending limb of the kidneys ( 24 , 25 ), which in turn affects the reabsorption of Ca 2+ and Mg 2+ in these nephron segments. Angiotensin II and aldosterone also indirectly influence Ca 2+ and Mg 2+ reabsorption in the kidneys by regulating Na + reabsorption. Finally, Ca 2+ and Mg 2+ have opposing effects on renal sympathetic nervous activity (RSNA) ( 26 , 27 ). Given these multiple interconnections, a dysregulation in one system can significantly impact the other. Therefore, understanding the interaction between these systems is increasingly important for accurately assessing their impact on health. Mechanistic modeling provides a comprehensive framework for understanding and analyzing complex physiological systems. In this study, we integrated our previously developed Ca 2+ -Mg 2+ homeostasis model in a male rat ( 28 ) with a blood pressure regulation model in a male rat ( 29 ), quantifying the interactions between these two systems. This integrated model was then used to simulate various conditions, including hypertension, Ca 2+ , Mg 2+ , and vitamin D 3 deficiencies, and primary hyperparathyroidism. 2. Methods We have developed a model that captures the interactions between blood pressure regulation and Ca 2+ -Mg 2+ homeostasis in a male rat. This model was developed by integrating our previously developed model of Ca 2+ and Mg 2+ homeostasis ( 28 ) with a blood pressure regulation model in a male rat ( 29 ). The blood pressure regulation model describes, using a large system of coupled nonlinear algebraic differential equations, the interactions among the cardiovascular system, the renal system, the renal sympathetic nervous system, and the RAAS. A schematic diagram is shown in Fig. 1 (A) . Model equations and parameter values can be found in Ref. ( 29 ). The Ca 2+ and Mg 2+ homeostasis model consists of five compartments: plasma, parathyroid gland, intestine, kidney, and bone. The model describes, using a large system of coupled nonlinear ordinary differential equations, the exchanges of Ca 2+ , Mg 2+ , PTH, and calcitriol. A schematic diagram is shown in Fig. 1 (B) . Model equations and parameter values can be found in Ref. ( 28 ). Download figure Open in new tab Figure 1: Schematic diagram of the integrated model. (A) Schematic model of blood pressure regulation. Pink nodes denote variables that describe cardiovascular function; green nodes, renal hemodynamics; yellow nodes, renal Na + and fluid handling; blue nodes, the renin-angiotensin-aldosterone system. Solid arrows indicate activation and dotted arrows indicate inhibition. (B) Schematic model of Ca 2+ -Mg 2+ homeostasis. The model consists of five compartments: plasma, intestine, kidney, parathyroid gland, and bone. Solid arrows with open arrowheads indicate fluxes, solid arrows with closed arrowheads indicate activation, and dotted arrows indicate inhibition. All arrows are color coded. Green arrows, Ca 2+ ; red arrows, Mg 2+ , blue arrows, parathyroid hormone (PTH); purple arrows, 1,25(OH) 2 D 3 . (C) Schematic representation of the interactions between the models shown in (A) and (B). Mauve nodes denote plasma [Ca 2+ ], [Mg 2+ ], [1,25(OH)2D3], and [PTH]; yellow nodes, renal Na + , Ca 2+ , and Mg 2+ handling; blue nodes, the renin-angiotensin-aldosterone system. Solid arrows indicate activation and dotted arrows indicate inhibition. The brown arrows indicate the direct links between components of the blood pressure regulation model and Ca 2+ -Mg 2+ homeostasis model. ACE, angiotensin-converting enzyme; AGT, angiotensinogen; ALD, aldosterone; Ang I, angiotensin I; Ang II, angiotensin II; AT1R-bound Ang II, angiotensin II type 1 receptor-bound angiotensin II; AT2R-bound Ang II, angiotensin II type 2 receptor-bound angiotensin II; PRA, plasma renin activity; PRC, plasma renin concentration. In the following sections we define the equations for the regulation of different components of the blood pressure regulation model by Ca 2+ , Mg 2+ , PTH, and 1,25(OH) 2 D 3 and vice-versa. Figure 1 (C) provides a schematic representation of the interactions between the two systems. All new parameter values and descriptions are listed in Table 1 . View this table: View inline View popup Table 1: Description and values of new model parameters and variables at baseline for male rat. 2.1 Renin secretion Renin is secreted by the juxtaglomerular (JG) cells in the kidneys. Renin secretion is given by where N rs represents the normalized renin secretion, and v md − sod , v rsna , v AT 1 R , v Ca , and represent the effect of tubular Na + flow past the macula densa, renal sympathetic nervous activity (RSNA), angiotensin II receptor type 1 (AT1R)-bound angiotensin II (Ang II) concentration, plasma [Ca 2+ ], and plasma [1,25(OH) 2 D 3 ] on renin secretion rate. All these terms are equal to 1 in the baseline condition. For definitions of N rs , v md − sod , v rsna ,and v AT 1 R refer to Ref. ( 29 ). The terms v Ca and are defined below. Although Ca 2 □ does not directly regulate renin secretion, its levels influence cAMP-stimulated renin secretion, with increased Ca 2 □ inhibiting and decreased Ca 2 □ enhancing this process. Acute hypercalcemia suppresses plasma renin activity (PRA) by acting on the calcium-sensing receptor (CaSR) ( 11 ). The JG cells, which express CaSR, reduce renin secretion when the receptor is activated ( 12 ). The basolateral surface of the JG cells is exposed to the renal cortical interstitium, so elevated Ca 2 □ levels in this area could directly stimulate the CaSR on JG cells, leading to a reduction in renin secretion. The effect of Ca 2+ on renin secretion is given by where K R − Ca represents the sensitivity of renin secretion to plasma Ca 2+ concentration ([ Ca 2+ ] p ). Renin secretion increases significantly in the presence of 1,25(OH) 2 D 3 deficiency as well as toxicity. Zhou et al. reported a 1.5-fold increase in PRA in 1α-hydroxylase knockout mice compared to control ( 13 ). Treatment of 1α-hydroxylase knockout mice with 1,25(OH) 2 D 3 led to the normalization of PRA ( 13 ). Thus, 1,25(OH) 2 D 3 deficiency leads to upregulation of renin secretion. In addition, administration of high doses of calcitriol to male rats increased PRA by ∼2.5-fold ( 14 ). Thus, sufficiently high levels of 1,25(OH) 2 D 3 also upregulates renin secretion. We defined such that (i) when 1,25(OH) 2 D 3 concentration is within the range of 80-170 pM, , (ii) when 1,25(OH) 2 D 3 concentration is less than 80 pM, gradually increases to a maximum of 1.5-fold as 1,25(OH) 2 D 3 concentration approaches zero, and (iii) when 1,25(OH) 2 D 3 concentration is greater than 170 pM, gradually increases to a maximum of 2-fold. Thus, the effect of 1,25(OH) 2 D 3 on renin secretion is given by where , and . The parameters, and , represent the sensitivity of renin secretion to low and high plasma 1,25(OH) 2 D 3 concentrations ([1,25( OH 2 ) D 3 ] p ), respectively. 2.2 Aldosterone secretion Normalized aldosterone secretion ( N als ) is given by ALD secretion is affected by the K + to Na + ratio ( ξ k / sod ), mean arterial pressure ( ξ map ), AT1R-bound Ang II ( ξ AT 1 R ), Ca 2+ ( ξ Ca ), Mg 2+ ( ξ Mg ), and PTH ( ξ PTH ). All these terms are equal to 1 in the baseline condition. For definitions of , and ξ AT 1 R refer to Ref. ( 29 ). The terms ξ Ca , ξ Mg , and ξ PTH are defined below. The influence of extracellular Ca 2+ on aldosterone synthesis and secretion was first reported in rat zona glomerulosa (ZG) cells ( 15 ). There were no changes in both cAMP and aldosterone levels when rat ZG cells were placed into Ca 2+ -deprived media. However, after rat ZG cells were treated with additional extracellular Ca 2+ , the concentrations of both aldosterone and cAMP were elevated in a dose-dependent manner. These findings suggested that extracellular Ca 2+ level could serve as an independent stimulator of aldosterone secretion. We model the effect of Ca 2+ on aldosterone secretion as where K ALD − Ca represents the sensitivity of aldosterone secretion to plasma Ca 2+ concentration. AT1R-bound Ang II stimulates aldosterone secretion by increasing Ca 2+ influx through the various voltage-gated Ca 2+ channels. Mg 2+ affects aldosterone secretion by blocking the voltage-gated Ca 2+ channels which reduce Ang II-stimulated aldosterone secretion ( 30 ). In adrenal cells in culture, increased extracellular Mg 2+ reduced Ang II-stimulated aldosterone release ( 16 ). This effect was also observed in vivo, as rats given an infusion of Ang II in combination with Mg 2+ sulfate exhibited diminished plasma aldosterone, as compared with rats given Ang II alone ( 17 ). In addition, in a clinical study, participants placed on a very low Mg 2+ diet for 3 weeks showed increased Ang II-stimulated aldosterone secretion ( 31 ). This increase in aldosterone secretion was attenuated by acute intravenous Mg 2+ repletion. Together, these studies suggest that extracellular Mg 2+ decreases sensitivity of adrenal glomerulosa cells to Ang II-stimulated aldosterone secretion. We model the effect of Mg 2+ on aldosterone secretion as where K ALD − Mg represents the sensitivity of aldosterone secretion to plasma Mg 2+ concentration ([ Mg 2+ ] p ). The presence of type 1 PTH receptor has been demonstrated in both rat and human adrenal gland ( 18 , 19 , 32 , 33 ). PTH binds to PTH receptor and facilitates Ca 2+ influx through the voltage-gated Ca 2+ channels, thus increasing Ang II-stimulated aldosterone secretion. We model the effect of PTH on aldosterone secretion as where K ALD − PTH represents the sensitivity of aldosterone secretion to plasma PTH concentration ([ PTH ] p ). 2.3 Effect of angiotensin II and aldosterone on PTH secretion Human parathyroid cells have been found to express mineralocorticoid receptors (MRs) ( 23 , 33 ) and AT1Rs ( 23 ). The AT1R expression level was found to be ∼100-fold lower than the MR expression level ( 23 ). Lenzini et al. reported that at physiological Ca 2+ concentrations cells exposed to aldosterone increased PTH secretion by 271% compared to control ( 23 ). This increase in PTH secretion was abolished on treatment with an MR blocker. In addition, at physiological Ca 2+ concentrations cells exposed to Ang II increased PTH secretion by 267% and this increase was abolished on treatment with an AT1R antagonist ( 23 ). However, co-stimulation with both aldosterone and Ang II did not produce any additive increase in PTH secretion, with PTH secretion increasing by 225% compared to control ( 23 ). Based on the observations reported in ( 23 ), we model the effect of aldosterone and Ang II on PTH secretion as where In Eqs. (9) and (10) , [ ALD ] p denotes plasma aldosterone concentration and [ AT 1 R ] denotes AT1R-bound Ang II concentration. K PTH − ALD and K PTH − AT 1 R denote the sensitivity of PTH secretion to aldosterone and AT1R-bound Ang II, respectively. Equations (1) and (6) of the Ca 2+ -Mg 2+ homeostasis model ( 28 ) representing the rates of change of parathyroid gland and plasma PTH concentrations, respectively, are modified as where [ PTH ] g and [ PTH ] p denote parathyroid gland and plasma PTH concentrations, respectively. For descriptions and values of all parameters in the above two equations refer to Table 2 of Ref. ( 28 ). View this table: View inline View popup Download powerpoint Table 2. Changes in model parameters to simulate five model instances of hypertension, each with different primary trigger(s), labelled RSNA, Renin, ALD, AA , and Combined . RSNA, renal sympathetic nervous activity; ALD, aldosterone; AA, afferent arterial. 2.4 Effect of calcium and magnesium on RSNA The regulation of RSNA is given by where N rsna represents the normalized RSNA, and α map , α rap , α Ca , and α Mg represent the effect of mean arterial pressure (MAP), right atrial pressure (RAP), Ca 2+ , and Mg 2+ on RSNA. All these terms are equal to 1 in the baseline condition. For definitions of α map and α rap refer to Ref. ( 29 ) and α Ca and α Mg are defined below. Ca 2+ influx through N-type Ca 2+ channels in sympathetic nerves increases RSNA, which leads to increased release of norepinephrine ( 26 ). Mg 2+ decreases RSNA and norepinephrine release by blocking N-type Ca 2+ channels in sympathetic nerves ( 27 ). Thus, the balance between Ca 2+ and Mg 2+ is important for RSNA. We model the regulation of RSNA by Ca 2+ and Mg 2+ as Where [ Ca 2+ ] p − eq and [ Mg 2+ ] p − eq denote the concentrations of plasma Ca 2+ and Mg 2+ at equilibrium, respectively. 2.5 Effect of angiotensin II on bone resorption Bone resorption rate is defined as where and denote the minimal and maximal resorption rates, respectively, and their values can be found in Table 2 of Ref ( 28 ). The terms and represent the effect of PTH and 1,25(OH) 2 D 3 on resorption, respectively, and their definitions are provided in Ref ( 28 ). The term represents the effect of AT1R-bound Ang II on bone resorption and is defined below. Bones express AT1R and Ang II binds to AT1R to activate osteoclasts through RANKL induction and hence promotes osteoporosis ( 34 ). Treatment with AT1R blocker ameliorates osteoporosis ( 34 ). We assume the following sigmoidal relation between bone resorption and AT1R-bound Ang II. where denotes the sensitivity of bone resorption to AT1R-bound Ang II. 2.6 Sodium reabsorption in the proximal tubule and thick ascending limb Fractional reabsorption of Na + in the proximal tubule and thick ascending limb is given by where and represent fractional Na + reabsorption in the proximal tubule and thick ascending limb at equilibrium and are assumed to be 0.60 and 0.20, respectively. γ PTH , γ CaSR , γ filsod , γ AT 1 R , and γ rsna denote the effect of PTH, CaSR, filtered Na + load, AT1R-bound Ang II, and RSNA, respectively, on fractional Na + reabsorption and are equal to 1 at baseline. The definitions of γ filsod , γ AT 1 R , and γ rsna can be found in Ref. ( 29 ) and γ PTH and γ CaSR are defined below. PTH inhibits Na + /H + exchanger 3 (NHE3) in the proximal tubule and hence reduces proximal tubule Na + reabsorption ( 24 ). We model the effect of PTH on fractional Na + reabsorption in the proximal tubule as where K sod − PTH represents the sensitivity of proximal tubule Na + reabsorption to plasma [PTH]. Ca 2+ inhibits Na + –K + –Cl − cotransporter 2 (NKCC2) in the thick ascending limb through the CaSR and hence reduces Na + reabsorption along this segment ( 25 ). We model the effect of Ca 2+ on fractional Na + reabsorption in the thick ascending limb as where K sod − Ca represents the sensitivity of Na + reabsorption in the thick ascending limb to plasma [Ca]. 2.7 Effect of angiotensin II on arterial resistance In vascular smooth muscle cells, Ang II binds to AT1R and increases intracellular Ca 2+ both through Ca 2+ influx from L-type Ca 2+ channels and Ca 2+ release from intracellular stores. Administration of angiotensin converting enzyme (ACE) inhibitor to spontaneously hypertensive rats reduced peripheral resistance by ∼40% ( 35 ) and Ang II infusion to male Wistar rats increased peripheral resistance by ∼140% ( 36 ). Based on these observations, we model the effect of AT1R-bound Ang II on arterial resistance as where [ AT 1 R ] eq denotes the concentration of AT1R-bound Ang II at equilibrium. 2.8 Effect of calcium, magnesium, and parathyroid hormone on vascular resistance Increased Ca 2+ influx into vascular smooth muscle cells increases vascular resistance. Low and high Ca 2+ supplementation in male Sprague-Dawley rats decreased and increased vascular resistance by 13.5% and 7%, respectively ( 20 ). Accordingly, we model the effect of plasma Ca 2+ on vascular resistance as where [ Ca 2+ ] p − eq denotes the concentration of plasma Ca 2+ at equilibrium. Mg 2+ causes vasodilation of vascular smooth muscle cells by blocking Ca 2+ influx through L-type Ca 2+ channels. High extracellular Mg 2+ reduced myogenic tone in wild-type male mice ( 21 ). We model the effect of plasma Mg 2+ on vascular resistance as where [ Mg 2+ ] p − eq denotes the concentration of plasma Ca 2+ at equilibrium. PTH binds to PTHr-1 and increases Ca 2+ influx into vascular smooth muscle cells ( 22 ). We modeled the effect of PTH on vascular resistance by assuming that at very low PTH vascular resistance would decrease by 20% and at high PTH vascular resistance would increase by 20%. where [ PTH ] eq denotes the concentration of plasma PTH at equilibrium. The regulation of arterial resistance is given by where R ba denotes the basic arterial resistance and ϵ aum denotes the autonomic multiplier effect and their definitions can be found in Ref. ( 29 ). The parameters Ψ AT 1 R , Ψ Ca , Ψ Mg , and Ψ PTH denote the effect of [AT1R-bound Ang II], [Ca 2+ ], [Mg 2+ ], and [PTH] on vascular resistance and are defined in Eqs. (21) , ( 22 ), ( 23 ), and ( 24 ), respectively. The regulation of afferent arteriolar resistance is defined as where R aa − eq denotes the afferent arteriolar resistance at equilibrium. The parameters β rsna , Σ tgf , Σ myo , Σ AT 1 R−AA , Ψ AT 2 R − AA , and ΨATR-AA denote the effect of RSNA, tubuloglomerular feedback (TGF) signal, myogenic response, [AT1R-bound Ang II], and [AT2R-bound Ang II] on afferent arteriolar resistance, respectively, and their definitions can be found in Ref. ( 29 ). The parameters Ψ Ca , Ψ Mg , and Ψ PTH denote the effect of [Ca 2+ ], [Mg 2+ ], and [PTH] on afferent arteriolar resistance and are defined in Eqs. (22) , ( 23 ), and ( 24 ), respectively. 2.9 Simulating hypertension Hypertension is a multifactorial disease that may involve a variety of triggers, including overactive RSNA, RAAS, or arterial stiffening. The model parameters adjusted to simulate hypertensive stimuli are the equilibrium values for RSNA, renin secretion rate, aldosterone secretion rate, and afferent arteriole resistance. We consider five hypertensive cases, featuring primarily an overactive RSNA, increased renin secretion, increased aldosterone secretion, increased vascular tone, or a combination of these stimuli. These models are referred to as HTN-RSNA, HTN-Renin, HTN-ALD, HTN-AA, and HTN-Combined, respectively. For each hypertensive case, parameters were adjusted so that the MAP predicted for the hypertensive model is approximately 120 mmHg. These parameter sets are shown in Table 2 . 3. Results 3.1 Sensitivity analysis We performed a local sensitivity analysis by varying each model parameter by ±5% and computing the corresponding steady state. The percentage changes in RSNA, glomerular filtration rate (GFR), MAP, aldosterone concentration, PRA, [PTH], [1,25(OH) 2 D 3 ], [Mg 2+ ], and [Ca 2+ ] corresponding to 5% increase in parameter values are shown in Fig. 2 . Download figure Open in new tab Figure 2: Local sensitivity analysis conducted by increasing individual parameters by 5%. The resulting percent change in model steady state concentrations from baseline is presented here. White indicates the resulting change was less than 1%. RSNA, renal sympathetic nervous activity; GFR, glomerular filtration rate; MAP, mean arterial pressure; [ALD], plasma aldosterone concentration; PRA, plasma renin activity; [PTH], plasma PTH concentration; [1,25(OH) 2 D 3 ], plasma 1,25(OH) 2 D 3 concentration; [Mg 2+ ], plasma Mg 2+ concentration; [Ca 2+ ], plasma Ca 2+ concentration. From Fig. 2 we see that the parameters, , and , have the largest impacts on different model variables. A 5% increase in the fractional reabsorption rates of Na + in the proximal tubule and thick ascending limb , distal tubule , and collecting duct causes significant change in aldosterone concentration. Additionally, has significant impact on GFR (since it determines the macula densa Na + flow), RSNA, and MAP (by regulating water reabsorption and consequently extracellular fluid volume). A 5% increase in minimal thick ascending limb fractional Mg 2+ reabsorption causes a significant change in plasma [PTH], [1,25(OH) 2 D 3 ], [Mg 2+ ], and [Ca 2+ ]. For instance, the increase in significantly elevates plasma [Mg 2+ ] and [Ca 2+ ], while suppressing plasma [PTH]. This occurs because increased plasma [Mg 2+ ] directly stimulates 1,25(OH) 2 D 3 production, which in turn enhances intestinal Ca 2+ absorption, thereby increasing plasma [Ca 2+ ]. Consequently, [PTH] decreases due to inhibition from both increased [1,25(OH) 2 D 3 ] and elevated [Mg 2+ ] and [Ca 2+ ]. In contrast, a similar change in fractional Ca 2+ reabsorption in the proximal tubule has minimal impact on these variables due to a negative feedback loop: increased plasma [Ca 2+ ] inhibits PTH and 1,25(OH) 2 D 3 , dampening further Ca 2+ changes. Unlike Ca 2+ , the feedback loop of Mg 2+ with 1,25(OH) 2 D 3 is reinforcing, amplifying the impact of renal Mg 2+ reabsorption changes. Local sensitivity analysis conducted by decreasing individual parameters by 5% also showed similar trends. 3.2 Effect of different hypertensive stimuli As described above, we adjusted selected parameters to investigate the models’ responses to different hypertensive stimuli: overactive RSNA, increased renin secretion, increased aldosterone secretion, increased vascular tone, or a combination of these stimuli ( Table 2 ). Also, these parameters were chosen to yield MAP of approximately 120 mmHg, corresponding to an increase of 16% ( Fig. 3A ). Model predictions for each of these stimuli are shown in Fig. 3 . Download figure Open in new tab Figure 3: Fractional change from baseline (denoted by grey line at zero) of model variables (A) and Ca 2+ -Mg 2+ fluxes (B) under five hypertensive stimuli: overactive RSNA (HTN-RSNA), increased renin secretion (HTN-Renin), increased aldosterone secretion (HTN-ALD), increased vascular tone (HTN-AA), and a combination of these stimuli (HTN-Combined). Bone to plasma and plasma to bone fluxes represent the exchange of Ca 2+ and Mg 2+ between plasma and the fast bone pool; bone resorption represents the release of Ca 2+ and Mg 2+ from the slow bone pool into plasma. MAP, mean arterial pressure; [ALD], aldosterone concentration; PRA, plasma renin activity; [AT1R-Ang II], plasma AT1R-bound Ang II concentration; RSNA, renal sympathetic nervous activity; RVR; renal vascular resistance; RBF, renal blood flow; GFR, glomerular filtration rate; V ecf , extracellular fluid volume; T Na , total plasma sodium; [PTH], plasma PTH concentration; [1,25(OH) 2 D 3 ], plasma 1,25(OH) 2 D 3 concentration; [Mg 2+ ], plasma Mg 2+ concentration; [Ca 2+ ], plasma Ca 2+ concentration. In the HTN-RSNA case, RSNA induces vasoconstriction and directly stimulates proximal tubule Na + reabsorption. Taken in isolation, afferent arteriolar constriction would lower GFR. However, the resulting reduced Na + flow at the macula densa inhibits the TGF signal and causes the afferent arteriole to slightly dilate. The higher MAP would also increase GFR. Together, these factors yield a GFR that is slightly higher than the normotensive values ( Fig. 3(A) ). RSNA-induced hypertension does not cause any significant changes in plasma Ca 2+ , Mg 2+ , PTH, and 1,25(OH) 2 D 3 levels or on any of Ca 2+ -Mg 2+ fluxes. In the HTN-Renin case (hyperreninemia), increased renin secretion elevates the level of AT1R-bound Ang II, which constricts both the afferent and efferent arterioles, but preferentially the latter. As a result, while renal blood flow was predicted to be almost unchanged from baseline, GFR was notably higher (22%; Fig. 3(A) ). The significantly increased aldosterone stimulates PTH secretion ( 39 , 40 ), thereby increasing plasma [PTH] by 33%. On one hand, this increased [PTH] inhibits proximal tubular Ca 2+ and Mg 2+ reabsorption, while on the other hand it increases Ca 2+ and Mg 2+ reabsorption along the thick ascending limb and distal tubule. Now, majority of Ca 2+ reabsorption occurs along the proximal tubule, while majority of Mg 2+ reabsorption occurs along the thick ascending limb. Hence, combined with the higher filtered load, our model predicts a notably higher increase in urinary Ca 2+ excretion than in urinary Mg 2+ excretion ( Fig. 3(B) ). Further, bone resorption increases by 13% under PTH, calcitriol, and AT1R-bound Ang II stimulation. Together, these factors do not cause any significant change in plasma Mg 2+ and Ca 2+ concentrations. The HTN-ALD case simulates primary hyperaldosteronism, where the renin secretion rate remains normal, but there is hypersecretion of aldosterone, with a 30-fold increase above baseline. Aldosterone secretion rate in primary aldosteronism is difficult to measure. However, we calculated the ratio of plasma aldosterone concentration (PAC) (ng/dL) to plasma renin activity (PRA) (pmol/L/min), which is commonly used in the diagnosis of primary aldosteronism. The proposed cut-off values for PAC/PRA ratio in the literature are 1.6, 2.5, and 3.1 ng/dL per pmol/L/min ( 41 ). We obtained a PAC/PRA ratio of 1.86 ng/dL per pmol/L/min with the predicted plasma aldosterone concentration and PRA values. The high levels of aldosterone cause the kidneys to retain Na + and increase blood volume, which in turn signals the kidneys to decrease renin production. Our model predicts a 41% decrease in plasma renin activity and AT1R-bound Ang II ( Fig. 3(A) ). The high aldosterone level also causes a 67% increase in PTH concentration ( Fig. 3(A) ) ( 39 , 40 ). This in turn inhibits proximal tubular Ca 2+ and Mg 2+ reabsorption, while increasing their reabsorption along the thick ascending limb. Consequently, our model predicts a 37% increase in urinary Ca 2+ excretion ( 40 , 42 ) while urinary Mg 2+ excretion is predicted to increase by 17% ( 43 ) ( Fig. 3(B) ). Under the combined effect of increased PTH (67%), increased calcitriol (23%), and decreased AT1R-bound Ang II (41%), bone resorption increases by 3.8% ( 39 , 44 , 45 ) ( Fig 3(B) ). Together, these factors keep plasma Mg 2+ and Ca 2+ concentrations near the baseline values ( 40 , 43 ). Afferent arteriole constriction in the HTN-AA case lowers GFR, whereas the increased MAP increases GFR. Under the influence of these two opposing factors GFR decreases by 8.5%. This in turn reduces proximal tubule Na + and water reabsorption by a small amount. The increased Na + delivery to the downstream segments increases Na + reabsorption in the distal tubule and collecting duct. Hence, total plasma Na + and extracellular fluid volume increase slightly. In addition, the reduced GFR lowers urinary Ca 2+ and Mg 2+ excretions. The HTN-Combined case involves an overactive RSNA, an overactive RAAS, and increased vascular tone, with the strength of these stimuli chosen so that the predicted MAP is ∼120 mmHg ( Table 2 ). The high aldosterone level increases [PTH] by 6.4%. However, it does not cause any notable change in any of the Ca 2+ and Mg 2+ fluxes. Thus, the HTN-Renin, HTN-ALD, and HTN-AA cases have significant effect on Ca 2+ and Mg 2+ fluxes. However, plasma Ca 2+ and Mg 2+ concentrations are predicted to remain within their respective physiological ranges for all hypertensive stimuli. 3.3 Effect of Mg 2+ , Ca 2+ , and vitamin D 3 deficiency Next, we simulated 70% dietary Mg 2+ intake ( I Mg ) restriction, 70% dietary Ca 2+ intake ( I Ca ) restriction, and 70% 25(OH)D (inactive form of vitamin D 3 ) deficiency for 1 month. Model predictions are shown in Fig. 4 . Download figure Open in new tab Figure 4: (A) Fractional change from baseline (denoted by grey line at zero) of model variables under 70% dietary Mg 2+ intake ( I Mg ) restriction, 70% dietary Ca 2+ intake ( I Ca ) restriction, and 70% 25(OH)D (inactive form of vitamin D 3 ) deficiency for 1 month. (B) Interplay between key variables that are affected by dietary Mg 2+ , dietary Ca 2+ , and 25(OH)D deficiency. Each variable is accompanied by their change over time for each of the three cases. Maroon bar plots, dietary Mg 2+ deficiency; blue bar plots, dietary Ca 2+ deficiency; green bar plots, 25(OH)D deficiency. The Y-axis range is [-0.7, 0.7]. MAP, mean arterial pressure; CO, cardiac output; TPR, total peripheral resistance; [ALD], aldosterone concentration; PRA, plasma renin activity; [AT1R-Ang II], AT1R-bound Ang II concentration; RSNA, renal sympathetic nervous activity; RVR; renal vascular resistance; GFR, glomerular filtration rate; V ecf , extracellular fluid volume; [PTH], plasma PTH concentration; [1,25(OH) 2 D 3 ], plasma 1,25(OH) 2 D 3 concentration; [Mg 2+ ], plasma Mg 2+ concentration; [Ca 2+ ], plasma Ca 2+ concentration; AR, arterial resistance. Our model predicts a 21% increase in MAP from 103 mmHg to 125 mmHg following 1 month of dietary Mg 2+ restriction ( Fig. 4(A) ). By contrast, 1 month of dietary Ca 2+ restriction and 25(OH)D deficiency have comparatively lesser effect on MAP (increases to 119 mmHg and 114 mmHg, respectively). Now, why does Mg 2+ deficiency have a higher effect on MAP compared to Ca 2+ and 25(OH)D deficiency? Figure 4(B) shows the key variables and the interplay between them to answer the above question. Each variable is accompanied by their change over time for each of the three cases. Now, MAP is modeled as the product of cardiac output and total peripheral resistance; the relative change in these two factors determines the change in MAP. Dietary Mg 2+ deficiency markedly lowers plasma [Mg 2+ ], which in turn inhibits PTH secretion. Hence plasma [PTH] drops by 40%. This in turn partially removes the inhibitory effect of PTH on proximal tubule Na + reabsorption. From Fig 4(B) , we see that RSNA (maroon bar plot) initially rises under the effect of lower plasma [Mg 2+ ]. However, as MAP rises, its inhibitory effect brings down RSNA. Also, GFR ( Fig. 4(B) , maroon bar plot) does not change initially, but as MAP rises it increases renal blood flow and hence GFR. Thus, proximal tubule Na + and water reabsorption is enhanced under the combined effect of increased GFR and removal of the inhibitory effect of PTH. Additionally, the lowered plasma [Mg 2+ ] removes the inhibitory effect on aldosterone secretion causing an increase in plasma aldosterone levels. The high aldosterone levels enhance Na + and water reabsorption in the distal tubule and collecting duct. Consequently, the extracellular fluid volume increases, which subsequently increases cardiac output by 12%. Now, the increased cardiac output increases the arterial resistance. This is because when more blood flows through any tissue of the body than is required by that tissue for its specific function, the local resistance to blood flow increases progressively to bring the blood flow back towards normal. On the other hand, the lower [PTH] decreases arterial resistance and lower [Mg 2+ ] increases arterial resistance. Under the combined effect of these and cardiac output, arterial resistance increases which in turn increases the total peripheral resistance by 8.3%. Thus, dietary Mg 2+ deficiency increases cardiac output and total peripheral resistance, which together cause a 21% increase in MAP. In fact, several observational studies, clinical trials, and meta-analyses have shown an inverse relationship between dietary Mg 2+ intake and hypertension ( 46 – 50 ). By contrast, dietary Ca 2+ deficiency significantly increases plasma [PTH] due to the drop in plasma [Ca 2+ ]. This reinforces the inhibitory effect of PTH on proximal tubule Na + reabsorption. In addition, RSNA ( Fig. 4(B) , blue bar plot) decreases under the combined effect of lower plasma [Ca 2+ ] and rising MAP. The increasing MAP also increases GFR ( Fig. 4(B) , blue bar plot). Furthermore, the lower plasma [Ca 2+ ] removes the inhibitory effect on renin secretion; hence PRA increases, which in turn increases [AT1R-bound Ang II] ( Fig. 4(B) , blue bar plot). Together these factors slightly increase proximal tubule Na + and water reabsorption. Additionally, the increased aldosterone (under the effect of increased [PTH] and [AT1R-bound Ang II]) increases Na + and water reabsorption in the distal tubule and collecting duct. Hence, the extracellular fluid volume increases, which in turn increases cardiac output. On the other hand, the higher [AT1R-bound Ang II] and [PTH] increase arterial resistance and the lower [Ca 2+ ] decreases arterial resistance. Together these factors increase total peripheral resistance by 15%. This increased resistance inhibits cardiac output. Consequently, cardiac output does not change from the baseline value. Thus, during dietary Ca 2+ deficiency the 15% increase in MAP is primarily due to increased total peripheral resistance. Several observational studies, clinical trials, and meta-analyses have shown an inverse relationship between dietary Ca 2+ intake and hypertension ( 51 – 53 ). Calcitriol (1,25(OH) 2 D 3 ) deficiency following 25(OH)D restriction lowers intestinal absorption of Ca 2+ and hence causes a drop in plasma [Ca 2+ ]. This in turn increases PTH secretion. The decreased plasma [1,25(OH) 2 D 3 ] also partially removes the inhibitory effect on PTH production. Hence, we see a higher rise in plasma [PTH] compared to the dietary Ca 2+ deficiency case. In calcitriol deficiency, RAAS, renal Na + and water reabsorption, and peripheral resistance undergo similar changes as in dietary Ca 2+ deficiency, though the impact is lower. Consequently, MAP increases by only 11% ( 54 – 56 ). Thus, according to our model predictions the factor that causes Mg 2+ deficiency to have a higher effect on MAP compared to Ca 2+ and 25(OH)D deficiency is the increased cardiac output. During Mg 2+ deficiency, changes in GFR, RSNA, [PTH], [AT1R-bound Ang II], and aldosterone significantly increase renal Na + and water reabsorption, leading to a considerable increase in extracellular fluid volume and thus cardiac output. On the other hand, during Ca 2+ and 25(OH)D deficiency, changes in these factors cause modest changes in extracellular fluid volume and hence cardiac output does not change significantly from baseline. 3.4 Primary hyperparathyroidism Primary hyperparathyroidism was simulated by increasing the baseline PTH synthesis rate by factors of 2, 3, 5, 7, 10. Shown in Fig. 5 are the predicted steady-state values of key model variables and fluxes. Download figure Open in new tab Figure 5: Fractional change from baseline (denoted by grey line at zero) of model variables (A, B) and Ca 2+ -Mg 2+ fluxes (C) after increasing the baseline PTH synthesis rate by factors of 2, 3, 5, 7, 10. [PTH], plasma PTH concentration; [1,25(OH) 2 D 3 ], plasma 1,25(OH) 2 D 3 concentration; [Mg 2+ ], plasma Mg 2+ concentration; [Ca 2+ ], plasma Ca 2+ concentration; MAP, mean arterial pressure; CO, cardiac output; TPR, total peripheral resistance; [ALD], aldosterone concentration; PRA, plasma renin activity; [AT1R-Ang II], AT1R-bound Ang II concentration; RSNA, renal sympathetic nervous activity; GFR, glomerular filtration rate; V ecf , extracellular fluid volume. Our model predicts plasma [PTH] to increase by 70%, 130%, 237%, 334%, and 468%, respectively, following 2-, 3-, 5-, 7-, and 10-fold increase in . Since PTH increases the synthesis of 1,25(OH) 2 D 3 we see a significant increase in plasma [1,25(OH) 2 D 3 ]. This in turn greatly enhances intestinal Ca 2+ absorption, while intestinal Mg 2+ absorption increases slightly. This is because 1,25(OH) 2 D 3 regulates 45% of intestinal Ca 2+ absorption but only 12% of intestinal Mg 2+ absorption. Further, bone resorption increases under the combined stimulation of PTH and 1,25(OH) 2 D 3 . Now, PTH inhibits proximal tubular Ca 2+ and Mg 2+ reabsorption, while stimulating Ca 2+ and Mg 2+ reabsorption along the thick ascending limb and distal tubule. Now, majority of Ca 2+ reabsorption occurs along the proximal tubule, while majority of Mg 2+ reabsorption occurs along the thick ascending limb. Hence, combined with the higher filtered load, our model predicts a notably higher increase in urinary Ca 2+ excretion than in urinary Mg 2+ excretion. Together these factors cause plasma [Ca 2+ ] to increase by 7% (1.32 mM), 11% (1.37 mM), 15% (1.41 mM), 18% (1.45 mM), and 20% (1.48 mM), respectively, for 2-, 3-, 5-, 7-, and 10-fold increase in . Thus, in all five cases, plasma [Ca 2+ ] is above its physiological range (1.1-1.3 mM) indicating hypercalcemia ( 57 ). By contrast, the model predicts no change in plasma [Mg 2+ ] ( 58 ). Now let us analyze the effect on RAAS. The elevated plasma [Ca 2+ ] inhibits renin secretion, whereas the elevated plasma [1,25(OH) 2 D 3 ] increases renin secretion. Under their combined effect PRA increases significantly, which in turn increases AT1R-bound Ang II and aldosterone. The increased PTH and Ca 2+ also increase aldosterone secretion. Thus, plasma aldosterone increases by 21%, 27%, 34%, 37%, and 42%, respectively, for 2-, 3-, 5-, 7-, and 10-fold increase in ( 33 ). Renal Na + and water reabsorption increases under the stimulation of AT1R-bound Ang II and aldosterone. An important point to note is that though PTH indirectly enhances Na + reabsorption through the RAAS, it also directly inhibits proximal tubule Na + reabsorption. Because of these two opposing factors, extracellular fluid volume and total plasma Na + increase only slightly. Additionally, the higher [AT1R-bound Ang II], [PTH], and [Ca 2+ ] significantly increase arterial resistance and consequently total peripheral resistance. Thus, the increased extracellular fluid volume increases cardiac output, whereas the increased arterial resistance inhibits cardiac output and together these two factors keep cardiac output close to the baseline value. Consequently, MAP increases by 13% (116 mmHg), 14% (117 mmHg), 15.5% (119 mmHg), 16% (119.5 mmHg), and 17% (121 mmHg), respectively, for 2-, 3-, 5-, 7-, and 10-fold increase in . Thus, primary hyperparathyroidism causes hyperaldosteronism ( 33 , 59 ) and increases the risk of hypertension. In fact primary hyperparathyroidism has been associated with increased risk of hypertension, with a prevalence ranging from 40-65% and parathyroidectomy has resulted in substantial fall in both mean systolic and diastolic blood pressures ( 60 – 64 ). Osteopenia and osteoporosis are also frequent complications of primary hyperparathyroidism ( 65 – 67 ). Our model predicts significant increase in bone resorption due to increased PTH, calcitriol, and AT1R-bound Ang II. 4 Discussion We have developed an integrated model of blood pressure regulation and Ca 2 □-Mg 2 □ homeostasis to gain insights into the complex interactions that govern these physiological processes. Our study highlights the bidirectional relationship between these two systems, where alterations in one can lead to significant changes in the other. Specifically, we demonstrated how dysregulation in Ca 2+ and Mg 2+ levels can affect blood pressure control, and how dysregulation in blood pressure control, such as in hypertension, can impact Ca 2 □ and Mg 2 □ homeostasis. Hypertension has been associated with elevated plasma PTH ( 68 ), increased Ca 2+ excretion ( 68 , 69 ), and reduced bone mineral density ( 70 ). We used our model to simulate hypertension using different stimuli, namely, increased RSNA, increased renin secretion, increased aldosterone secretion, increased vascular tone, and a combination of all these stimuli. The model simulations, as depicted in Fig. 3 , suggest that hypertensive states driven by elevated renin (HTN-Renin) and aldosterone (HTN-ALD) secretions significantly influence PTH, calcitriol, and the renal handling of Ca 2+ and Mg 2+ . Notably, both conditions exhibit increased urinary excretion of Ca 2+ and Mg 2+ , as well as elevated bone resorption ( Fig. 3 ). Primary hyperaldosteronism, which results from increased aldosterone secretion, has been associated with hyperparathyroidism ( 39 , 40 ) and increased urinary excretions of Ca 2+ ( 40 , 42 ) and Mg 2+ ( 43 ), although plasma Ca 2+ and Mg 2+ remain normal ( 40 , 43 ). In fact, primary aldosteronism has been associated with nephrocalcinosis ( 71 ) and nephrolithiasis ( 72 ) caused by hypercalciuria. In addition, primary aldosteronism also causes bone loss and reduced bone mineral density ( 39 , 44 , 45 ). Now, hyperreninemia, caused by increased renin secretion, has been associated with hyperaldosteronism ( 73 , 74 ). Thus, the elevated aldosterone levels in hyperreninemia also increase PTH levels and hence urinary excretions of Ca 2+ and Mg 2+ . Our model predicts a significantly higher increase in bone resorption rate in the HTN-Renin case compared to the HTN-ALD case ( Fig. 3 ). This is because increased renin secretion increases ATIR-bound Ang II, which increases the risk of osteoporosis. In fact, the use of angiotensin-converting enzyme (ACE) inhibitors have been associated with higher bone mineral density and reduced risk of fracture ( 75 , 76 ). Despite these changes in urinary excretion and bone resorption rate, the model simulations indicate that plasma Ca 2+ and Mg 2+ concentrations remain relatively stable across all simulated hypertensive conditions (HTN-RSNA, HTN-Renin, HTN-ALD, HTN-AA, HTN-Combined) ( Fig. 3 ), suggesting that the body’s compensatory mechanisms effectively maintain mineral homeostasis even under pathological conditions. Cross-sectional and longitudinal epidemiological studies have consistently reported an inverse relationship between dietary Mg 2+ and blood pressure and/or hypertension ( 77 – 84 ). Additionally, two large meta-analyses of randomized trials reported that Mg 2+ supplementation significantly lowers blood pressure ( 48 , 49 ). Hypomagnesemia has also been associated with pre-eclampsia ( 85 – 87 ), a pregnancy specific hypertensive disorder, and Mg 2+ supplementation has been reported to reduce the risk of eclampsia in pregnant women by over 50% ( 88 ). Thus, all these studies highlight the importance of Mg 2+ homeostasis in blood pressure regulation. With our model simulations, we investigated the mechanisms responsible for increased mean arterial pressure during Mg 2+ deficiency. Our model simulations showed that Mg 2+ deficiency increased both cardiac output and total peripheral resistance ( Fig. 4 ). The increase in cardiac output was primarily due to decreased PTH and increased aldosterone, which increased renal Na + and water reabsorption. Total peripheral resistance increased mainly due to increased cardiac output and removal of the inhibitory effect of Mg + . Several epidemiological studies have reported an inverse relationship between dietary Ca 2+ intake and blood pressure and/or hypertension ( 52 , 77 , 78 , 81 , 86 , 89 – 94 ). Our model predictions are aligned with the observations from these studies. Our model simulations showed that Ca + deficiency increased the total peripheral resistance but did not change cardiac output ( Fig. 4 ). Additionally, our model predicted that dietary Mg 2+ deficiency has a stronger effect on mean arterial pressure than dietary Ca 2+ deficiency ( Fig. 4 ). In fact, two cross-sectional studies have reported dietary Mg 2+ intake to have a stronger association with blood pressure compared to dietary Ca 2+ intake ( 81 , 95 ). Since calcitriol deficiency significantly lowers plasma [Ca 2+ ], it has same effect as dietary Ca 2+ deficiency on mean arterial pressure, i.e., an inverse association ( 54 – 56 , 96 , 97 ), though the impact is slightly lower. Primary hyperparathyroidism has been associated with osteoporosis ( 65 – 67 ) and hypertension ( 60 – 64 ). Our model predictions suggested that the elevated plasma PTH, Ca 2+ , and calcitriol are primarily responsible for these two disorders ( Fig. 5 ). These three factors overactivate the RAAS and increase vascular resistance, which in turn increases the mean arterial pressure. The elevated PTH, calcitriol, and AT1R-bound Ang II also increase bone loss ( Fig. 5 ). In summary, we have developed a computational model representing the interplay between Ca 2+ and Mg 2+ homeostasis and blood pressure regulation in a male rat. The model was used to understand the underlying mechanisms involved in (i) regulating Ca 2+ and Mg 2+ balance during different hypertensive stimuli, (ii) blood pressure regulation during dietary Mg 2+ deficiency, dietary Ca 2+ deficiency, and vitamin D 3 deficiency, and (iii) Ca 2+ , Mg 2+ , and blood pressure regulation during primary hyperparathyroidism. Limitations of the study The present model is based primarily on a male rat. However, there are many known sex differences in blood pressure regulation ( 29 , 98 , 99 ). Sex differences also occur in renal handling of Na + , Ca 2+ , and Mg 2+ ( 100 – 103 ). A worthwhile extension would be to develop sex-specific models for Ca 2+ , Mg 2+ , and blood pressure regulation under various physiological and pathophysiological conditions. The actions of the transporters and channels along the nephron cell membranes that regulate Na + , Ca 2+ , Mg 2+ , and fluid balance are represented implicitly in our model. A possible extension of the model would be to explicitly model these transporters and channels as done in epithelial transport models ( 101 , 102 , 104 ). The benefit of coupling individual nephron with whole kidney dynamics would be in simulating the administration of drugs that target these transporters. The exact action of the drug could be simulated instead of inferred. The present model does not include potassium (K + ) which is a key mineral in blood pressure regulation. Higher K + levels have been associated with lower blood pressure ( 105 – 107 ). Its blood pressure-lowering effects stem from its capacity to induce vasodilation, a process mediated by vascular cell hyperpolarization ( 108 ). Additionally, K + influences blood pressure by increasing Na + excretion, modulating baroreceptor sensitivity, reducing vasoconstrictive sensitivity to norepinephrine and angiotensin II, and increasing Na-K-ATPase activity ( 108 ). A future extension of the model would be inclusion of K + regulation ( 109 , 110 ) and its interaction with various components of blood pressure regulation. Data and code availability The code generated in this study can be accessed at https://github.com/Pritha17/Blood-pressure-and-calcium-magnesium-homeostasis-regulation . Author contributions Conceptualization, P.D. and A.T.L.; Methodology, P.D. and A.T.L.; Software, Validation, Formal Analysis, and Investigation, P.D.; Resources, A.T.L.; Data Curation, P.D.; Writing – Original Draft, P.D. and A.T.L; Writing – Review & Editing, P.D. and A.T.L.; Visualization, P.D.; Supervision, P.D. and A.T.L.; Funding Acquisition, A.T.L. Declaration of interests The authors declare no competing interests. Acknowledgement This work was supported by the Canada 150 Research Chair program, National Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (RGPIN-2019-03916), and Canada Institutes of Health Research (CIHR) Project Grant (TNC-174963) to A.T.L. Funder Information Declared Canada 150 Research Chair program National Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant , RGPIN-2019-03916 Canada Institutes of Health Research (CIHR) , TNC-174963 References 1. ↵ Kearney PM , Whelton M , Reynolds K , Muntner P , Whelton PK , He J. Global burden of hypertension: analysis of worldwide data . Lancet . 2005/01/18 ed. 2005 Jan 15; 365 ( 9455 ): 217 – 23 . OpenUrl CrossRef PubMed Web of Science 2. ↵ Mills KT , Bundy JD , Kelly TN , Reed JE , Kearney PM , Reynolds K , et al. Global Disparities of Hypertension Prevalence and Control: a systematic analysis of population-based studies from 90 countries . Circulation . 2016 ; 134 : 441 – 50 . OpenUrl Abstract / FREE Full Text 3. ↵ DiNicolantonio JJ , O’Keefe JH , Wilson W. Subclinical magnesium deficiency: a principal driver of cardiovascular disease and a public health crisis . Open Heart . 2018 ; 5 ( 1 ): e000668 . OpenUrl Abstract / FREE Full Text 4. ↵ Balk E , Adam G , Langberg V , Earley A , Clark P , Ebeling P , et al. Global dietary calcium intake among adults: a systematic review . Osteoporos Int . 2017 ; 28 : 3315 – 24 . OpenUrl CrossRef PubMed 5. ↵ Costello RB , Elin RJ , Rosanoff A , Wallace TC , Guerrero-Romero F , Hruby A , et al. Perspective: the case for an evidence-based reference interval for serum magnesium: the time has come . Adv Nutr . 2016 ; 7 ( 6 ): 977 – 93 . OpenUrl Abstract / FREE Full Text 6. ↵ Yu Z , Li Y , Ba DM , Veldheer SJ , Sun L , Geng T , et al. Trends in Calcium Intake among the US Population: Results from the NHANES (1999–2018) . Nutrients . 2024 ; 16 ( 5 ): 726 . OpenUrl PubMed 7. ↵ Bilezikian JP . Primary hyperparathyroidism . J Clin Endocrinol Metab . 2018 ; 103 ( 11 ): 3993 – 4004 . OpenUrl PubMed 8. ↵ Vaidya A , Brown JM , Williams JS . The renin–angiotensin–aldosterone system and calcium-regulatory hormones . J Hum Hypertens . 2015 ; 29 ( 9 ): 515 – 21 . OpenUrl CrossRef PubMed 9. Zheng MH , Li FXZ , Xu F , Lin X , Wang Y , Xu QS , et al. The interplay between the renin-angiotensin-aldosterone system and parathyroid hormone . Front Endocrinol . 2020 ; 11 : 539 . OpenUrl 10. ↵ Schutten JC , Joosten MM , de Borst MH , Bakker SJ . Magnesium and blood pressure: a physiology-based approach . Adv Chronic Kidney Dis . 2018 ; 25 ( 3 ): 244 – 50 . OpenUrl PubMed 11. ↵ Atchison DK , Harding P , Beierwaltes WH . Hypercalcemia reduces plasma renin via parathyroid hormone, renal interstitial calcium, and the calcium-sensing receptor . Hypertension . 2011 ; 58 ( 4 ): 604 – 10 . OpenUrl CrossRef PubMed 12. ↵ Atchison DK , Ortiz-Capisano MC , Beierwaltes WH . Acute activation of the calcium-sensing receptor inhibits plasma renin activity in vivo . Am J Physiol-Regul Integr Comp Physiol . 2010 ; 299 ( 4 ): R1020 – 6 . OpenUrl 13. ↵ Zhou C , Lu F , Cao K , Xu D , Goltzman D , Miao D. Calcium-independent and 1, 25 (OH) 2D3-dependent regulation of the renin-angiotensin system in 1α-hydroxylase knockout mice . Kidney Int . 2008 ; 74 ( 2 ): 170 – 9 . OpenUrl CrossRef PubMed Web of Science 14. ↵ Atchison DK , Harding P , Beierwaltes WH . Vitamin D increases plasma renin activity independently of plasma Ca2+ via hypovolemia and β-adrenergic activity . Am J Physiol-Ren Physiol . 2013 ; 305 ( 8 ): F1109 – 17 . OpenUrl 15. ↵ Schiebinger RJ , Braley LM , Menachery A , Williams GH . Calcium, a” third messenger” of cAMP-stimulated adrenal steroid secretion . Am J Physiol-Endocrinol Metab . 1985 ; 248 ( 1 ): E89 – 94 . OpenUrl PubMed 16. ↵ Atarashi K , Matsuoka H , Takagi M , Sugimoto T. Magnesium ion: a possible physiological regulator of aldosterone production . Life Sci . 1989 ; 44 ( 20 ): 1483 – 9 . OpenUrl CrossRef PubMed Web of Science 17. ↵ Atarashi K , Takagi M , Matsuoka H , Sugimoto T. Effects of magnesium on changes in blood pressure and plasma aldosterone induced by angiotensin II . Am J Hypertens . 1990 ; 3 ( 6_Pt_1 ): 488 – 90 . OpenUrl PubMed 18. ↵ Isales CM , Barrett PQ , Brines M , Bollag W , Rasmussen H. Parathyroid hormone modulates angiotensin II-induced aldosterone secretion from the adrenal glomerulosa cell . Endocrinology . 1991 ; 129 ( 1 ): 489 – 95 . OpenUrl CrossRef PubMed Web of Science 19. ↵ Mazzocchi G , Aragona F , Malendowicz LK , Nussdorfer GG . PTH and PTH-related peptide enhance steroid secretion from human adrenocortical cells . Am J Physiol-Endocrinol Metab . 2001 ; 280 ( 2 ): E209 – 13 . OpenUrl PubMed Web of Science 20. ↵ Kaufmann M , Pargger H , Castelli I , Steiner L , Drop L. Renal vascular responses to high and low ionized calcium: influence of norepinephrine in the isolated perfused rat kidney . J Trauma Acute Care Surg . 1996 ; 40 ( 1 ): 110 – 5 . OpenUrl 21. ↵ Zhang J , Berra-Romani R , Sinnegger-Brauns MJ , Striessnig J , Blaustein MP , Matteson DR . Role of Cav1 . 2 L-type Ca2+ channels in vascular tone: effects of nifedipine and Mg2+. Am J Physiol-Heart Circ Physiol . 2007 ; 292 ( 1 ): H415 – 25 . OpenUrl 22. ↵ Kawashima H. Parathyroid hormone causes a transient rise in intracellular ionized calcium in vascular smooth muscle cells . Biochem Biophys Res Commun . 1990 ; 166 ( 2 ): 709 – 14 . OpenUrl CrossRef PubMed Web of Science 23. ↵ Lenzini L , Prisco S , Vanderriele PE , Lerco S , Torresan F , Maiolino G , et al. PTH modulation by aldosterone and angiotensin II is blunted in hyperaldosteronism and rescued by adrenalectomy . J Clin Endocrinol Metab . 2019 ; 104 ( 9 ): 3726 – 34 . OpenUrl PubMed 24. ↵ Girardi AC , Titan SM , Malnic G , Rebouças NA . Chronic effect of parathyroid hormone on NHE3 expression in rat renal proximal tubules . Kidney Int . 2000 ; 58 ( 4 ): 1623 – 31 . OpenUrl CrossRef PubMed Web of Science 25. ↵ Toka HR , Al-Romaih K , Koshy JM , DiBartolo SI , Kos CH , Quinn SJ , et al. Deficiency of the Calcium-Sensing Receptor in the Kidney Causes Parathyroid Hormone–Independent Hypocalciuria . J Am Soc Nephrol . 2012 Nov ; 23 ( 11 ): 1879 . OpenUrl Abstract / FREE Full Text 26. ↵ Hirning LD , Fox AP , McCleskey EW , Olivera BM , Thayer SA , Miller RJ , et al. Dominant role of N-type Ca2+ channels in evoked release of norepinephrine from sympathetic neurons . Science . 1988 ; 239 ( 4835 ): 57 – 61 . OpenUrl Abstract / FREE Full Text 27. ↵ Shimosawa T , Takano K , Ando K , Fujita T. Magnesium inhibits norepinephrine release by blocking N-type calcium channels at peripheral sympathetic nerve endings . Hypertension . 2004 ; 44 ( 6 ): 897 – 902 . OpenUrl 28. ↵ Dutta P , Layton AT . Modeling calcium and magnesium balance: Regulation by calciotropic hormones and adaptations under varying dietary intake . iScience . 2024 ; 27 ( 11 ). 29. ↵ Ahmed S , Layton AT . Sex-specific computational models for blood pressure regulation in the rat . Am J Physiol Ren Physiol . 2020 ; 318 ( 4 ): F888 – 900 . OpenUrl CrossRef PubMed 30. ↵ Lotshaw DP , Li F. Angiotensin II activation of Ca (2+)-permeant nonselective cation channels in rat adrenal glomerulosa cells . Am J Physiol-Cell Physiol . 1996 ; 271 ( 5 ): C1705 – 15 . OpenUrl PubMed Web of Science 31. ↵ Rude R , Manoogian C , Ehrlich L , DeRusso P , Ryzen E , Nadler J. Mechanisms of blood pressure regulation by magnesium in man . Magnesium . 1989 ; 8 ( 5–6 ): 266 – 73 . OpenUrl PubMed Web of Science 32. ↵ Urena P , Kong X , Abou-Samra AB , Jüppner H , Kronenberg HM , Potts Jr JT , et al. Parathyroid hormone (PTH)/PTH-related peptide receptor messenger ribonucleic acids are widely distributed in rat tissues . Endocrinology . 1993 ; 133 ( 2 ): 617 – 23 . OpenUrl CrossRef PubMed Web of Science 33. ↵ Maniero C , Fassina A , Guzzardo V , Lenzini L , Amadori G , Pelizzo MR , et al. Primary hyperparathyroidism with concurrent primary aldosteronism . Hypertension . 2011 ; 58 ( 3 ): 341 – 6 . OpenUrl CrossRef 34. ↵ Shimizu H , Nakagami H , Osako MK , Hanayama R , Kunugiza Y , Kizawa T , et al. Angiotensin II accelerates osteoporosis by activating osteoclasts . FASEB J . 2008 ; 22 ( 7 ): 2465 – 75 . OpenUrl CrossRef PubMed Web of Science 35. ↵ Richer C , Doussau M , Giudicelli JF . Effects of captopril and enalapril on regional vascular resistance and reactivity in spontaneously hypertensive rats . Hypertension . 1983 ; 5 ( 3 ): 312 – 20 . OpenUrl 36. ↵ Heeneman S , Smits JF , Leenders PJ , Schiffers PM , Daemen MJ . Effects of angiotensin II on cardiac function and peripheral vascular structure during compensated heart failure in the rat . Arterioscler Thromb Vasc Biol . 1997 ; 17 ( 10 ): 1985 – 94 . OpenUrl Abstract / FREE Full Text 37. Olgaard K , Lewin E , Bro S , Daugaard H , Egfjord M , Pless V. Enhancement of the stimulatory effect of calcium on aldosterone secretion by parathyroid hormone . Miner Electrolyte Metab . 1994 ; 20 ( 5 ): 309 – 14 . OpenUrl PubMed 38. Brown EM , Chen CJ . Calcium, magnesium and the control of PTH secretion . Bone Miner . 1989 Mar 1; 5 ( 3 ): 249 – 57 . OpenUrl CrossRef PubMed 39. ↵ Ceccoli L , Ronconi V , Giovannini L , Marcheggiani M , Turchi F , Boscaro M , et al. Bone health and aldosterone excess . Osteoporos Int . 2013 ; 24 : 2801 – 7 . OpenUrl CrossRef PubMed 40. ↵ Fortina F , Bellosta S. Hyperparathyroidism Secondary to Hyperaldosteronism . High Blood Press Cardiovasc Prev . 2010 ; 17 : 27 – 30 . OpenUrl 41. ↵ Funder JW , Carey RM , Mantero F , Murad MH , Reincke M , Shibata H , et al. The management of primary aldosteronism: case detection, diagnosis, and treatment: an endocrine society clinical practice guideline . J Clin Endocrinol Metab . 2016 ; 101 ( 5 ): 1889 – 916 . OpenUrl CrossRef PubMed 42. ↵ Rastegar A , Agus Z , Connor TB , Goldberg M. Renal handling of calcium and phosphate during mineralocorticoid “escape” in man . Kidney Int . 1972 ; 2 ( 5 ): 279 – 86 . OpenUrl CrossRef PubMed Web of Science 43. ↵ Horton R , Biglieri EG . Effect of aldosterone on the metabolism of magnesium . J Clin Endocrinol Metab . 1962 ; 22 ( 12 ): 1187 – 92 . OpenUrl CrossRef PubMed Web of Science 44. ↵ Shi S , Lu C , Tian H , Ren Y , Chen T. Primary aldosteronism and bone metabolism: a systematic review and meta-analysis . Front Endocrinol . 2020 ; 11 : 574151 . OpenUrl 45. ↵ Salcuni AS , Palmieri S , Carnevale V , Morelli V , Battista C , Guarnieri V , et al. Bone involvement in aldosteronism . J Bone Miner Res . 2012 ; 27 ( 10 ): 2217 – 22 . OpenUrl CrossRef PubMed 46. ↵ Han H , Fang X , Wei X , Liu Y , Jin Z , Chen Q , et al. Dose-response relationship between dietary magnesium intake, serum magnesium concentration and risk of hypertension: a systematic review and meta-analysis of prospective cohort studies . Nutr J . 2017 ; 16 : 1 – 12 . OpenUrl CrossRef PubMed 47. Peacock JM , Folsom AR , Arnett DK , Eckfeldt JH , Szklo M. Relationship of serum and dietary magnesium to incident hypertension: the Atherosclerosis Risk in Communities (ARIC) Study . Ann Epidemiol . 1999 ; 9 ( 3 ): 159 – 65 . OpenUrl CrossRef PubMed Web of Science 48. ↵ Kass L , Weekes J , Carpenter L. Effect of magnesium supplementation on blood pressure: a meta-analysis . Eur J Clin Nutr . 2012 ; 66 ( 4 ): 411 – 8 . OpenUrl CrossRef PubMed Web of Science 49. ↵ Zhang X , Li Y , Del Gobbo LC , Rosanoff A , Wang J , Zhang W , et al. Effects of magnesium supplementation on blood pressure: a meta-analysis of randomized double-blind placebo-controlled trials . Hypertension . 2016 ; 68 ( 2 ): 324 – 33 . OpenUrl 50. ↵ Alharran AM , Alzayed MM , Jamilian P , Prabahar K , Kamal AH , Alotaibi MN , et al. Impact of magnesium supplementation on blood pressure: An umbrella meta-analysis of randomized controlled trials . Curr Ther Res . 2024 ; 100755 . 51. ↵ van Mierlo LA , Arends LR , Streppel MT , Zeegers M , Kok FJ , Grobbee DE , et al. Blood pressure response to calcium supplementation: a meta-analysis of randomized controlled trials . J Hum Hypertens . 2006 ; 20 ( 8 ): 571 – 80 . OpenUrl CrossRef PubMed Web of Science 52. ↵ Cormick G , Ciapponi A , Cafferata ML , Cormick MS , Belizán JM. Calcium supplementation for prevention of primary hypertension . Cochrane Database Syst Rev . 2021 ;( 8 ). 53. ↵ Villa-Etchegoyen C , Lombarte M , Matamoros N , Belizán JM , Cormick G. Mechanisms involved in the relationship between low calcium intake and high blood pressure . Nutrients . 2019 ; 11 ( 5 ): 1112 . OpenUrl PubMed 54. ↵ Martins D , Wolf M , Pan D , Zadshir A , Tareen N , Thadhani R , et al. Prevalence of cardiovascular risk factors and the serum levels of 25-hydroxyvitamin D in the United States: data from the Third National Health and Nutrition Examination Survey . Arch Intern Med . 2007 ; 167 ( 11 ): 1159 – 65 . OpenUrl CrossRef PubMed Web of Science 55. Pilz S , Tomaschitz A , Ritz E , Pieber TR . Vitamin D status and arterial hypertension: a systematic review . Nat Rev Cardiol . 2009 ; 6 ( 10 ): 621 . OpenUrl CrossRef PubMed Web of Science 56. ↵ Almirall J , Vaqueiro M , Baré ML , Anton E. Association of low serum 25-hydroxyvitamin D levels and high arterial blood pressure in the elderly . Nephrol Dial Transplant . 2010 ; 25 ( 2 ): 503 – 9 . OpenUrl CrossRef PubMed Web of Science 57. ↵ Bilezikian JP , Cusano NE , Khan AA , Liu JM , Marcocci C , Bandeira F. Primary hyperparathyroidism . Nat Rev Dis Primer . 2016 ; 2 ( 1 ): 1 – 16 . OpenUrl CrossRef 58. ↵ King R , Stanbury S. Magnesium metabolism in primary hyperparathyroidism . Clin Sci . 1970 ; 39 ( 2 ): 281 – 303 . OpenUrl PubMed 59. ↵ Brunaud L , Germain A , Zarnegar R , Rancier M , Alrasheedi S , Caillard C , et al. Serum aldosterone is correlated positively to parathyroid hormone (PTH) levels in patients with primary hyperparathyroidism . Surgery . 2009 ; 146 ( 6 ): 1035 – 41 . OpenUrl CrossRef PubMed Web of Science 60. ↵ Broulik P , Brouliková A , Adámek S , Libansk P , Tvrdon J , Broulikova K , et al. Improvement of hypertension after parathyroidectomy of patients suffering from primary hyperparathyroidism . Int J Endocrinol . 2011 ; 2011 ( 1 ): 309068 . OpenUrl PubMed 61. Schiffl H , Lang SM . Hypertension secondary to PHPT: cause or coincidence? Int J Endocrinol . 2011 ; 2011 ( 1 ): 974647 . OpenUrl PubMed 62. Heyliger A , Tangpricha V , Weber C , Sharma J. Parathyroidectomy decreases systolic and diastolic blood pressure in hypertensive patients with primary hyperparathyroidism . Surgery . 2009 ; 146 ( 6 ): 1042 – 7 . OpenUrl CrossRef PubMed Web of Science 63. Letizia C , Ferrari P , Cotesta D , Caliumi C , Cianci R , Cerci S , et al. Ambulatory monitoring of blood pressure (AMBP) in patients with primary hyperparathyroidism . J Hum Hypertens . 2005 ; 19 ( 11 ): 901 – 6 . OpenUrl CrossRef PubMed 64. ↵ Kalla A , Krishnamoorthy P , Gopalakrishnan A , Garg J , Patel N , Figueredo V. Primary hyperparathyroidism predicts hypertension: results from the National Inpatient Sample . Int J Cardiol . 2017 ; 227 : 335 – 7 . OpenUrl PubMed 65. ↵ Cormier C , Souberbielle JC , Kahan A. Primary hyperparathyroidism and osteoporosis in 2004 . Joint Bone Spine . 2004 ; 71 ( 3 ): 183 – 9 . OpenUrl CrossRef PubMed Web of Science 66. Lewiecki EM , Miller PD . Skeletal effects of primary hyperparathyroidism: bone mineral density and fracture risk . J Clin Densitom . 2013 ; 16 ( 1 ): 28 – 32 . OpenUrl CrossRef PubMed 67. ↵ Kanis JA , Harvey NC , Liu E , Vandenput L , Lorentzon M , McCloskey EV , et al. Primary hyperparathyroidism and fracture probability . Osteoporos Int . 2023 ; 34 ( 3 ): 489 – 99 . OpenUrl PubMed 68. ↵ Strazzullo P , Nunziata V , Cirillo M , Giannattasio R , Ferrara LA , Mattioli P , et al. Abnormalities of calcium metabolism in essential hypertension . Clin Sci Lond Engl 1979 . 1983 ; 65 ( 2 ): 137 – 41 . OpenUrl 69. ↵ Young EW , Morris CD , McCarron DA . Urinary calcium excretion in essential hypertension . J Lab Clin Med . 1992 ; 120 ( 4 ): 624 – 32 . OpenUrl PubMed 70. ↵ Ye Z , Lu H , Liu P. Association between essential hypertension and bone mineral density: a systematic review and meta-analysis . Oncotarget . 2017 ; 8 ( 40 ): 68916 . OpenUrl PubMed 71. ↵ Yang C , Kim S , Kim Y , Koo W , Choi E , Chang Y , et al. Nephrocalcinosis associated with primary aldosteronism . Nephron . 1994 ; 68 ( 4 ): 507 – 8 . OpenUrl CrossRef PubMed 72. ↵ Shey J , Cameron MA , Sakhaee K , Moe OW . Recurrent calcium nephrolithiasis associated with primary aldosteronism . Am J Kidney Dis . 2004 ; 44 ( 1 ): e7 – 12 . OpenUrl CrossRef PubMed 73. ↵ Trnka P , Orellana L , Walsh M , Pool L , Borzi P. Reninoma: an uncommon cause of renin-mediated hypertension . Front Pediatr . 2014 ; 2 : 89 . OpenUrl PubMed 74. ↵ Schambelan M , Howes E , Stockigt J , Noakes C , Biglieri E. Role of renin and aldosterone in hypertension due to a renin-secreting tumor . Am J Med . 1973 ; 55 ( 1 ): 86 – 92 . OpenUrl CrossRef PubMed Web of Science 75. ↵ Lynn H , Kwok T , Wong S , Woo J , Leung P. Angiotensin converting enzyme inhibitor use is associated with higher bone mineral density in elderly Chinese . Bone . 2006 ; 38 ( 4 ): 584 – 8 . OpenUrl CrossRef PubMed Web of Science 76. ↵ Rejnmark L , Vestergaard P , Mosekilde L. Treatment with beta-blockers, ACE inhibitors, and calcium-channel blockers is associated with a reduced fracture risk: a nationwide case–control study . J Hypertens . 2006 ; 24 ( 3 ): 581 – 9 . OpenUrl CrossRef PubMed Web of Science 77. ↵ Wabo TMC , Wu X , Sun C , Boah M , Nkondjock VRN , Cheruiyot JK , et al. Association of dietary calcium, magnesium, sodium, and potassium intake and hypertension: a study on an 8-year dietary intake data from the National Health and Nutrition Examination Survey . Nutr Res Pract . 2022 ; 16 ( 1 ): 74 – 93 . OpenUrl PubMed 78. ↵ Beydoun MA , Gary TL , Caballero BH , Lawrence RS , Cheskin LJ , Wang Y. Ethnic differences in dairy and related nutrient consumption among US adults and their association with obesity, central obesity, and the metabolic syndrome . Am J Clin Nutr . 2008 ; 87 ( 6 ): 1914 – 25 . OpenUrl Abstract / FREE Full Text 79. Ford ES , Li C , McGuire LC , Mokdad AH , Liu S. Intake of dietary magnesium and the prevalence of the metabolic syndrome among US adults . Obesity . 2007 ; 15 ( 5 ): 1139 – 46 . OpenUrl PubMed 80. Tan MY , Mo CY , Zhao Q. The Association between Magnesium Depletion score and hypertension in US adults: evidence from the National Health and Nutrition Examination Survey (2007–2018) . Biol Trace Elem Res . 2024 ; 202 ( 10 ): 4418 – 30 . OpenUrl PubMed 81. ↵ VAN LEER EM , Seidell JC , Kromhout D. Dietary calcium, potassium, magnesium and blood pressure in the Netherlands . Int J Epidemiol . 1995 ; 24 ( 6 ): 1117 – 23 . OpenUrl CrossRef PubMed Web of Science 82. Bain LK , Myint PK , Jennings A , Lentjes MA , Luben RN , Khaw KT , et al. The relationship between dietary magnesium intake, stroke and its major risk factors, blood pressure and cholesterol, in the EPIC-Norfolk cohort . Int J Cardiol . 2015 ; 196 : 108 – 14 . OpenUrl PubMed 83. He K , Liu K , Daviglus ML , Morris SJ , Loria CM , Van Horn L , et al. Magnesium intake and incidence of metabolic syndrome among young adults . Circulation . 2006 ; 113 ( 13 ): 1675 – 82 . OpenUrl Abstract / FREE Full Text 84. ↵ Dominguez LJ , Gea A , Ruiz-Estigarribia L , Sayon-Orea C , Fresan U , Barbagallo M , et al. Low dietary magnesium and overweight/obesity in a mediterranean population: a detrimental synergy for the development of hypertension . The SUN Project. Nutrients . 2020 ; 13 ( 1 ): 125 . OpenUrl PubMed 85. ↵ Enaruna N , Ande A , Okpere E. Clinical significance of low serum magnesium in pregnant women attending the University of Benin Teaching Hospital . Niger J Clin Pract . 2013 ; 16 ( 4 ). 86. ↵ Kanagal DV , Rajesh A , Rao K , Devi UH , Shetty H , Kumari S , et al. Levels of serum calcium and magnesium in pre-eclamptic and normal pregnancy: A study from Coastal India . J Clin Diagn Res JCDR . 2014 ; 8 ( 7 ): OC01 . OpenUrl 87. ↵ Jafrin W , Mia A , Chakraborty P , Hoque M , Paul U , Shaha K , et al. An evaluation of serum magnesium status in pre-eclampsia compared to the normal pregnancy . Mymensingh Med J MMJ . 2014 ; 23 ( 4 ): 649 – 53 . OpenUrl PubMed 88. ↵ Group MTC , others. Do women with pre-eclampsia, and their babies, benefit from magnesium sulphate? The Magpie Trial: a randomised placebo-controlled trial . The Lancet . 2002 ; 359 ( 9321 ): 1877 – 90 . OpenUrl 89. ↵ van Mierlo LA , Arends LR , Streppel MT , Zeegers M , Kok FJ , Grobbee DE , et al. Blood pressure response to calcium supplementation: a meta-analysis of randomized controlled trials . J Hum Hypertens . 2006 ; 20 ( 8 ): 571 – 80 . OpenUrl CrossRef PubMed Web of Science 90. Witteman J , Willett W , Stampfer M , Colditz G , Sacks F , Speizer F , et al. A prospective study of nutritional factors and hypertension among US women . Circulation . 1989 ; 80 ( 5 ): 1320 – 7 . OpenUrl Abstract / FREE Full Text 91. Ascherio A , Rimm EB , Giovannucci EL , Colditz GA , Rosner B , Willett WC , et al. A prospective study of nutritional factors and hypertension among US men . Circulation . 1992 ; 86 ( 5 ): 1475 – 84 . OpenUrl Abstract / FREE Full Text 92. Wang L , Manson JE , Buring JE , Lee IM , Sesso HD . Dietary intake of dairy products, calcium, and vitamin D and the risk of hypertension in middle-aged and older women . Hypertension . 2008 ; 51 ( 4 ): 1073 – 9 . OpenUrl CrossRef 93. Hofmeyr GJ , Lawrie TA , Atallah ÁN , Torloni MR . Calcium supplementation during pregnancy for preventing hypertensive disorders and related problems . Cochrane Database Syst Rev . 2018 ;( 10 ). 94. ↵ Hofmeyr G , Duley L , Atallah A. Dietary calcium supplementation for prevention of pre-eclampsia and related problems: a systematic review and commentary . BJOG Int J Obstet Gynaecol . 2007 ; 114 ( 8 ): 933 – 43 . OpenUrl 95. ↵ Joffres MR , Reed D , Yano K. Relationship of magnesium intake and other dietary factors to blood pressure: the Honolulu heart study . Am J Clin Nutr . 1987 ; 45 ( 2 ): 469 – 75 . OpenUrl Abstract / FREE Full Text 96. ↵ Bricio-Barrios JA , Palacios-Fonseca AJ , del Toro-Equihua M , Sanchez-Ramirez CA . Effect of calcitriol supplementation on blood pressure in older adults . J Nutr Gerontol Geriatr . 2016 ; 35 ( 4 ): 243 – 52 . OpenUrl PubMed 97. ↵ Kristal-Boneh E , Froom P , Harari G , Ribak J. Association of calcitriol and blood pressure in normotensive men . Hypertension . 1997 ; 30 ( 5 ): 1289 – 94 . OpenUrl CrossRef 98. ↵ Ahmed S , Hu R , Leete J , Layton AT . Understanding sex differences in long-term blood pressure regulation: insights from experimental studies and computational modeling . Am J Physiol-Heart Circ Physiol . 2019 ; 316 ( 5 ): H1113 – 23 . OpenUrl CrossRef PubMed 99. ↵ Leete J , Layton AT . Sex-specific long-term blood pressure regulation: Modeling and analysis . Comput Biol Med . 2019 Jan ; 104 : 139 – 48 . OpenUrl CrossRef PubMed 100. ↵ Veiras LC , Girardi ACC , Curry J , Pei L , Ralph DL , Tran A , et al. Sexual Dimorphic Pattern of Renal Transporters and Electrolyte Homeostasis . J Am Soc Nephrol . 2017 Aug ; 28 ( 12 ): 3504 – 17 . OpenUrl Abstract / FREE Full Text 101. ↵ Dutta P , Hakimi S , Layton AT . How the kidney regulates magnesium: a modelling study . R Soc Open Sci . 2024 ; 11 ( 3 ): 231484 . OpenUrl PubMed 102. ↵ Hakimi S , Dutta P , Layton AT . Coupling of renal sodium and calcium transport: A modeling analysis of transporter inhibition and sex differences . Am J Physiol-Ren Physiol . 2023 ; 325 ( 5 ):F536--F551. 103. ↵ Hu R , McDonough AA , Layton AT . Sex differences in solute and water handling in the human kidney: Modeling and functional implications . IScience . 2021 ; 24 ( 6 ): 102667 . OpenUrl PubMed 104. ↵ Layton AT , Laghmani K , Vallon V , Edwards A. Solute transport and oxygen consumption along the nephrons: effects of Na+ transport inhibitors . Am J Physiol Ren Physiol . 2016 Dec 1; 311 ( 6 ): F1217 – 29 . OpenUrl CrossRef PubMed 105. ↵ Filippini T , Violi F , D’Amico R , Vinceti M. The effect of potassium supplementation on blood pressure in hypertensive subjects: a systematic review and meta-analysis . Int J Cardiol . 2017 ; 230 : 127 – 35 . OpenUrl CrossRef PubMed 106. Chan Q , Wren GM , Lau CHE , Ebbels TM , Gibson R , Loo RL , et al. Blood pressure interactions with the DASH dietary pattern, sodium, and potassium: The International Study of Macro-/Micronutrients and Blood Pressure (INTERMAP) . Am J Clin Nutr . 2022 ; 116 ( 1 ): 216 – 29 . OpenUrl PubMed 107. ↵ Yu J , Thout SR , Li Q , Tian M , Marklund M , Arnott C , et al. Effects of a reduced-sodium added-potassium salt substitute on blood pressure in rural Indian hypertensive patients: a randomized, double-blind, controlled trial . Am J Clin Nutr . 2021 ; 114 ( 1 ): 185 – 93 . OpenUrl PubMed 108. ↵ Haddy FJ , Vanhoutte PM , Feletou M. Role of potassium in regulating blood flow and blood pressure . Am J Physiol-Regul Integr Comp Physiol . 2006 ; 290 ( 3 ): R546 – 52 . OpenUrl 109. ↵ Stadt MM , Leete J , Devinyak S , Layton AT . A mathematical model of potassium homeostasis: Effect of feedforward and feedback controls . PLOS Comput Biol . 2022 ; 18 ( 12 ): e1010607 . OpenUrl PubMed 110. ↵ Stadt MM , Layton AT . Modulation of blood pressure by dietary potassium and sodium: Sex differences and modeling analysis . Am J Physiol-Ren Physiol . 2024 ; View the discussion thread. Back to top Previous Next Posted October 27, 2025. Download PDF Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. You are going to email the following Unraveling the Mechanistic Links Between Blood Pressure Regulation and Calcium-Magnesium Homeostasis: Insights into Hypertension, Hyperparathyroidism, and Mineral Disorders Message Subject (Your Name) has forwarded a page to you from bioRxiv Message Body (Your Name) thought you would like to see this page from the bioRxiv website. Your Personal Message CAPTCHA This question is for testing whether or not you are a human visitor and to prevent automated spam submissions. Share Unraveling the Mechanistic Links Between Blood Pressure Regulation and Calcium-Magnesium Homeostasis: Insights into Hypertension, Hyperparathyroidism, and Mineral Disorders Pritha Dutta , Anita T. Layton bioRxiv 2025.10.26.684662; doi: https://doi.org/10.1101/2025.10.26.684662 Share This Article: Copy Citation Tools Unraveling the Mechanistic Links Between Blood Pressure Regulation and Calcium-Magnesium Homeostasis: Insights into Hypertension, Hyperparathyroidism, and Mineral Disorders Pritha Dutta , Anita T. Layton bioRxiv 2025.10.26.684662; doi: https://doi.org/10.1101/2025.10.26.684662 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Systems Biology Subject Areas All Articles Animal Behavior and Cognition (7636) Biochemistry (17698) Bioengineering (13896) Bioinformatics (41959) Biophysics (21457) Cancer Biology (18597) Cell Biology (25523) Clinical Trials (138) Developmental Biology (13381) Ecology (19904) Epidemiology (2067) Evolutionary Biology (24323) Genetics (15612) Genomics (22511) Immunology (17738) Microbiology (40401) Molecular Biology (17184) Neuroscience (88624) Paleontology (667) Pathology (2833) Pharmacology and Toxicology (4825) Physiology (7644) Plant Biology (15158) Scientific Communication and Education (2046) Synthetic Biology (4296) Systems Biology (9825) Zoology (2271)